12.partial_ar_model.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7732b0e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "import warnings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f5290f43",
   "metadata": {},
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = 'retina'\n",
    "#az.style.use('arviz-darkgrid')\n",
    "sns.set_style('darkgrid')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fbc925e",
   "metadata": {},
   "source": [
    "# PAR with synthetic data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b0914ac2",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 300 # number of datapoints\n",
    "\n",
    "sigma_M = 1\n",
    "sigma_R = 0.5\n",
    "rho = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "667d0c4f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.tsa.arima_process import arma_generate_sample\n",
    "\n",
    "np.random.seed(44)\n",
    "ar_M = np.r_[1, -rho]\n",
    "ar_R = np.r_[1, -1]\n",
    "ma = np.r_[1]\n",
    "\n",
    "M = arma_generate_sample(ar_M, ma, N, scale=sigma_M)\n",
    "R = arma_generate_sample(ar_R, ma, N, scale=sigma_R)\n",
    "X = M + R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9f91fc59",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Sum of both components')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x576 with 3 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 481,
       "width": 1040
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1,ax2,ax3) = plt.subplots(3, 1, figsize=(18,8), sharex=True)\n",
    "ax1.plot(M)\n",
    "ax1.set_title(f'Mean reverting component (rho={rho}, sigma_M={sigma_M})')\n",
    "ax2.plot(R)\n",
    "ax2.set_title(f'Random walk component (sigma_R={sigma_R})')\n",
    "ax3.plot(X)\n",
    "ax3.set_title('Sum of both components')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4f5c6d8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4910008106257636"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(np.diff(R)) # sigma_R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e5eed1db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0165856295123856"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(M[1:] - rho*M[:-1]) # sigma_M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "69da0939",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8421052631578947"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# proportion of variance attributable to mean reversion\n",
    "(2*sigma_M**2) / (2*sigma_M**2 + (1+rho) * sigma_R**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7671dc53",
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_par(N, rho, sigma_M, sigma_R):\n",
    "    '''\n",
    "    Generate PAR sample of length N with parameters rho, sigma_M, sigma_R\n",
    "    '''\n",
    "    from statsmodels.tsa.arima_process import arma_generate_sample\n",
    "    \n",
    "    ar_M = np.r_[1, -rho]\n",
    "    ar_R = np.r_[1, -1]\n",
    "    ma = np.r_[1]\n",
    "\n",
    "    M = arma_generate_sample(ar_M, ma, N, scale=sigma_M)\n",
    "    R = arma_generate_sample(ar_R, ma, N, scale=sigma_R)\n",
    "    \n",
    "    return M+R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "676089e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_Rsq(rho, sigma_M, sigma_R):\n",
    "    '''\n",
    "    Calculate R^2 - proportion of variance attributable to mean reversion\n",
    "    '''    \n",
    "    return (2*sigma_M**2) / (2*sigma_M**2 + (1+rho) * sigma_R**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8d11317",
   "metadata": {},
   "source": [
    "# Estimate parameters using lagged variances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "549ef61a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate a sample\n",
    "N = 2500\n",
    "sigma_M = 1\n",
    "sigma_R = 0.5\n",
    "rho = 0.5\n",
    "\n",
    "np.random.seed(44)\n",
    "X = generate_par(N, rho, sigma_M, sigma_R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7d337278",
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate lagged variances\n",
    "v1 = np.var(X[1:] - X[:-1])\n",
    "v2 = np.var(X[2:] - X[:-2])\n",
