11.em_for_lmar_part2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "36e8fdcb",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "from itertools import product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8fbea531",
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_a(N, ksi, zeta_1, var_1, zeta_2, var_2):\n",
    "    '''\n",
    "    generate a of size N with given parameters\n",
    "    '''\n",
    "    a = np.zeros(N)\n",
    "    p1 = np.zeros(N)\n",
    "    p2 = np.zeros(N)\n",
    "\n",
    "    for i in range(N):\n",
    "\n",
    "        # find lags of a_t\n",
    "        if i>=2:\n",
    "            a_lag1 = a[i-1]\n",
    "            a_lag2 = a[i-2]\n",
    "        elif i==1:\n",
    "            a_lag1 = a[i-1]\n",
    "            a_lag2 = 0\n",
    "        elif i==0:\n",
    "            a_lag1 = 0\n",
    "            a_lag2 = 0\n",
    "\n",
    "        # solve probability equation\n",
    "        p1[i] = (np.exp(np.dot(ksi, [1, abs(a_lag1), abs(a_lag2)])) / \n",
    "                 (1 + np.exp(np.dot(ksi, [1, abs(a_lag1), abs(a_lag2)]))))\n",
    "        p2[i] = 1-p1[i]\n",
    "\n",
    "        # calculate means of two regimes\n",
    "        e1 = np.dot(zeta_1, np.array([1, a_lag1, a_lag2]))\n",
    "        e2 = np.dot(zeta_2, np.array([1, a_lag1]))\n",
    "\n",
    "\n",
    "        regime = np.random.choice([1,2], p=[p1[i],p2[i]])\n",
    "        if regime==1:\n",
    "            a[i] = stats.norm(loc=e1, scale=np.sqrt(var_1)).rvs()\n",
    "        else:\n",
    "            a[i] = stats.norm(loc=e2, scale=np.sqrt(var_2)).rvs()\n",
    "    \n",
    "    return a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d3b7ac62",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 500 # number of datapoints to generate\n",
    "ksi = [-1.3, 0.6, 0.3]\n",
    "zeta_1 = [0, 0.6, -0.2]\n",
    "var_1 = 1\n",
    "zeta_2 = [0, 1.5]\n",
    "var_2 = 3\n",
    "\n",
    "np.random.seed(5)\n",
    "a = generate_a(N, ksi, zeta_1, var_1, zeta_2, var_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8059eae4",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7feddc1294f0>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(18,6))\n",
    "plt.plot(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "948e7665",
   "metadata": {},
   "source": [
    "# EM Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "79bccd1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def outer(x):\n",
    "    '''\n",
    "    calculate outer product of a vector x with itself\n",
    "    '''\n",
    "    return np.outer(x,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5b032653",
   "metadata": {},
   "outputs": [],
   "source": [
    "def em_algorithm(a, max_iter, tol):\n",
    "    '''\n",
    "    run em algorithm for max_iter iterations or until convergence\n",
    "    '''\n",
    "    \n",
    "    npdf = stats.norm.pdf\n",
    "    \n",
    "    converged = False\n",
    "    \n",
    "    while not converged:\n",
    "        try:\n",
    "            # random initial guess\n",
    "            ksi = np.random.uniform(-3,3,(3))\n",
    "            zeta_1 = np.random.uniform(-3,3,(3))\n",
    "            zeta_2 = np.random.uniform(-3,3,(2))\n",
    "            var_1 = np.random.uniform(0,6,(1))\n",
    "            var_2 = np.random.uniform(0,6,(1))\n",
    "\n",
    "            # create dataframe\n",
    "            df = pd.DataFrame(columns=['const', 'a', 'a_l1', 'a_l2', 'abs_l1', 'abs_l2', 'p1', 'p2', \n",
    "                                       'tau1', 'tau2', 'e1', 'e2'])\n",
    "            df['a'] = a[2:]\n",
    "            df['a_l1'] = a[1:-1]\n",
    "            df['a_l2'] = a[:-2]\n",
    "            df['abs_l1'] = abs(df['a_l1'])\n",
    "            df['abs_l2'] = abs(df['a_l2'])\n",
    "            df['const'] = 1\n",
    "\n",
    "\n",
    "            for s in range(max_iter):\n",
    "                # E-step\n",
    "                # solve for mixing probabilities\n",
    "                num = np.exp((df[['const', 'abs_l1', 'abs_l2']] * ksi).sum(axis=1))\n",
    "                denom = (1 + np.exp((df[['const', 'abs_l1', 'abs_l2']] * ksi).sum(axis=1)))\n",
    "                df['p1'] = num/denom\n",
    "                df['p2'] = 1 - df['p1']\n",
    "\n",
    "                # calculate e\n",
    "                df['e1'] = df['a'] - (zeta_1 * df[['const', 'a_l1', 'a_l2']]).sum(axis=1)\n",
    "                df['e2'] = df['a'] - (zeta_2 * df[['const', 'a_l1']]).sum(axis=1)\n",
    "\n",
    "                # calculate tau\n",
    "                sigma_1 = np.sqrt(var_1)\n",
    "                sigma_2 = np.sqrt(var_2)\n",
    "                denom = ((df['p1'] / sigma_1) * stats.norm.pdf(df['e1'] / sigma_1) + \n",
    "                         (df['p2'] / sigma_2) * stats.norm.pdf(df['e2'] / sigma_2))\n",
    "                df['tau1'] = (df['p1'] / sigma_1) * stats.norm.pdf(df['e1'] / sigma_1) / denom\n",
    "                df['tau2'] = (df['p2'] / sigma_2) * stats.norm.pdf(df['e2'] / sigma_2) / denom\n",
    "\n",
    "\n",
    "                # M-step\n",
    "\n",
    "                # compute ksi\n",
    "                dr_dksi = df[['const', 'abs_l1', 'abs_l2']]\n",
    "                dQ_dksi = (np.tile((df['tau1'] - df['p1']), (3,1)).T * dr_dksi).sum().values\n",
    "                df['dr_dksi^2'] = df[['const', 'abs_l1', 'abs_l2']].apply(outer, axis=1).apply(np.array)\n",
    "                d2Q_dksi2 = -(df['p1'] * df['p2'] * df['dr_dksi^2']).sum()\n",
    "                new_ksi = ksi - np.linalg.inv(d2Q_dksi2) @ dQ_dksi\n",
    "\n",
    "                # compute zeta\n",
    "                df['de1_dzeta1^2'] = df[['const', 'a_l1', 'a_l2']].apply(outer, axis=1).apply(np.array)\n",
    "                df['de2_dzeta2^2'] = df[['const', 'a_l1']].apply(outer, axis=1).apply(np.array)\n",
    "                zeta1_sum1 = (df['tau1'] * df['de1_dzeta1^2']).sum()\n",
    "                zeta2_sum1 = (df['tau2'] * df['de2_dzeta2^2']).sum()\n",
    "                zeta1_sum2 = (-np.tile(df['tau1'] * df['a'], (3,1)).T * -df[['const', 'a_l1', 'a_l2']]).sum().values\n",
    "                zeta2_sum2 = (-np.tile(df['tau2'] * df['a'], (2,1)).T * -df[['const', 'a_l1']]).sum().values\n",
    "                new_zeta_1 = np.linalg.inv(zeta1_sum1) @ zeta1_sum2\n",
    "                new_zeta_2 = np.linalg.inv(zeta2_sum1) @ zeta2_sum2\n",
    "\n",
    "                # compute variance\n",
    "                sigma1_sum2 = (df['tau1'] * (df['a'] + np.dot(-df[['const', 'a_l1', 'a_l2']], new_zeta_1))**2).sum()\n",
    "                sigma2_sum2 = (df['tau2'] * (df['a'] + np.dot(-df[['const', 'a_l1']], new_zeta_2))**2).sum()\n",
    "                new_var_1 = 1/df['tau1'].sum() * sigma1_sum2\n",
    "                new_var_2 = 1/df['tau2'].sum() * sigma2_sum2\n",
    "\n",
    "                # calculate the difference between old and new values of parameters\n",
    "                delta_ksi = np.sum(abs(new_ksi - ksi))\n",
    "                delta_zeta_1 = np.sum(abs(new_zeta_1 - zeta_1))\n",
    "                delta_zeta_2 = np.sum(abs(new_zeta_2 - zeta_2))\n",
    "                delta_var_1 = np.sum(abs(new_var_1 - var_1))\n",
    "                delta_var_2 = np.sum(abs(new_var_2 - var_2))\n",
    "\n",
    "                # update parameters\n",
    "                ksi = new_ksi\n",
    "                zeta_1 = new_zeta_1\n",
    "                zeta_2 = new_zeta_2\n",
    "                var_1 = new_var_1\n",
    "                var_2 = new_var_2\n",
    "\n",
    "                # calculate total difference between old and new parameters\n",
    "                delta_total = delta_ksi + delta_zeta_1 + delta_zeta_2 + delta_var_1 + delta_var_2\n",
    "\n",
    "                # check convergence\n",
    "                if delta_total < tol:\n",
    "                    # convergence conditions\n",
    "                    conv_cond = zeta_2[1] >= 1 # second regime is non-stationary\n",
    "                    if conv_cond:\n",
    "                        print('Converged at iteration ', s)\n",
    "                        converged = True\n",
    "                        break\n",
    "                    else:\n",
    "                        break\n",
    "\n",
    "                # if any parameter is nan, stop\n",
    "                nansum = (np.isnan(ksi).sum() + np.isnan(zeta_1).sum() + np.isnan(zeta_2).sum() + \n",
    "                          np.isnan(var_1).sum() + np.isnan(var_2).sum())\n",
    "                if nansum != 0:\n",
    "                    break\n",
    "\n",
    "            if not converged:\n",
    "                print(f'Algorithm not converged')\n",
    "                print('Repeating with different initital values')\n",
    "        except:\n",
    "            continue\n",
    "        \n",
    "    return ksi, zeta_1, var_1, zeta_2, var_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0c8d7ec9",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Running sim  0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  28\n",
      "\n",
      "Running sim  1\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  2\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "\n",
      "Running sim  3\n",
      "Converged at iteration  34\n",
      "\n",
      "Running sim  4\n",
      "Converged at iteration  43\n",
      "\n",
      "Running sim  5\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  30\n",
      "\n",
      "Running sim  6\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  7\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  8\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  33\n",
      "\n",
      "Running sim  9\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  49\n",
      "\n",
      "Running sim  10\n",
      "Converged at iteration  31\n",
      "\n",
      "Running sim  11\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  12\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  20\n",
      "\n",
      "Running sim  13\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  28\n",
      "\n",