    "v3 = np.var(X[3:] - X[:-3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "772d0ef1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5310977377515682"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# rho\n",
    "rho_lv = -(v1 - 2*v2 + v3) / (2*v1 - v2)\n",
    "rho_lv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "72a74052",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0296704460001678"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sigma_M\n",
    "sigma_M_lv = np.sqrt(1/2 * (rho_lv+1) / (rho_lv-1) * (v2 - 2*v1))\n",
    "sigma_M_lv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "bb0ea89d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4254865860508296"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sigma_R\n",
    "sigma_R_lv = np.sqrt(1/2 * (v2 - 2*sigma_M_lv**2))    \n",
    "sigma_R_lv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "278e2803",
   "metadata": {},
   "outputs": [],
   "source": [
    "def lagvar_estimate_par(X):\n",
    "    '''\n",
    "    estimate parameters of partial AR model using lagged variances\n",
    "    '''\n",
    "    \n",
    "    # calculate lagged variances\n",
    "    v1 = np.var(X[1:] - X[:-1])\n",
    "    v2 = np.var(X[2:] - X[:-2])\n",
    "    v3 = np.var(X[3:] - X[:-3])\n",
    "    \n",
    "    # rho\n",
    "    rho_lv = -(v1 - 2*v2 + v3) / (2*v1 - v2)\n",
    "    \n",
    "    # sigma_M\n",
    "    if (rho_lv+1) / (rho_lv-1) * (v2 - 2*v1) > 0:\n",
    "        sigma_M_lv = np.sqrt(1/2 * (rho_lv+1) / (rho_lv-1) * (v2 - 2*v1))\n",
    "    else:\n",
    "        sigma_M_lv = 0\n",
    "        \n",
    "    # sigma_R\n",
    "    if v2 > 2*sigma_M_lv**2:\n",
    "        sigma_R_lv = np.sqrt(1/2 * (v2 - 2*sigma_M_lv**2))\n",
    "    else:\n",
    "        sigma_R_lv = 0\n",
    "    \n",
    "    return rho_lv, sigma_M_lv, sigma_R_lv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0dd0de88",
   "metadata": {},
   "outputs": [],
   "source": [
    "def lagvar_estimate_rw(X):\n",
    "    '''\n",
    "    estimate parameters of randow walk model using lagged variances\n",
    "    '''\n",
    "    \n",
    "    # calculate lagged variances\n",
    "    v1 = np.var(X[1:] - X[:-1])\n",
    "    v2 = np.var(X[2:] - X[:-2])\n",
    "    v3 = np.var(X[3:] - X[:-3])\n",
    "    \n",
    "    # rho\n",
    "    rho_lv = 0\n",
    "    # sigma_M\n",
    "    sigma_M_lv = 0\n",
    "    # sigma_R\n",
    "    sigma_R_lv = np.sqrt(1/2 * (v2 - 2*sigma_M_lv**2))\n",
    "    \n",
    "    return sigma_R_lv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "231483c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def lagvar_estimate_ar(X):\n",
    "    '''\n",
    "    estimate parameters of AR model using lagged variances\n",
    "    '''\n",
    "    \n",
    "    # calculate lagged variances\n",
    "    v1 = np.var(X[1:] - X[:-1])\n",
    "    v2 = np.var(X[2:] - X[:-2])\n",
    "    v3 = np.var(X[3:] - X[:-3])\n",
    "    \n",
    "    # rho\n",
    "    rho_lv = -(v1 - 2*v2 + v3) / (2*v1 - v2)\n",
    "    # sigma_M\n",
    "    if (rho_lv+1) / (rho_lv-1) * (v2 - 2*v1) > 0:\n",
    "        sigma_M_lv = np.sqrt(1/2 * (rho_lv+1) / (rho_lv-1) * (v2 - 2*v1))\n",
    "    else:\n",
    "        sigma_M_lv = 0\n",
    "    \n",
    "    return rho_lv, sigma_M_lv"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88c6a9aa",
   "metadata": {},
   "source": [
    "# Estimating parameters with MLE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "984541b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def kalman_estimate(X, rho, sigma_M, sigma_R):\n",
    "    '''\n",
    "    Calculate estimates of mean-reverting and random walk components\n",
    "    '''\n",
    "    \n",
    "    # create arrays for storing both components and prediction errors\n",
    "    M = np.zeros(len(X))\n",
    "    R = np.zeros(len(X))\n",
    "    eps = np.zeros(len(X))\n",
    "    \n",
    "    # set initial state\n",
    "    if sigma_R==0:\n",
    "        M[0] = X[0]\n",
    "        R[0] = 0\n",
    "    else:\n",
    "        M[0] = 0\n",
    "        R[0] = X[0]\n",
    "    \n",
    "    # calculate Kalman gain    \n",
    "    if sigma_M==0:\n",
    "        K_M = 0\n",
    "        K_R = 1\n",
    "    elif sigma_R==0:\n",
    "        K_M = 1\n",
    "        K_R = 0\n",
    "    else:\n",
    "        sqr = np.sqrt((1+rho)**2 * sigma_R**2 + 4*sigma_M**2)\n",
    "        K_M = 2*sigma_M**2 / (sigma_R * (sqr + rho*sigma_R + sigma_R) + 2*sigma_M**2)\n",
    "        K_R = 2*sigma_R / (sqr - rho*sigma_R + sigma_R)\n",
    "    \n",
    "    # calculate estimates\n",
    "    for i in range(1, len(X)):\n",
    "        xhat = rho * M[i-1] + R[i-1]\n",
    "        eps[i] = X[i] - xhat\n",
    "        M[i] = rho * M[i-1] + eps[i] * K_M\n",
    "        R[i] = R[i-1] + eps[i] * K_R\n",
    "        \n",
    "    return M, R, eps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "a28bcb41",
   "metadata": {},
   "outputs": [],
   "source": [
    "M_est, R_est, eps = kalman_estimate(X, 0.7, 1, 0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "8466ded0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def log_like(X, rho, sigma_M, sigma_R):\n",
    "    '''\n",
    "    Compute log likelihood function\n",
    "    '''\n",
    "    \n",
    "    N = len(X)\n",
    "    _,_,eps = kalman_estimate(X, rho, sigma_M, sigma_R)\n",
    "    ll = -(N-1)/2 * np.log(2*np.pi * (sigma_M**2 + sigma_R**2)) - 1 / (2 * (sigma_M**2 + sigma_R**2)) * np.sum(eps[1:]**2)\n",
    "    \n",
    "    return ll"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "2f4f2a25",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4043.0071158041537"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_like(X, 0.7, 1, 0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "75330c13",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_to_min_par(parameters, X):\n",
    "    rho, sigma_M, sigma_R = parameters\n",
    "    return -log_like(X, rho, sigma_M, sigma_R)\n",
    "\n",
    "def f_to_min_rw(sigma_R, X):\n",
    "    rho = 0\n",
    "    sigma_M = 0 # remove mean-reverting component\n",
    "    return -log_like(X, rho, sigma_M, sigma_R)\n",
    "\n",
    "def f_to_min_ar(parameters, X):\n",
    "    rho, sigma_M = parameters\n",
    "    sigma_R = 0 # remove random walk component\n",
    "    return -log_like(X, rho, sigma_M, sigma_R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "ac57e2a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate a sample\n",
    "N = 250\n",
    "rho = 0.7\n",
    "sigma_M = 1\n",
    "sigma_R = 0.5\n",
    "\n",
    "np.random.seed(11)\n",
    "X = generate_par(N, rho, sigma_M, sigma_R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b68484a6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.456889197696379 0.6919248220826052 0.7965348709773407\n"
     ]
    }
   ],
   "source": [
    "rho_lv, sigma_M_lv, sigma_R_lv = lagvar_estimate_par(X)\n",
    "print(rho_lv, sigma_M_lv, sigma_R_lv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "08f80b50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      fun: 380.9134029123813\n",
       " hess_inv: <3x3 LbfgsInvHessProduct with dtype=float64>\n",
       "      jac: array([-1.81065047, -0.46545665,  3.13200984])\n",
       "  message: 'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH'\n",
       "     nfev: 16\n",
       "      nit: 2\n",
       "     njev: 4\n",
       "   status: 0\n",
       "  success: True\n",
       "        x: array([0.46223886, 0.74599543, 0.83852531])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "minimize(f_to_min_par, (rho_lv, sigma_M_lv, sigma_R_lv), args=(X),\n",
    "         bounds=((-1,1), (0,np.inf), (0,np.inf)), tol=0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "2c699d38",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      fun: 385.28226986727634\n",
       " hess_inv: array([[0.00259537]])\n",
       "      jac: array([0.])\n",
       "  message: 'Optimization terminated successfully.'\n",
       "     nfev: 28\n",
       "      nit: 8\n",
       "     njev: 14\n",
       "   status: 0\n",
       "  success: True\n",
       "        x: array([1.13698476])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "minimize(f_to_min_rw, (sigma_R_lv), args=(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "a095f157",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      fun: 383.23981479329143\n",
       " hess_inv: array([[3.15995463e-04, 1.60756326e-06],\n",