      "Running sim  14\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  15\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  16\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  19\n",
      "\n",
      "Running sim  17\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  18\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  32\n",
      "\n",
      "Running sim  19\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  20\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  22\n",
      "\n",
      "Running sim  21\n",
      "Converged at iteration  36\n",
      "\n",
      "Running sim  22\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  23\n",
      "Converged at iteration  45\n",
      "\n",
      "Running sim  24\n",
      "Converged at iteration  35\n",
      "\n",
      "Running sim  25\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "\n",
      "Running sim  26\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  27\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  21\n",
      "\n",
      "Running sim  28\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "\n",
      "Running sim  29\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "\n",
      "Running sim  30\n",
      "Converged at iteration  30\n",
      "\n",
      "Running sim  31\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "\n",
      "Running sim  32\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  41\n",
      "\n",
      "Running sim  33\n",
      "Converged at iteration  48\n",
      "\n",
      "Running sim  34\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  35\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  15\n",
      "\n",
      "Running sim  36\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  46\n",
      "\n",
      "Running sim  37\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "\n",
      "Running sim  38\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  39\n",
      "\n",
      "Running sim  39\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  49\n",
      "\n",
      "Running sim  40\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  40\n",
      "\n",
      "Running sim  41\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  46\n",
      "\n",
      "Running sim  42\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  48\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  49\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  22\n",
      "\n",
      "Running sim  50\n",
      "Converged at iteration  35\n",
      "\n",
      "Running sim  51\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  52\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "\n",
      "Running sim  53\n",
      "Converged at iteration  26\n",
      "\n",
      "Running sim  54\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  41\n",
      "\n",
      "Running sim  55\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "\n",
      "Running sim  56\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  33\n",
      "\n",
      "Running sim  57\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  25\n",
      "\n",
      "Running sim  58\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  26\n",
      "\n",
      "Running sim  59\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  30\n",
      "\n",
      "Running sim  60\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  61\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  62\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  63\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "\n",
      "Running sim  64\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  47\n",
      "\n",
      "Running sim  65\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  39\n",
      "\n",
      "Running sim  66\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  36\n",
      "\n",
      "Running sim  67\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  43\n",
      "\n",
      "Running sim  68\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  18\n",
      "\n",
      "Running sim  69\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "\n",
      "Running sim  70\n",
      "Converged at iteration  42\n",
      "\n",
      "Running sim  71\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  72\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "\n",
      "Running sim  73\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "\n",
      "Running sim  74\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "\n",
      "Running sim  75\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  36\n",
      "\n",
      "Running sim  76\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  77\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  78\n",
      "Converged at iteration  26\n",
      "\n",
      "Running sim  79\n",
      "Converged at iteration  44\n",
      "\n",
      "Running sim  80\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  28\n",
      "\n",
      "Running sim  81\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  15\n",
      "\n",
      "Running sim  82\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  83\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "\n",
      "Running sim  84\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  46\n",
      "\n",
      "Running sim  85\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  86\n",
      "Converged at iteration  43\n",
      "\n",
      "Running sim  87\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  35\n",
      "\n",
      "Running sim  88\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  20\n",
      "\n",
      "Running sim  89\n",
      "Converged at iteration  42\n",
      "\n",
      "Running sim  90\n",
      "Converged at iteration  43\n",
      "\n",
      "Running sim  91\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  92\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  93\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  15\n",
      "\n",
      "Running sim  94\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "\n",
      "Running sim  95\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  43\n",
      "\n",
      "Running sim  96\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  97\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  98\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  33\n",
      "\n",
      "Running sim  99\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  44\n"
     ]
    }
   ],
   "source": [
    "delta_0s = []\n",
    "delta_1s = []\n",
    "delta_2s = []\n",
    "phi_10s = []\n",
    "phi_11s = []\n",
    "phi_12s = []\n",
    "phi_20s = []\n",
    "phi_21s = []\n",
    "var_1s = []\n",
    "var_2s = []\n",
    "\n",
    "max_iter=50\n",
    "tol = 0.05\n",
    "\n",
    "N = 1000 # number of datapoints to generate\n",
    "N_sim = 100 # number of simulations to run\n",
    "\n",
    "# parameters used to generate a\n",
    "ksi = [-1.3, 0.6, 0.3]\n",
    "zeta_1 = [0, 0.6, -0.2]\n",
    "var_1 = 1\n",
    "zeta_2 = [0, 1.5]\n",
    "var_2 = 3\n",
    "\n",
    "for s in range(N_sim):\n",
    "    print()\n",
    "    print('Running sim ', s)\n",
    "    \n",
    "    # generate a\n",
    "    np.random.seed(123+s)\n",
    "    a = generate_a(N, ksi, zeta_1, var_1, zeta_2, var_2)\n",
    "    \n",
    "    # run EM algorithm\n",
    "    ksi_hat, zeta_1_hat, var_1_hat, zeta_2_hat, var_2_hat = em_algorithm(a, max_iter, tol)\n",
    "    \n",
    "    # save results\n",
    "    delta_0s.append(ksi_hat[0])\n",
    "    delta_1s.append(ksi_hat[1])\n",
    "    delta_2s.append(ksi_hat[2])\n",
    "    phi_10s.append(zeta_1_hat[0])\n",
    "    phi_11s.append(zeta_1_hat[1])\n",
    "    phi_12s.append(zeta_1_hat[2])\n",
    "    phi_20s.append(zeta_2_hat[0])\n",
    "    phi_21s.append(zeta_2_hat[1])\n",
    "    var_1s.append(var_1_hat)\n",
    "    var_2s.append(var_2_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7ee83383",
   "metadata": {},
   "outputs": [],
   "source": [
    "res = pd.DataFrame.from_dict({r'$\\sigma_1^2$':var_1s, r'$\\phi_{1,0}$':phi_10s, r'$\\phi_{1,1}$':phi_11s, \n",
    "                        r'$\\phi_{1,2}$':phi_12s, r'$\\sigma_2^2$':var_2s, r'$\\phi_{2,0}$':phi_20s, \n",
    "                        r'$\\phi_{2,1}$':phi_21s, r'$\\delta_0$':delta_0s, r'$\\delta_1$':delta_1s, \n",
    "                        r'$\\delta_2$':delta_2s})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f7a12190",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\sigma_1^2$</th>\n",
       "      <th>$\\phi_{1,0}$</th>\n",
       "      <th>$\\phi_{1,1}$</th>\n",
       "      <th>$\\phi_{1,2}$</th>\n",
       "      <th>$\\sigma_2^2$</th>\n",
       "      <th>$\\phi_{2,0}$</th>\n",
       "      <th>$\\phi_{2,1}$</th>\n",
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       "      <th>$\\delta_1$</th>\n",
       "      <th>$\\delta_2$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.894221</td>\n",
       "      <td>-0.019048</td>\n",
       "      <td>0.577595</td>\n",
       "      <td>-0.185419</td>\n",
       "      <td>2.707574</td>\n",
       "      <td>-0.207625</td>\n",
       "      <td>1.590736</td>\n",
       "      <td>-1.392787</td>\n",
       "      <td>0.653440</td>\n",
       "      <td>0.314996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.965440</td>\n",
       "      <td>0.050168</td>\n",
       "      <td>0.584820</td>\n",
       "      <td>-0.223871</td>\n",
       "      <td>3.143177</td>\n",
       "      <td>0.006323</td>\n",
       "      <td>1.484688</td>\n",
       "      <td>-1.090314</td>\n",
       "      <td>0.634214</td>\n",
       "      <td>0.320480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.068524</td>\n",
       "      <td>-0.004078</td>\n",
       "      <td>0.579087</td>\n",
       "      <td>-0.204501</td>\n",
       "      <td>2.940133</td>\n",
       "      <td>0.068320</td>\n",
       "      <td>1.496375</td>\n",
       "      <td>-1.072032</td>\n",
       "      <td>0.580037</td>\n",
       "      <td>0.238617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.961893</td>\n",
       "      <td>0.021295</td>\n",