       "       [1.60756326e-06, 2.55424202e-03]])\n",
       "      jac: array([-3.81469727e-06,  0.00000000e+00])\n",
       "  message: 'Optimization terminated successfully.'\n",
       "     nfev: 45\n",
       "      nit: 12\n",
       "     njev: 15\n",
       "   status: 0\n",
       "  success: True\n",
       "        x: array([0.96356424, 1.12769664])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "minimize(f_to_min_ar, (rho_lv, sigma_M_lv), args=(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "42079414",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "\n",
    "def mle_fit(X, mode, tol=0.001):\n",
    "    '''\n",
    "    fit model using MLE\n",
    "    '''\n",
    "    \n",
    "    estimates = []\n",
    "    lls = []\n",
    "    \n",
    "    # distribution for random guesses\n",
    "    rnd_rho = stats.uniform(loc=-1, scale=2)\n",
    "    \n",
    "    if mode=='PAR':\n",
    "        # get initial guesses using lagged variances\n",
    "        x0 = lagvar_estimate_par(X)\n",
    "        # set boundaries\n",
    "        bounds = ((-1,1), (0,np.inf), (0,np.inf))\n",
    "        # function to use in minimization\n",
    "        f_to_min = f_to_min_par\n",
    "        # function to generate random initial values\n",
    "        std = np.std(np.diff(X))\n",
    "        rnd_sigma = stats.norm(loc=std, scale=std/2)\n",
    "        def gen_x0():\n",
    "            return rnd_rho.rvs(), rnd_sigma.rvs(), rnd_sigma.rvs()\n",
    "        \n",
    "    elif mode=='AR':\n",
    "        x0 = lagvar_estimate_ar(X)\n",
    "        bounds = ((-1,1), (0,np.inf))\n",
    "        f_to_min = f_to_min_ar\n",
    "        std = np.std(np.diff(X))\n",
    "        rnd_sigma = stats.norm(loc=std, scale=std/2)\n",
    "        def gen_x0():\n",
    "            return rnd_rho.rvs(), rnd_sigma.rvs()\n",
    "        \n",
    "    elif mode=='RW':\n",
    "        x0 = lagvar_estimate_rw(X)\n",
    "        bounds = ((0,np.inf),)\n",
    "        f_to_min = f_to_min_rw\n",
    "        std = np.std(np.diff(X))\n",
    "        rnd_sigma = stats.norm(loc=std, scale=std/2)\n",
    "        def gen_x0():\n",
    "            return rnd_sigma.rvs()\n",
    "    \n",
    "    # minimize\n",
    "    res = minimize(f_to_min, (x0), args=(X), bounds=bounds, tol=tol)\n",
    "    \n",
    "    if res.success:\n",
    "        estimates.append(res.x)\n",
    "        lls.append(-res.fun) # save log-likelihood\n",
    "    \n",
    "    # repeat minimization with different (random) initial values\n",
    "    n_att = 0\n",
    "    while len(lls)<10 and n_att<100: \n",
    "        n_att += 1\n",
    "        x0 = gen_x0()\n",
    "        res = minimize(f_to_min, (x0), args=(X), bounds=bounds, tol=tol)\n",
    "        if res.success:\n",
    "            estimates.append(res.x)\n",
    "            lls.append(-res.fun) # save log-likelihood\n",
    "    \n",
    "    try:\n",
    "        argmax = np.argmax(lls) # index of the biggest likelihood\n",
    "        return estimates[argmax]\n",
    "    except:\n",
    "        #print('Estimation failed!')\n",
    "        return len(x0)*[np.nan] # return nans"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01f1a523",
   "metadata": {},
   "source": [
    "## PAR mode + PAR sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "f27f6ce4",
   "metadata": {},
   "outputs": [],
   "source": [
    "rho = 0.7\n",
    "sigma_M = 1\n",
    "sigma_R = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "13b525c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8247422680412372"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# proportion of variance attributable to mean reversion\n",
    "(2*sigma_M**2) / (2*sigma_M**2 + (1+rho) * sigma_R**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "2ef3fac1",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [04:54<00:00,  3.40it/s]\n"
     ]
    }
   ],
   "source": [
    "from tqdm import tqdm\n",
    "\n",
    "rhos = []\n",
    "sigmaMs = []\n",
    "sigmaRs = []\n",
    "N_sim = 1000\n",
    "N = 500\n",
    "\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter('ignore')\n",
    "    \n",
    "    for i in tqdm(range(N_sim)):\n",
    "        np.random.seed(i)\n",
    "        sample = generate_par(N, rho, sigma_M, sigma_R)\n",
    "        params = mle_fit(sample, mode='PAR')\n",
    "        rhos.append(params[0])\n",
    "        sigmaMs.append(params[1])\n",
    "        sigmaRs.append(params[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "da19028d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8f9810aaf0>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1296x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 263,
       "width": 1044
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1,ax2,ax3) = plt.subplots(1, 3, figsize=(18,4))\n",
    "ax1.hist(rhos, bins=25, label='Estimates')\n",
    "ax1.set_title('Estimates of rho')\n",
    "ax1.axvline(x=rho, label='True value', c='r')\n",
    "ax1.legend()\n",
    "ax2.hist(sigmaMs, bins=25, label='Estimates')\n",
    "ax2.set_title('Estimates of sigma_M')\n",
    "ax2.axvline(x=sigma_M, label='True value', c='r')\n",
    "ax2.legend()\n",
    "ax3.hist(sigmaRs, bins=25, label='Estimates')\n",
    "ax3.set_title('Estimates of sigma_R')\n",
    "ax3.axvline(x=sigma_R, label='True value', c='r')\n",
    "ax3.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6e11b31",
   "metadata": {},
   "source": [
    "## PAR mode + AR sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "3b36ebc6",
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma_M = 1\n",
    "sigma_R = 0\n",
    "rho = 0.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "3acf1b3c",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [07:01<00:00,  2.37it/s]\n"
     ]
    }
   ],
   "source": [
    "rhos = []\n",
    "sigmaMs = []\n",
    "sigmaRs = []\n",
    "N_sim = 1000\n",
    "N = 500\n",
    "\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter('ignore')\n",
    "    \n",
    "    for i in tqdm(range(N_sim)):\n",
    "        np.random.seed(i)\n",
    "        sample = generate_par(N, rho, sigma_M, sigma_R)\n",
    "        params = mle_fit(sample, mode='PAR')\n",
    "        rhos.append(params[0])\n",
    "        sigmaMs.append(params[1])\n",
    "        sigmaRs.append(params[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "94fa2fdb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8f93f22340>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 263,
       "width": 1044
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1,ax2,ax3) = plt.subplots(1, 3, figsize=(18,4))\n",
    "ax1.hist(rhos, bins=25, label='Estimates')\n",
    "ax1.set_title('Estimates of rho')\n",
    "ax1.axvline(x=rho, label='True value', c='r')\n",
    "ax1.legend()\n",
    "ax2.hist(sigmaMs, bins=25, label='Estimates')\n",
    "ax2.set_title('Estimates of sigma_M')\n",
    "ax2.axvline(x=sigma_M, label='True value', c='r')\n",
    "ax2.legend()\n",
    "ax3.hist(sigmaRs, bins=25, label='Estimates')\n",
    "ax3.set_title('Estimates of sigma_R')\n",
    "ax3.axvline(x=sigma_R, label='True value', c='r')\n",
    "ax3.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fbce53a",
   "metadata": {},
   "source": [
    "## AR mode + AR sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "c52b1d0d",
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma_M = 1\n",
    "sigma_R = 0\n",
    "rho = 0.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "b8c9e8fa",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [04:52<00:00,  3.42it/s]\n"
     ]
    }
   ],
   "source": [
    "rhos = []\n",
    "sigmaMs = []\n",
    "N_sim = 1000\n",
    "N = 500\n",
    "\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter('ignore')\n",
    "    \n",
    "    for i in tqdm(range(N_sim)):\n",
    "        np.random.seed(i)\n",
    "        sample = generate_par(N, rho, sigma_M, sigma_R)\n",
    "        params = mle_fit(sample, mode='AR')\n",
    "        rhos.append(params[0])\n",
    "        sigmaMs.append(params[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "b08814f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8f93d0adf0>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 263,
       "width": 710
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1,ax2) = plt.subplots(1, 2, figsize=(12,4))\n",
    "ax1.hist(rhos, bins=25, label='Estimates')\n",