       "      <td>0.575999</td>\n",
       "      <td>-0.148828</td>\n",
       "      <td>2.720907</td>\n",
       "      <td>-0.073152</td>\n",
       "      <td>1.469632</td>\n",
       "      <td>-1.445670</td>\n",
       "      <td>0.606285</td>\n",
       "      <td>0.339199</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.905894</td>\n",
       "      <td>-0.163154</td>\n",
       "      <td>0.586048</td>\n",
       "      <td>-0.199668</td>\n",
       "      <td>3.280227</td>\n",
       "      <td>0.010195</td>\n",
       "      <td>1.428144</td>\n",
       "      <td>-1.950154</td>\n",
       "      <td>0.700772</td>\n",
       "      <td>0.359498</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   $\\sigma_1^2$  $\\phi_{1,0}$  $\\phi_{1,1}$  $\\phi_{1,2}$  $\\sigma_2^2$  \\\n",
       "0      0.894221     -0.019048      0.577595     -0.185419      2.707574   \n",
       "1      0.965440      0.050168      0.584820     -0.223871      3.143177   \n",
       "2      1.068524     -0.004078      0.579087     -0.204501      2.940133   \n",
       "3      0.961893      0.021295      0.575999     -0.148828      2.720907   \n",
       "4      0.905894     -0.163154      0.586048     -0.199668      3.280227   \n",
       "\n",
       "   $\\phi_{2,0}$  $\\phi_{2,1}$  $\\delta_0$  $\\delta_1$  $\\delta_2$  \n",
       "0     -0.207625      1.590736   -1.392787    0.653440    0.314996  \n",
       "1      0.006323      1.484688   -1.090314    0.634214    0.320480  \n",
       "2      0.068320      1.496375   -1.072032    0.580037    0.238617  \n",
       "3     -0.073152      1.469632   -1.445670    0.606285    0.339199  \n",
       "4      0.010195      1.428144   -1.950154    0.700772    0.359498  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "80a9c0cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\sigma_1^2$</th>\n",
       "      <th>$\\phi_{1,0}$</th>\n",
       "      <th>$\\phi_{1,1}$</th>\n",
       "      <th>$\\phi_{1,2}$</th>\n",
       "      <th>$\\sigma_2^2$</th>\n",
       "      <th>$\\phi_{2,0}$</th>\n",
       "      <th>$\\phi_{2,1}$</th>\n",
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       "      <th>$\\delta_2$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.062045</td>\n",
       "      <td>0.001032</td>\n",
       "      <td>0.604038</td>\n",
       "      <td>-0.196105</td>\n",
       "      <td>2.940641</td>\n",
       "      <td>-0.005328</td>\n",
       "      <td>1.479187</td>\n",
       "      <td>-1.722063</td>\n",
       "      <td>1.497534</td>\n",
       "      <td>0.533087</td>\n",
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       "   $\\sigma_1^2$  $\\phi_{1,0}$  $\\phi_{1,1}$  $\\phi_{1,2}$  $\\sigma_2^2$  \\\n",
       "0      1.062045      0.001032      0.604038     -0.196105      2.940641   \n",
       "\n",
       "   $\\phi_{2,0}$  $\\phi_{2,1}$  $\\delta_0$  $\\delta_1$  $\\delta_2$  \n",
       "0     -0.005328      1.479187   -1.722063    1.497534    0.533087  "
      ]
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     "execution_count": 10,
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   ],
   "source": [
    "pd.DataFrame(res.mean()).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ee09097a",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\sigma_1^2$</th>\n",
       "      <th>$\\phi_{1,0}$</th>\n",
       "      <th>$\\phi_{1,1}$</th>\n",
       "      <th>$\\phi_{1,2}$</th>\n",
       "      <th>$\\sigma_2^2$</th>\n",
       "      <th>$\\phi_{2,0}$</th>\n",
       "      <th>$\\phi_{2,1}$</th>\n",
       "      <th>$\\delta_0$</th>\n",
       "      <th>$\\delta_1$</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.381689</td>\n",
       "      <td>0.064487</td>\n",
       "      <td>0.044192</td>\n",
       "      <td>0.026028</td>\n",
       "      <td>0.389203</td>\n",
       "      <td>0.101297</td>\n",
       "      <td>0.118633</td>\n",
       "      <td>2.558627</td>\n",
       "      <td>5.641816</td>\n",
       "      <td>1.905792</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "   $\\sigma_1^2$  $\\phi_{1,0}$  $\\phi_{1,1}$  $\\phi_{1,2}$  $\\sigma_2^2$  \\\n",
       "0      0.381689      0.064487      0.044192      0.026028      0.389203   \n",
       "\n",
       "   $\\phi_{2,0}$  $\\phi_{2,1}$  $\\delta_0$  $\\delta_1$  $\\delta_2$  \n",
       "0      0.101297      0.118633    2.558627    5.641816    1.905792  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(res.std()).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c47f51a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>$\\sigma_1^2$</th>\n",
       "      <th>$\\phi_{1,0}$</th>\n",
       "      <th>$\\phi_{1,1}$</th>\n",
       "      <th>$\\phi_{1,2}$</th>\n",
       "      <th>$\\sigma_2^2$</th>\n",
       "      <th>$\\phi_{2,0}$</th>\n",
       "      <th>$\\phi_{2,1}$</th>\n",
       "      <th>$\\delta_0$</th>\n",
       "      <th>$\\delta_1$</th>\n",
       "      <th>$\\delta_2$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.062045</td>\n",
       "      <td>0.001032</td>\n",
       "      <td>0.604038</td>\n",
       "      <td>-0.196105</td>\n",
       "      <td>2.940641</td>\n",
       "      <td>-0.005328</td>\n",
       "      <td>1.479187</td>\n",
       "      <td>-1.722063</td>\n",
       "      <td>1.497534</td>\n",
       "      <td>0.533087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.381689</td>\n",
       "      <td>0.064487</td>\n",
       "      <td>0.044192</td>\n",
       "      <td>0.026028</td>\n",
       "      <td>0.389203</td>\n",
       "      <td>0.101297</td>\n",
       "      <td>0.118633</td>\n",
       "      <td>2.558627</td>\n",
       "      <td>5.641816</td>\n",
       "      <td>1.905792</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.652769</td>\n",
       "      <td>-0.163154</td>\n",
       "      <td>0.543313</td>\n",
       "      <td>-0.260744</td>\n",
       "      <td>0.005133</td>\n",
       "      <td>-0.370878</td>\n",
       "      <td>1.151861</td>\n",
       "      <td>-20.961640</td>\n",
       "      <td>0.280673</td>\n",
       "      <td>-0.973211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.918361</td>\n",
       "      <td>-0.042646</td>\n",
       "      <td>0.578895</td>\n",
       "      <td>-0.210842</td>\n",
       "      <td>2.810590</td>\n",
       "      <td>-0.054512</td>\n",
       "      <td>1.424586</td>\n",
       "      <td>-1.626328</td>\n",
       "      <td>0.559556</td>\n",
       "      <td>0.231274</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.993479</td>\n",
       "      <td>0.002837</td>\n",
       "      <td>0.597609</td>\n",
       "      <td>-0.199454</td>\n",
       "      <td>2.940683</td>\n",
       "      <td>-0.010071</td>\n",
       "      <td>1.483769</td>\n",
       "      <td>-1.339830</td>\n",
       "      <td>0.628430</td>\n",
       "      <td>0.298502</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.068892</td>\n",
       "      <td>0.047261</td>\n",
       "      <td>0.616779</td>\n",
       "      <td>-0.180328</td>\n",
       "      <td>3.171634</td>\n",
       "      <td>0.050386</td>\n",
       "      <td>1.555870</td>\n",
       "      <td>-1.130637</td>\n",
       "      <td>0.717860</td>\n",
       "      <td>0.347236</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.026059</td>\n",
       "      <td>0.155552</td>\n",
       "      <td>0.797314</td>\n",
       "      <td>-0.138728</td>\n",
       "      <td>3.647432</td>\n",
       "      <td>0.210560</td>\n",
       "      <td>1.784993</td>\n",
       "      <td>-0.291053</td>\n",
       "      <td>48.722239</td>\n",
       "      <td>15.911444</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       $\\sigma_1^2$  $\\phi_{1,0}$  $\\phi_{1,1}$  $\\phi_{1,2}$  $\\sigma_2^2$  \\\n",
       "count    100.000000    100.000000    100.000000    100.000000    100.000000   \n",
       "mean       1.062045      0.001032      0.604038     -0.196105      2.940641   \n",
       "std        0.381689      0.064487      0.044192      0.026028      0.389203   \n",
       "min        0.652769     -0.163154      0.543313     -0.260744      0.005133   \n",
       "25%        0.918361     -0.042646      0.578895     -0.210842      2.810590   \n",
       "50%        0.993479      0.002837      0.597609     -0.199454      2.940683   \n",
       "75%        1.068892      0.047261      0.616779     -0.180328      3.171634   \n",
       "max        3.026059      0.155552      0.797314     -0.138728      3.647432   \n",
       "\n",
       "       $\\phi_{2,0}$  $\\phi_{2,1}$  $\\delta_0$  $\\delta_1$  $\\delta_2$  \n",
       "count    100.000000    100.000000  100.000000  100.000000  100.000000  \n",
       "mean      -0.005328      1.479187   -1.722063    1.497534    0.533087  \n",
       "std        0.101297      0.118633    2.558627    5.641816    1.905792  \n",
       "min       -0.370878      1.151861  -20.961640    0.280673   -0.973211  \n",
       "25%       -0.054512      1.424586   -1.626328    0.559556    0.231274  \n",
       "50%       -0.010071      1.483769   -1.339830    0.628430    0.298502  \n",
       "75%        0.050386      1.555870   -1.130637    0.717860    0.347236  \n",
       "max        0.210560      1.784993   -0.291053   48.722239   15.911444  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b1609730",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>$\\sigma_1^2$</th>\n",
       "      <th>$\\phi_{1,0}$</th>\n",
       "      <th>$\\phi_{1,1}$</th>\n",
       "      <th>$\\phi_{1,2}$</th>\n",
       "      <th>$\\sigma_2^2$</th>\n",
       "      <th>$\\phi_{2,0}$</th>\n",
       "      <th>$\\phi_{2,1}$</th>\n",
       "      <th>$\\delta_0$</th>\n",
       "      <th>$\\delta_1$</th>\n",
       "      <th>$\\delta_2$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.993479</td>\n",
       "      <td>0.002837</td>\n",
       "      <td>0.597609</td>\n",
       "      <td>-0.199454</td>\n",
       "      <td>2.940683</td>\n",
       "      <td>-0.010071</td>\n",
       "      <td>1.483769</td>\n",
       "      <td>-1.33983</td>\n",
       "      <td>0.62843</td>\n",