    "ax1.set_title('Estimates of rho')\n",
    "ax1.axvline(x=rho, label='True value', c='r')\n",
    "ax1.legend()\n",
    "ax2.hist(sigmaMs, bins=25, label='Estimates')\n",
    "ax2.set_title('Estimates of sigma_M')\n",
    "ax2.axvline(x=sigma_M, label='True value', c='r')\n",
    "ax2.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8e5c845",
   "metadata": {},
   "source": [
    "## RW mode + RW sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "4a345405",
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma_M = 0\n",
    "sigma_R = 1\n",
    "rho = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "c5a9a127",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [02:09<00:00,  7.71it/s]\n"
     ]
    }
   ],
   "source": [
    "sigmaRs = []\n",
    "N_sim = 1000\n",
    "N = 500\n",
    "\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter('ignore')\n",
    "    \n",
    "    for i in tqdm(range(N_sim)):\n",
    "        np.random.seed(i)\n",
    "        sample = generate_par(N, rho, sigma_M, sigma_R)\n",
    "        params = mle_fit(sample, mode='RW')\n",
    "        sigmaRs.append(params[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "1b2476f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8f93bc33d0>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 375
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(sigmaRs, bins=25, label='Estimates')\n",
    "plt.axvline(x=sigma_R, label='True value', c='r')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe005e96",
   "metadata": {},
   "source": [
    "# Likelihood ratio test\n",
    "\n",
    "## RW samples + RW null"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "e6c38f20",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [28:50<00:00,  1.73s/it]\n"
     ]
    }
   ],
   "source": [
    "rho = 0\n",
    "sigma_M = 0\n",
    "sigma_R = 1\n",
    "\n",
    "n_sim = 1000\n",
    "n_samples = 2500\n",
    "\n",
    "lambdas = []\n",
    "\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter('ignore')\n",
    "    \n",
    "    for i in tqdm(range(n_sim)):\n",
    "        np.random.seed(i)\n",
    "        sample = generate_par(n_samples, rho, sigma_M, sigma_R)\n",
    "\n",
    "        # log likelihood of RW\n",
    "        sigmaR_rw = mle_fit(sample, mode='RW')\n",
    "        ll_rw = log_like(sample, 0, 0, sigmaR_rw)\n",
    "\n",
    "        # log likelihood of PAR\n",
    "        rho_par, sigmaM_par, sigmaR_par = mle_fit(sample, mode='PAR')\n",
    "        ll_par = log_like(sample, rho_par, sigmaM_par, sigmaR_par)\n",
    "\n",
    "        lambdas.append(ll_rw - ll_par)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "75a2f189",
   "metadata": {},
   "outputs": [],
   "source": [
    "lambdas = np.array(lambdas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "31c402f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.6355796 , -2.37553225, -1.73262375])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.quantile(lambdas, [0.01, 0.05, 0.1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "1200a301",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  2.,   2.,   3.,   0.,   3.,   1.,   7.,   6.,  11.,  10.,  11.,\n",
       "         18.,  28.,  24.,  22.,  50.,  68.,  98., 133., 483.,  11.,   5.,\n",
       "          3.,   0.,   1.]),\n",
       " array([-5.12189218, -4.85870898, -4.59552578, -4.33234259, -4.06915939,\n",
       "        -3.8059762 , -3.542793  , -3.2796098 , -3.01642661, -2.75324341,\n",
       "        -2.49006022, -2.22687702, -1.96369382, -1.70051063, -1.43732743,\n",
       "        -1.17414424, -0.91096104, -0.64777785, -0.38459465, -0.12141145,\n",
       "         0.14177174,  0.40495494,  0.66813813,  0.93132133,  1.19450453,\n",
       "         1.45768772]),\n",
       " <BarContainer object of 25 artists>)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 249,
       "width": 375
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(lambdas, bins=25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "75568ef9",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.03885328, -2.73686515, -1.99006283])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.quantile(lambdas[lambdas<0], [0.01, 0.05, 0.1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4693275",