       "      <td>0.298502</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   $\\sigma_1^2$  $\\phi_{1,0}$  $\\phi_{1,1}$  $\\phi_{1,2}$  $\\sigma_2^2$  \\\n",
       "0      0.993479      0.002837      0.597609     -0.199454      2.940683   \n",
       "\n",
       "   $\\phi_{2,0}$  $\\phi_{2,1}$  $\\delta_0$  $\\delta_1$  $\\delta_2$  \n",
       "0     -0.010071      1.483769    -1.33983     0.62843    0.298502  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(res.median()).T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21717729",
   "metadata": {},
   "source": [
    "# EM algorithm for a general case of LMAR(m1,m2,n) model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e9036385",
   "metadata": {},
   "outputs": [],
   "source": [
    "def em_algorithm(a, m1, m2, n, max_iter, tol):\n",
    "    '''\n",
    "    run em algorithm for max_iter iterations or until convergence\n",
    "    \n",
    "    a: time series\n",
    "    m1: order of the first (stationary) AR model\n",
    "    m2: order of the second (non-stationary) AR model\n",
    "    n: number of lags in logistic equation\n",
    "    '''\n",
    "    \n",
    "    npdf = stats.norm.pdf\n",
    "    \n",
    "    max_lag = max(m1,m2,n)\n",
    "    \n",
    "    converged = False\n",
    "    \n",
    "    while not converged:\n",
    "        #try:\n",
    "        # random initial guess\n",
    "        ksi = np.random.uniform(-3,3,(n+1))\n",
    "        zeta_1 = np.random.uniform(-3,3,(m1+1))\n",
    "        zeta_2 = np.random.uniform(-3,3,(m2+1))\n",
    "        var_1 = np.random.uniform(0,6,(1))\n",
    "        var_2 = np.random.uniform(0,6,(1))\n",
    "\n",
    "        # create dataframe\n",
    "        a_lags = [f'a_l{i}' for i in range(1,max_lag+1)]\n",
    "        abs_lags = [f'abs_l{i}' for i in range(1,n+1)]\n",
    "        columns = ['const', 'a'] + a_lags + abs_lags + ['p1', 'p2', 'tau1', 'tau2', 'e1', 'e2']\n",
    "        df = pd.DataFrame(columns=columns)\n",
    "        df['a'] = a[max_lag:]\n",
    "        df['const'] = 1\n",
    "        for l in range(1,max_lag+1):\n",
    "            df[a_lags[l-1]] = a[max_lag-l:-l]\n",
    "        for l in range(1,n+1):\n",
    "            df[abs_lags[l-1]] = abs(df[a_lags[l-1]])\n",
    "\n",
    "\n",
    "        for s in range(max_iter):\n",
    "            # E-step\n",
    "            # solve for mixing probabilities\n",
    "            num = np.exp((df[['const'] + abs_lags] * ksi).sum(axis=1))\n",
    "            denom = (1 + np.exp((df[['const'] + abs_lags] * ksi).sum(axis=1)))\n",
    "            df['p1'] = num/denom\n",
    "            df['p2'] = 1 - df['p1']\n",
    "\n",
    "            # calculate e\n",
    "            df['e1'] = df['a'] - (zeta_1 * df[['const'] + a_lags[:m1]]).sum(axis=1)\n",
    "            df['e2'] = df['a'] - (zeta_2 * df[['const'] + a_lags[:m2]]).sum(axis=1)\n",
    "\n",
    "            # calculate tau\n",
    "            sigma_1 = np.sqrt(var_1)\n",
    "            sigma_2 = np.sqrt(var_2)\n",
    "            denom = ((df['p1'] / sigma_1) * stats.norm.pdf(df['e1'] / sigma_1) + \n",
    "                     (df['p2'] / sigma_2) * stats.norm.pdf(df['e2'] / sigma_2))\n",
    "            df['tau1'] = (df['p1'] / sigma_1) * stats.norm.pdf(df['e1'] / sigma_1) / denom\n",
    "            df['tau2'] = (df['p2'] / sigma_2) * stats.norm.pdf(df['e2'] / sigma_2) / denom\n",
    "\n",
    "\n",
    "            # M-step\n",
    "\n",
    "            # compute ksi\n",
    "            dr_dksi = df[['const'] + abs_lags]\n",
    "            dQ_dksi = (np.tile((df['tau1'] - df['p1']), (n+1,1)).T * dr_dksi).sum().values\n",
    "            df['dr_dksi^2'] = df[['const'] + abs_lags].apply(outer, axis=1).apply(np.array)\n",
    "            d2Q_dksi2 = -(df['p1'] * df['p2'] * df['dr_dksi^2']).sum()\n",
    "            new_ksi = ksi - np.linalg.inv(d2Q_dksi2) @ dQ_dksi\n",
    "\n",
    "            # compute zeta\n",
    "            df['de1_dzeta1^2'] = df[['const'] + a_lags[:m1]].apply(outer, axis=1).apply(np.array)\n",
    "            df['de2_dzeta2^2'] = df[['const'] + a_lags[:m2]].apply(outer, axis=1).apply(np.array)\n",
    "            zeta1_sum1 = (df['tau1'] * df['de1_dzeta1^2']).sum()\n",
    "            zeta2_sum1 = (df['tau2'] * df['de2_dzeta2^2']).sum()\n",
    "            zeta1_sum2 = (-np.tile(df['tau1'] * df['a'], (m1+1,1)).T * -df[['const'] + a_lags[:m1]]).sum().values\n",
    "            zeta2_sum2 = (-np.tile(df['tau2'] * df['a'], (m2+1,1)).T * -df[['const'] + a_lags[:m2]]).sum().values\n",
    "            new_zeta_1 = np.linalg.inv(zeta1_sum1) @ zeta1_sum2\n",
    "            new_zeta_2 = np.linalg.inv(zeta2_sum1) @ zeta2_sum2\n",
    "\n",
    "            # compute variance\n",
    "            sigma1_sum2 = (df['tau1'] * (df['a'] + np.dot(-df[['const'] + a_lags[:m1]], new_zeta_1))**2).sum()\n",
    "            sigma2_sum2 = (df['tau2'] * (df['a'] + np.dot(-df[['const'] + a_lags[:m2]], new_zeta_2))**2).sum()\n",
    "            new_var_1 = 1/df['tau1'].sum() * sigma1_sum2\n",
    "            new_var_2 = 1/df['tau2'].sum() * sigma2_sum2\n",
    "\n",
    "            # calculate the difference between old and new values of parameters\n",
    "            delta_ksi = np.sum(abs(new_ksi - ksi))\n",
    "            delta_zeta_1 = np.sum(abs(new_zeta_1 - zeta_1))\n",
    "            delta_zeta_2 = np.sum(abs(new_zeta_2 - zeta_2))\n",
    "            delta_var_1 = np.sum(abs(new_var_1 - var_1))\n",
    "            delta_var_2 = np.sum(abs(new_var_2 - var_2))\n",
    "\n",
    "            # update parameters\n",
    "            ksi = new_ksi\n",
    "            zeta_1 = new_zeta_1\n",
    "            zeta_2 = new_zeta_2\n",
    "            var_1 = new_var_1\n",
    "            var_2 = new_var_2\n",
    "\n",
    "            # if any parameter is nan, stop\n",
    "            nansum = (np.isnan(ksi).sum() + np.isnan(zeta_1).sum() + np.isnan(zeta_2).sum() + \n",
    "                      np.isnan(var_1).sum() + np.isnan(var_2).sum())\n",
    "            if nansum != 0:\n",
    "                break\n",
    "\n",
    "            # calculate total difference between old and new parameters\n",
    "            delta_total = delta_ksi + delta_zeta_1 + delta_zeta_2 + delta_var_1 + delta_var_2\n",
    "\n",
    "            # check convergence\n",
    "            if delta_total < tol:\n",
    "                # calculate roots of characteristic polynomial of the second regime\n",
    "                char_pol = np.polynomial.polynomial.Polynomial(np.concatenate(([1],-zeta_2[1:])))\n",
    "                # calculate reciprocal roots and take absolute value\n",
    "                roots = np.abs(1/char_pol.roots())\n",
    "\n",
    "                # convergence conditions\n",
    "                # second regime is non-stationary\n",
    "                conv_cond = sum(roots>=1) > 0 # at least one reciprocal root >= 1\n",
    "\n",
    "                if conv_cond:\n",
    "                    print('Converged at iteration ', s)\n",
    "                    converged = True\n",
    "                    break\n",
    "                else:\n",
    "                    break\n",
    "\n",
    "        if not converged:\n",
    "            print(f'Algorithm not converged')\n",
    "            print('Repeating with different initital values')\n",
    "        #except:\n",
    "        #    continue\n",
    "        \n",
    "    return ksi, zeta_1, var_1, zeta_2, var_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "f2e30d4e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Running sim  0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  28\n",
      "\n",
      "Running sim  1\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  2\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "\n",
      "Running sim  3\n",
      "Converged at iteration  34\n",
      "\n",
      "Running sim  4\n",
      "Converged at iteration  43\n",
      "\n",
      "Running sim  5\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  30\n",
      "\n",
      "Running sim  6\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  7\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  8\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  33\n",
      "\n",
      "Running sim  9\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  49\n"
     ]
    }
   ],
   "source": [
    "delta_0s = []\n",
    "delta_1s = []\n",
    "delta_2s = []\n",
    "phi_10s = []\n",
    "phi_11s = []\n",
    "phi_12s = []\n",
    "phi_20s = []\n",
    "phi_21s = []\n",
    "var_1s = []\n",
    "var_2s = []\n",
    "\n",
    "max_iter=50\n",
    "tol = 0.05\n",
    "\n",
    "N = 1000 # number of datapoints to generate\n",
    "N_sim = 10 # number of simulations to run\n",
    "\n",
    "# assume the order of the model is known\n",
    "m1 = 2\n",
    "m2 = 1\n",
    "n = 2\n",
    "\n",
    "# parameters used to generate a\n",
    "ksi = [-1.3, 0.6, 0.3]\n",
    "zeta_1 = [0, 0.6, -0.2]\n",
    "var_1 = 1\n",
    "zeta_2 = [0, 1.5]\n",
    "var_2 = 3\n",
    "\n",
    "for s in range(N_sim):\n",
    "    print()\n",
    "    print('Running sim ', s)\n",
    "    \n",
    "    # generate a\n",
    "    np.random.seed(123+s)\n",
    "    a = generate_a(N, ksi, zeta_1, var_1, zeta_2, var_2)\n",
    "    \n",
    "    # run EM algorithm\n",
    "    ksi_hat, zeta_1_hat, var_1_hat, zeta_2_hat, var_2_hat = em_algorithm(a, m1, m2, n, max_iter, tol)\n",
    "    \n",
    "    # save results\n",
    "    delta_0s.append(ksi_hat[0])\n",
    "    delta_1s.append(ksi_hat[1])\n",
    "    delta_2s.append(ksi_hat[2])\n",
    "    phi_10s.append(zeta_1_hat[0])\n",
    "    phi_11s.append(zeta_1_hat[1])\n",
    "    phi_12s.append(zeta_1_hat[2])\n",
    "    phi_20s.append(zeta_2_hat[0])\n",
    "    phi_21s.append(zeta_2_hat[1])\n",
    "    var_1s.append(var_1_hat)\n",
    "    var_2s.append(var_2_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4d227cfc",
   "metadata": {},
   "outputs": [],
   "source": [
    "res = pd.DataFrame.from_dict({r'$\\sigma_1^2$':var_1s, r'$\\phi_{1,0}$':phi_10s, r'$\\phi_{1,1}$':phi_11s, \n",
    "                        r'$\\phi_{1,2}$':phi_12s, r'$\\sigma_2^2$':var_2s, r'$\\phi_{2,0}$':phi_20s, \n",
    "                        r'$\\phi_{2,1}$':phi_21s, r'$\\delta_0$':delta_0s, r'$\\delta_1$':delta_1s, \n",
    "                        r'$\\delta_2$':delta_2s})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "1fd76e4e",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\sigma_1^2$</th>\n",
       "      <th>$\\phi_{1,0}$</th>\n",
       "      <th>$\\phi_{1,1}$</th>\n",
       "      <th>$\\phi_{1,2}$</th>\n",
       "      <th>$\\sigma_2^2$</th>\n",
       "      <th>$\\phi_{2,0}$</th>\n",
       "      <th>$\\phi_{2,1}$</th>\n",
       "      <th>$\\delta_0$</th>\n",
       "      <th>$\\delta_1$</th>\n",
       "      <th>$\\delta_2$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.125074</td>\n",
       "      <td>-0.023144</td>\n",
       "      <td>0.620569</td>\n",
       "      <td>-0.199713</td>\n",
       "      <td>2.657217</td>\n",
       "      <td>0.307646</td>\n",
       "      <td>1.105197</td>\n",
       "      <td>-0.940240</td>\n",
       "      <td>0.804132</td>\n",
       "      <td>0.290207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.555737</td>\n",
       "      <td>0.068501</td>\n",
       "      <td>0.071861</td>\n",
       "      <td>0.021865</td>\n",
       "      <td>0.955070</td>\n",
       "      <td>1.034000</td>\n",
       "      <td>1.157046</td>\n",
       "      <td>1.688079</td>\n",
       "      <td>0.464359</td>\n",
       "      <td>0.084422</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.652769</td>\n",
       "      <td>-0.163154</td>\n",
       "      <td>0.575999</td>\n",
       "      <td>-0.228265</td>\n",
       "      <td>0.000118</td>\n",
       "      <td>-0.207625</td>\n",
       "      <td>-2.180527</td>\n",
       "      <td>-2.286513</td>\n",
       "      <td>0.580037</td>\n",
       "      <td>0.069089</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.914872</td>\n",
       "      <td>-0.045601</td>\n",
       "      <td>0.580520</td>\n",
       "      <td>-0.205329</td>\n",
       "      <td>2.710907</td>\n",
       "      <td>-0.065265</td>\n",
       "      <td>1.413093</td>\n",
       "      <td>-1.732390</td>\n",
       "      <td>0.613267</td>\n",
       "      <td>0.295607</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.963666</td>\n",
       "      <td>-0.001515</td>\n",
       "      <td>0.599962</td>\n",
       "      <td>-0.203253</td>\n",
       "      <td>2.968173</td>\n",
       "      <td>0.008259</td>\n",
       "      <td>1.477160</td>\n",
       "      <td>-1.368767</td>\n",
       "      <td>0.666157</td>\n",
       "      <td>0.317738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.082901</td>\n",
       "      <td>0.020569</td>\n",
       "      <td>0.623053</td>\n",
       "      <td>-0.195767</td>\n",
       "      <td>3.061246</td>\n",
       "      <td>0.079576</td>\n",
       "      <td>1.513269</td>\n",
       "      <td>-1.076602</td>\n",
       "      <td>0.724699</td>\n",
       "      <td>0.336038</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2.662819</td>\n",
       "      <td>0.050168</td>\n",
       "      <td>0.816410</td>\n",
       "      <td>-0.148828</td>\n",
       "      <td>3.280227</td>\n",
       "      <td>3.234676</td>\n",
       "      <td>1.590736</td>\n",
       "      <td>3.673539</td>\n",
       "      <td>2.115385</td>\n",
       "      <td>0.359498</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       $\\sigma_1^2$  $\\phi_{1,0}$  $\\phi_{1,1}$  $\\phi_{1,2}$  $\\sigma_2^2$  \\\n",
       "count     10.000000     10.000000     10.000000     10.000000     10.000000   \n",
       "mean       1.125074     -0.023144      0.620569     -0.199713      2.657217   \n",
       "std        0.555737      0.068501      0.071861      0.021865      0.955070   \n",
       "min        0.652769     -0.163154      0.575999     -0.228265      0.000118   \n",
       "25%        0.914872     -0.045601      0.580520     -0.205329      2.710907   \n",
       "50%        0.963666     -0.001515      0.599962     -0.203253      2.968173   \n",
       "75%        1.082901      0.020569      0.623053     -0.195767      3.061246   \n",
       "max        2.662819      0.050168      0.816410     -0.148828      3.280227   \n",
       "\n",
       "       $\\phi_{2,0}$  $\\phi_{2,1}$  $\\delta_0$  $\\delta_1$  $\\delta_2$  \n",
       "count     10.000000     10.000000   10.000000   10.000000   10.000000  \n",
       "mean       0.307646      1.105197   -0.940240    0.804132    0.290207  \n",
       "std        1.034000      1.157046    1.688079    0.464359    0.084422  \n",
       "min       -0.207625     -2.180527   -2.286513    0.580037    0.069089  \n",
       "25%       -0.065265      1.413093   -1.732390    0.613267    0.295607  \n",
       "50%        0.008259      1.477160   -1.368767    0.666157    0.317738  \n",
       "75%        0.079576      1.513269   -1.076602    0.724699    0.336038  \n",
       "max        3.234676      1.590736    3.673539    2.115385    0.359498  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "5a4d117c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\sigma_1^2$</th>\n",
       "      <th>$\\phi_{1,0}$</th>\n",
       "      <th>$\\phi_{1,1}$</th>\n",
       "      <th>$\\phi_{1,2}$</th>\n",
       "      <th>$\\sigma_2^2$</th>\n",
       "      <th>$\\phi_{2,0}$</th>\n",
       "      <th>$\\phi_{2,1}$</th>\n",
       "      <th>$\\delta_0$</th>\n",
       "      <th>$\\delta_1$</th>\n",
       "      <th>$\\delta_2$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.963666</td>\n",
       "      <td>-0.001515</td>\n",
       "      <td>0.599962</td>\n",
       "      <td>-0.203253</td>\n",
       "      <td>2.968173</td>\n",
       "      <td>0.008259</td>\n",
       "      <td>1.47716</td>\n",
       "      <td>-1.368767</td>\n",
       "      <td>0.666157</td>\n",
       "      <td>0.317738</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   $\\sigma_1^2$  $\\phi_{1,0}$  $\\phi_{1,1}$  $\\phi_{1,2}$  $\\sigma_2^2$  \\\n",
       "0      0.963666     -0.001515      0.599962     -0.203253      2.968173   \n",
       "\n",
       "   $\\phi_{2,0}$  $\\phi_{2,1}$  $\\delta_0$  $\\delta_1$  $\\delta_2$  \n",
       "0      0.008259       1.47716   -1.368767    0.666157    0.317738  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(res.median()).T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1295b47a",
   "metadata": {},
   "source": [
    "# Model selection based on BIC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "05de530a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def em_algorithm(a, m1, m2, n, max_iter, tol):\n",
    "    '''\n",
    "    run em algorithm for max_iter iterations or until convergence\n",
    "    \n",
    "    a: time series\n",
    "    m1: order of the first (stationary) AR model\n",
    "    m2: order of the second (non-stationary) AR model\n",
    "    n: number of lags in logistic equation\n",
    "    '''\n",
    "    \n",
    "    npdf = stats.norm.pdf\n",
    "    \n",
    "    max_lag = max(m1,m2,n)\n",
    "    \n",
    "    converged = False\n",
    "    \n",
    "    while not converged:\n",
    "        #try:\n",
    "        # random initial guess\n",
    "        ksi = np.random.uniform(-3,3,(n+1))\n",
    "        zeta_1 = np.random.uniform(-3,3,(m1+1))\n",
    "        zeta_2 = np.random.uniform(-3,3,(m2+1))\n",
    "        var_1 = np.random.uniform(0,6,(1))\n",
    "        var_2 = np.random.uniform(0,6,(1))\n",
    "\n",
    "        # create dataframe\n",
    "        a_lags = [f'a_l{i}' for i in range(1,max_lag+1)]\n",
    "        abs_lags = [f'abs_l{i}' for i in range(1,n+1)]\n",
    "        columns = ['const', 'a'] + a_lags + abs_lags + ['p1', 'p2', 'tau1', 'tau2', 'e1', 'e2']\n",
    "        df = pd.DataFrame(columns=columns)\n",
    "        df['a'] = a[max_lag:]\n",
    "        df['const'] = 1\n",
    "        for l in range(1,max_lag+1):\n",
    "            df[a_lags[l-1]] = a[max_lag-l:-l]\n",
    "        for l in range(1,n+1):\n",
    "            df[abs_lags[l-1]] = abs(df[a_lags[l-1]])\n",
    "\n",
    "\n",
    "        for s in range(max_iter):\n",
    "            # E-step\n",
    "            # solve for mixing probabilities\n",
    "            num = np.exp((df[['const'] + abs_lags] * ksi).sum(axis=1))\n",
    "            denom = (1 + np.exp((df[['const'] + abs_lags] * ksi).sum(axis=1)))\n",
    "            df['p1'] = num/denom\n",
    "            df['p2'] = 1 - df['p1']\n",
    "\n",
    "            # calculate e\n",
    "            df['e1'] = df['a'] - (zeta_1 * df[['const'] + a_lags[:m1]]).sum(axis=1)\n",
    "            df['e2'] = df['a'] - (zeta_2 * df[['const'] + a_lags[:m2]]).sum(axis=1)\n",
    "\n",
    "            # calculate tau\n",
    "            sigma_1 = np.sqrt(var_1)\n",
    "            sigma_2 = np.sqrt(var_2)\n",
    "            denom = ((df['p1'] / sigma_1) * stats.norm.pdf(df['e1'] / sigma_1) + \n",
    "                     (df['p2'] / sigma_2) * stats.norm.pdf(df['e2'] / sigma_2))\n",
    "            df['tau1'] = (df['p1'] / sigma_1) * stats.norm.pdf(df['e1'] / sigma_1) / denom\n",
    "            df['tau2'] = (df['p2'] / sigma_2) * stats.norm.pdf(df['e2'] / sigma_2) / denom\n",
    "\n",
    "\n",
    "            # M-step\n",
    "\n",
    "            # compute ksi\n",
    "            dr_dksi = df[['const'] + abs_lags]\n",
    "            dQ_dksi = (np.tile((df['tau1'] - df['p1']), (n+1,1)).T * dr_dksi).sum().values\n",
    "            df['dr_dksi^2'] = df[['const'] + abs_lags].apply(outer, axis=1).apply(np.array)\n",
    "            d2Q_dksi2 = -(df['p1'] * df['p2'] * df['dr_dksi^2']).sum()\n",
    "            new_ksi = ksi - np.linalg.inv(d2Q_dksi2) @ dQ_dksi\n",
    "\n",
    "            # compute zeta\n",
    "            df['de1_dzeta1^2'] = df[['const'] + a_lags[:m1]].apply(outer, axis=1).apply(np.array)\n",
    "            df['de2_dzeta2^2'] = df[['const'] + a_lags[:m2]].apply(outer, axis=1).apply(np.array)\n",
    "            zeta1_sum1 = (df['tau1'] * df['de1_dzeta1^2']).sum()\n",
    "            zeta2_sum1 = (df['tau2'] * df['de2_dzeta2^2']).sum()\n",
    "            zeta1_sum2 = (-np.tile(df['tau1'] * df['a'], (m1+1,1)).T * -df[['const'] + a_lags[:m1]]).sum().values\n",
    "            zeta2_sum2 = (-np.tile(df['tau2'] * df['a'], (m2+1,1)).T * -df[['const'] + a_lags[:m2]]).sum().values\n",
    "            new_zeta_1 = np.linalg.inv(zeta1_sum1) @ zeta1_sum2\n",
    "            new_zeta_2 = np.linalg.inv(zeta2_sum1) @ zeta2_sum2\n",
    "\n",
    "            # compute variance\n",
    "            sigma1_sum2 = (df['tau1'] * (df['a'] + np.dot(-df[['const'] + a_lags[:m1]], new_zeta_1))**2).sum()\n",
    "            sigma2_sum2 = (df['tau2'] * (df['a'] + np.dot(-df[['const'] + a_lags[:m2]], new_zeta_2))**2).sum()\n",
    "            new_var_1 = 1/df['tau1'].sum() * sigma1_sum2\n",
    "            new_var_2 = 1/df['tau2'].sum() * sigma2_sum2\n",
    "\n",
    "            # calculate the difference between old and new values of parameters\n",
    "            delta_ksi = np.sum(abs(new_ksi - ksi))\n",
    "            delta_zeta_1 = np.sum(abs(new_zeta_1 - zeta_1))\n",
    "            delta_zeta_2 = np.sum(abs(new_zeta_2 - zeta_2))\n",
    "            delta_var_1 = np.sum(abs(new_var_1 - var_1))\n",
    "            delta_var_2 = np.sum(abs(new_var_2 - var_2))\n",
    "\n",
    "            # update parameters\n",
    "            ksi = new_ksi\n",
    "            zeta_1 = new_zeta_1\n",
    "            zeta_2 = new_zeta_2\n",
    "            var_1 = new_var_1\n",
    "            var_2 = new_var_2\n",
    "\n",
    "            # if any parameter is nan, stop\n",
    "            nansum = (np.isnan(ksi).sum() + np.isnan(zeta_1).sum() + np.isnan(zeta_2).sum() + \n",
    "                      np.isnan(var_1).sum() + np.isnan(var_2).sum())\n",
    "            if nansum != 0:\n",
    "                break\n",
    "\n",
    "            # calculate total difference between old and new parameters\n",
    "            delta_total = delta_ksi + delta_zeta_1 + delta_zeta_2 + delta_var_1 + delta_var_2\n",
    "\n",
    "            # check convergence\n",
    "            if delta_total < tol:\n",
    "                # calculate roots of characteristic polynomial of the second regime\n",
    "                char_pol = np.polynomial.polynomial.Polynomial(np.concatenate(([1],-zeta_2[1:])))\n",
    "                # calculate reciprocal roots and take absolute value\n",
    "                roots = np.abs(1/char_pol.roots())\n",
    "\n",
    "                # convergence conditions\n",
    "                # second regime is non-stationary\n",
    "                conv_cond = sum(roots>=1) > 0 # at least one reciprocal root >= 1\n",
    "\n",
    "                if conv_cond:\n",
    "                    print('Converged at iteration ', s)\n",
    "                    converged = True\n",
    "                    break\n",
    "                else:\n",
    "                    break\n",
    "\n",
    "        if not converged:\n",
    "            print(f'Algorithm not converged')\n",
    "            print('Repeating with different initital values')\n",
    "        #except:\n",
    "        #    continue\n",
    "        \n",
    "        # calculate Q\n",
    "        Q_sum1 = (df['tau1'] * (np.log(df['p1']) - 1/2*np.log(var_1) - df['e1']**2 / (2 * var_1))).sum()\n",
    "        Q_sum2 = (df['tau2'] * (np.log(df['p2']) - 1/2*np.log(var_2) - df['e2']**2 / (2 * var_2))).sum()\n",
    "        Q = Q_sum1 + Q_sum2\n",
    "        \n",
    "    return ksi, zeta_1, var_1, zeta_2, var_2, Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "84f03c92",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running sim  0\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  18\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "Converged at iteration  43\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  22\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  26\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  41\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  33\n",
      "m1=1, m2=1, n=2, BIC=2104.8755220327153\n",
      "\n",
      "Running sim  1\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  32\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  33\n",
      "Converged at iteration  15\n",
      "Converged at iteration  39\n",
      "Converged at iteration  36\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  27\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  33\n",
      "m1=1, m2=2, n=1, BIC=2183.04449922491\n",
      "\n",
      "Running sim  2\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  28\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  25\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  44\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  27\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "Converged at iteration  16\n",
      "Converged at iteration  39\n",
      "m1=2, m2=1, n=2, BIC=2763.7785972625447\n",
      "\n",
      "Running sim  3\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  36\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  44\n",
      "Converged at iteration  46\n",
      "Converged at iteration  32\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  28\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  43\n",
      "Converged at iteration  29\n",
      "m1=2, m2=2, n=2, BIC=2666.0805705958464\n",
      "\n",
      "Running sim  4\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  6\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  35\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  16\n",
      "Converged at iteration  22\n",
      "Converged at iteration  18\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  41\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  20\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  29\n",
      "m1=1, m2=1, n=1, BIC=2457.3655703356512\n",
      "\n",
      "Running sim  5\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  32\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  42\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  43\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  44\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  33\n",
      "Converged at iteration  30\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "m1=2, m2=2, n=1, BIC=2623.5795359404233\n",
      "\n",
      "Running sim  6\n",
      "Converged at iteration  35\n",
      "Converged at iteration  15\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  29\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  30\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  49\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  33\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "Converged at iteration  27\n",
      "m1=2, m2=2, n=2, BIC=2224.91918416692\n",
      "\n",
      "Running sim  7\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  30\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  28\n",
      "Converged at iteration  40\n",
      "Converged at iteration  28\n",
      "Converged at iteration  27\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  26\n",
      "Converged at iteration  25\n",
      "Converged at iteration  26\n",
      "m1=2, m2=1, n=1, BIC=2672.655349102259\n",
      "\n",
      "Running sim  8\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  20\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  4\n",
      "Converged at iteration  44\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  15\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  33\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  11\n",
      "Converged at iteration  36\n",
      "m1=1, m2=2, n=1, BIC=2236.939470601421\n",
      "\n",
      "Running sim  9\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  42\n",
      "Converged at iteration  30\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  22\n",
      "Converged at iteration  15\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  18\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  29\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  30\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "m1=1, m2=1, n=1, BIC=2167.953708246542\n",
      "\n",
      "Running sim  10\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  10\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  24\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  44\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  43\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  20\n",
      "Converged at iteration  31\n",
      "m1=2, m2=1, n=1, BIC=2299.9377643747907\n",
      "\n",
      "Running sim  11\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  16\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  25\n",
      "Converged at iteration  29\n",
      "Converged at iteration  33\n",
      "Converged at iteration  35\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  12\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  35\n",
      "m1=2, m2=2, n=2, BIC=2749.722687339591\n",
      "\n",
      "Running sim  12\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  16\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  42\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  25\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  13\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  33\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  26\n",
      "m1=2, m2=2, n=1, BIC=2222.8262488326013\n",
      "\n",
      "Running sim  13\n",
      "Converged at iteration  13\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  22\n",
      "Converged at iteration  29\n",
      "Converged at iteration  19\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  13\n",
      "Converged at iteration  23\n",
      "Converged at iteration  20\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  16\n",
      "m1=2, m2=1, n=2, BIC=2629.8791158244253\n",
      "\n",
      "Running sim  14\n",
      "Converged at iteration  30\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  15\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  27\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "Converged at iteration  31\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  17\n",
      "Converged at iteration  26\n",
      "m1=2, m2=1, n=1, BIC=2636.766768620379\n",
      "\n",
      "Running sim  15\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  25\n",
      "Converged at iteration  27\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  35\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  41\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  27\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  26\n",
      "Converged at iteration  24\n",
      "m1=1, m2=2, n=1, BIC=2132.6681900448234\n",
      "\n",
      "Running sim  16\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  21\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  32\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  37\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  45\n",
      "Converged at iteration  20\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  25\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  14\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "m1=1, m2=1, n=1, BIC=2728.649439665211\n",
      "\n",
      "Running sim  17\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  32\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  14\n",
      "Converged at iteration  31\n",
      "Converged at iteration  30\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "Converged at iteration  42\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  21\n",
      "Converged at iteration  43\n",
      "m1=2, m2=2, n=1, BIC=2706.833314935207\n",
      "\n",
      "Running sim  18\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  12\n",
      "Converged at iteration  27\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  15\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  40\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  22\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  47\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  22\n",
      "m1=2, m2=1, n=2, BIC=2683.5342835991655\n",
      "\n",
      "Running sim  19\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  28\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  48\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  15\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  25\n",
      "Converged at iteration  36\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  35\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  41\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  36\n",
      "m1=2, m2=2, n=1, BIC=2695.89529539648\n",
      "\n",
      "Running sim  20\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  42\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  9\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  22\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  26\n",
      "Converged at iteration  44\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  19\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  32\n",
      "m1=1, m2=2, n=1, BIC=2165.6088991623565\n",
      "\n",
      "Running sim  21\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  8\n",
      "Converged at iteration  26\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  24\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  22\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  7\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  41\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  47\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "m1=2, m2=1, n=1, BIC=2238.4369624821807\n",
      "\n",
      "Running sim  22\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  14\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  25\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  13\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  19\n",
      "Converged at iteration  22\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  17\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  17\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  18\n",
      "m1=1, m2=2, n=1, BIC=2001.9592683318597\n",
      "\n",
      "Running sim  23\n",
      "Converged at iteration  46\n",
      "Converged at iteration  24\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  46\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  35\n",
      "Converged at iteration  49\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  48\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  7\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  43\n",
      "m1=2, m2=2, n=1, BIC=2185.101636762369\n",
      "\n",
      "Running sim  24\n",
      "Converged at iteration  34\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  17\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  45\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  28\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  13\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  22\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  25\n",
      "Converged at iteration  30\n",
      "m1=2, m2=1, n=2, BIC=2080.602164933257\n",
      "\n",
      "Running sim  25\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  46\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  22\n",
      "Converged at iteration  12\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  32\n",
      "Converged at iteration  25\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  41\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  22\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "m1=2, m2=2, n=1, BIC=2701.542558271552\n",
      "\n",
      "Running sim  26\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  35\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  18\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  12\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  35\n",
      "Converged at iteration  24\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  12\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  30\n",
      "m1=2, m2=1, n=1, BIC=2755.2149212855425\n",
      "\n",
      "Running sim  27\n",
      "Converged at iteration  26\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  39\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  18\n",
      "Converged at iteration  24\n",
      "Converged at iteration  30\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  30\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  12\n",
      "m1=2, m2=1, n=2, BIC=2730.86539040867\n",
      "\n",
      "Running sim  28\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  15\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  18\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  42\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  39\n",
      "Converged at iteration  20\n",
      "Converged at iteration  14\n",
      "Converged at iteration  35\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  43\n",
      "m1=2, m2=1, n=2, BIC=2706.037045131949\n",
      "\n",
      "Running sim  29\n",
      "Converged at iteration  33\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  29\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  32\n",
      "Converged at iteration  27\n",
      "Converged at iteration  20\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  15\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  41\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  25\n",
      "m1=2, m2=2, n=1, BIC=2684.040974290299\n",
      "\n",
      "Running sim  30\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "Converged at iteration  31\n",
      "Converged at iteration  28\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  35\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  12\n",
      "Converged at iteration  29\n",
      "Converged at iteration  44\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  32\n",
      "m1=2, m2=1, n=1, BIC=2761.5160257359853\n",
      "\n",
      "Running sim  31\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "Converged at iteration  17\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  41\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  28\n",
      "Converged at iteration  23\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  24\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  33\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  15\n",
      "m1=2, m2=1, n=2, BIC=2580.518099085954\n",
      "\n",
      "Running sim  32\n",
      "Converged at iteration  25\n",
      "Converged at iteration  9\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  19\n",
      "Converged at iteration  41\n",
      "Converged at iteration  35\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  26\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  41\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "m1=2, m2=1, n=2, BIC=2672.527448764434\n",
      "\n",
      "Running sim  33\n",
      "Converged at iteration  24\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  41\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "Converged at iteration  33\n",
      "Converged at iteration  19\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  39\n",
      "Converged at iteration  8\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  21\n",
      "m1=2, m2=2, n=1, BIC=2077.4469244183615\n",
      "\n",
      "Running sim  34\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  36\n",
      "Converged at iteration  30\n",
      "Converged at iteration  38\n",
      "Converged at iteration  48\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  45\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  18\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  11\n",
      "Converged at iteration  48\n",
      "m1=2, m2=1, n=2, BIC=2626.6035453406057\n",
      "\n",
      "Running sim  35\n",
      "Converged at iteration  34\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  26\n",
      "Converged at iteration  36\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  18\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  13\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  15\n",
      "Converged at iteration  21\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  37\n",
      "m1=1, m2=2, n=1, BIC=2180.826610357002\n",
      "\n",
      "Running sim  36\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  37\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  37\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  28\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  5\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  24\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  19\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  35\n",
      "m1=2, m2=1, n=1, BIC=2284.345446310816\n",
      "\n",
      "Running sim  37\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  49\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  20\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  19\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  33\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  26\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  20\n",
      "m1=2, m2=2, n=1, BIC=2071.6518884610787\n",
      "\n",
      "Running sim  38\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  45\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  16\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  15\n",
      "Converged at iteration  31\n",
      "Converged at iteration  26\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  20\n",
      "Converged at iteration  29\n",
      "m1=2, m2=2, n=2, BIC=2730.4672500422357\n",
      "\n",
      "Running sim  39\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  49\n",
      "Converged at iteration  40\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  35\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  17\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  41\n",
      "Converged at iteration  30\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  18\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  14\n",
      "m1=2, m2=2, n=2, BIC=2760.7077060308275\n",
      "\n",
      "Running sim  40\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  27\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  28\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  22\n",
      "Converged at iteration  28\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  46\n",
      "Converged at iteration  48\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  28\n",
      "m1=2, m2=1, n=1, BIC=2212.2574663561827\n",
      "\n",
      "Running sim  41\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  42\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  21\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  11\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  35\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  49\n",
      "Converged at iteration  13\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  39\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  42\n",
      "m1=2, m2=2, n=1, BIC=2406.2293521963543\n",
      "\n",
      "Running sim  42\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  20\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  40\n",
      "Converged at iteration  15\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  35\n",
      "Converged at iteration  19\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  26\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  30\n",
      "m1=2, m2=1, n=1, BIC=2739.914803536564\n",
      "\n",
      "Running sim  43\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  10\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  18\n",
      "Converged at iteration  26\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  40\n",
      "Converged at iteration  19\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  22\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  26\n",
      "m1=2, m2=2, n=1, BIC=2121.4864750751017\n",
      "\n",
      "Running sim  44\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  28\n",
      "Converged at iteration  25\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  10\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  26\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  32\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  19\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "Converged at iteration  33\n",
      "m1=2, m2=1, n=2, BIC=2108.830807862759\n",
      "\n",
      "Running sim  45\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "Converged at iteration  30\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  40\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  37\n",
      "Converged at iteration  7\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  32\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  45\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  43\n",
      "m1=2, m2=2, n=2, BIC=2684.4828143794\n",
      "\n",
      "Running sim  46\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  18\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  32\n",
      "Converged at iteration  47\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  27\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  18\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  20\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  21\n",
      "m1=2, m2=2, n=2, BIC=2660.715744803806\n",
      "\n",
      "Running sim  47\n",
      "Converged at iteration  20\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  36\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  11\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  40\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  41\n",
      "m1=2, m2=2, n=2, BIC=2655.998763022054\n",
      "\n",
      "Running sim  48\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  17\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  21\n",
      "Converged at iteration  30\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  24\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  40\n",
      "Converged at iteration  32\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  37\n",
      "m1=1, m2=2, n=1, BIC=2266.068565245746\n",
      "\n",
      "Running sim  49\n",
      "Converged at iteration  49\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  48\n",
      "Converged at iteration  31\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "Converged at iteration  17\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  20\n",
      "Converged at iteration  24\n",
      "Converged at iteration  15\n",
      "m1=2, m2=1, n=2, BIC=2712.2830399286327\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import warnings\n",
    "import itertools\n",
    "\n",
    "bic_df = pd.DataFrame(columns=['m1', 'm2', 'n', 'BIC'])\n",
    "\n",
    "max_iter=50\n",
    "tol = 0.05\n",
    "\n",
    "N = 1000 # number of datapoints to generate\n",
    "N_sim = 50 # number of simulations to run\n",
    "\n",
    "# parameters used to generate a\n",
    "ksi = [-1.3, 0.6, 0.3]\n",
    "zeta_1 = [0, 0.6, -0.2]\n",
    "var_1 = 1\n",
    "zeta_2 = [0, 1.5]\n",
    "var_2 = 3\n",
    "\n",
    "for s in range(N_sim):\n",
    "    print('Running sim ', s)\n",
    "    \n",
    "    # generate a\n",
    "    np.random.seed(123+s)\n",
    "    a = generate_a(N, ksi, zeta_1, var_1, zeta_2, var_2)\n",
    "    \n",
    "    best_bic = np.inf\n",
    "    best_m1, best_m2, best_n = 0,0,0\n",
    "    \n",
    "    for m1,m2,n in itertools.product([1,2],[1,2],[1,2]):\n",
    "        \n",
    "        with warnings.catch_warnings():\n",
    "            warnings.simplefilter('ignore') # supress warnings from EM algorithm\n",
    "            # run EM algorithm to estimate parameters\n",
    "            ksi_hat, zeta_1_hat, var_1_hat, zeta_2_hat, var_2_hat, Q = em_algorithm(a, m1, m2, n, max_iter, tol)\n",
    "        \n",
    "        # compute bic\n",
    "        bic = -2*Q + np.log(N - max(m1,m2,n)) * (m1 + m2 + n)\n",
    "        \n",
    "        if bic < best_bic:\n",
    "            best_bic = bic\n",
    "            best_m1, best_m2, best_n = m1,m2,n\n",
    "    print(f'm1={best_m1}, m2={best_m2}, n={best_n}, BIC={best_bic}')\n",
    "    bic_df.loc[s] = best_m1, best_m2, best_n, best_bic\n",
    "    print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "29ecd03f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>m1</th>\n",
       "      <th>m2</th>\n",
       "      <th>n</th>\n",
       "      <th>BIC</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2104.875522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2183.044499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2763.778597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2666.080571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2457.365570</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    m1   m2    n          BIC\n",
       "0  1.0  1.0  2.0  2104.875522\n",
       "1  1.0  2.0  1.0  2183.044499\n",
       "2  2.0  1.0  2.0  2763.778597\n",
       "3  2.0  2.0  2.0  2666.080571\n",
       "4  1.0  1.0  1.0  2457.365570"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bic_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "6838801c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.78"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(bic_df[bic_df['m1']==2]) / len(bic_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "2056d59e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.48"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(bic_df[bic_df['m2']==1]) / len(bic_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "f9e0385c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(bic_df[bic_df['n']==2]) / len(bic_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "12ee6101",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.22"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(bic_df[(bic_df['m1']==2) & (bic_df['m2']==1) & (bic_df['n']==2)]) / len(bic_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a9e1bce2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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