   "metadata": {},
   "source": [
    "# PAR with real data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "f3f7b3ba",
   "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>IEX</th>\n",
       "      <th>NUAN</th>\n",
       "      <th>MOH</th>\n",
       "      <th>NVAX</th>\n",
       "      <th>SBNY</th>\n",
       "      <th>PWR</th>\n",
       "      <th>WSM</th>\n",
       "      <th>FANG</th>\n",
       "      <th>BRO</th>\n",
       "      <th>STLD</th>\n",
       "      <th>...</th>\n",
       "      <th>RES</th>\n",
       "      <th>LE</th>\n",
       "      <th>APEI</th>\n",
       "      <th>FF</th>\n",
       "      <th>WK</th>\n",
       "      <th>PKI</th>\n",
       "      <th>ALGT</th>\n",
       "      <th>SAGE</th>\n",
       "      <th>OII</th>\n",
       "      <th>DRQ</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2002-01-02</th>\n",
       "      <td>11.232835</td>\n",
       "      <td>3.852814</td>\n",
       "      <td>NaN</td>\n",
       "      <td>272.4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.865090</td>\n",
       "      <td>14.170295</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.453000</td>\n",
       "      <td>1.985875</td>\n",
       "      <td>...</td>\n",
       "      <td>1.702178</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>28.196012</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.741946</td>\n",
       "      <td>11.250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002-01-03</th>\n",
       "      <td>11.397299</td>\n",
       "      <td>4.017316</td>\n",
       "      <td>NaN</td>\n",
       "      <td>266.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.489702</td>\n",
       "      <td>14.335989</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.505086</td>\n",
       "      <td>1.968888</td>\n",
       "      <td>...</td>\n",
       "      <td>1.726847</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>28.872910</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.810350</td>\n",
       "      <td>11.220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002-01-04</th>\n",
       "      <td>11.420323</td>\n",
       "      <td>4.329004</td>\n",
       "      <td>NaN</td>\n",
       "      <td>263.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.628003</td>\n",
       "      <td>14.525847</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.639308</td>\n",
       "      <td>1.999466</td>\n",
       "      <td>...</td>\n",
       "      <td>1.717966</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>29.187184</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.843449</td>\n",
       "      <td>11.095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002-01-07</th>\n",
       "      <td>11.364406</td>\n",
       "      <td>4.458874</td>\n",
       "      <td>NaN</td>\n",
       "      <td>263.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.786061</td>\n",
       "      <td>14.553462</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.450997</td>\n",
       "      <td>2.038538</td>\n",
       "      <td>...</td>\n",
       "      <td>1.697244</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>28.244362</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.836829</td>\n",
       "      <td>11.600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002-01-08</th>\n",
       "      <td>11.486109</td>\n",
       "      <td>4.701299</td>\n",
       "      <td>NaN</td>\n",
       "      <td>264.8</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.282250</td>\n",
       "      <td>14.646665</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.298745</td>\n",
       "      <td>2.106489</td>\n",
       "      <td>...</td>\n",
       "      <td>1.726847</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>28.204070</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.841242</td>\n",
       "      <td>11.550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-24</th>\n",
       "      <td>65.672753</td>\n",
       "      <td>13.281385</td>\n",
       "      <td>33.51</td>\n",
       "      <td>101.6</td>\n",
       "      <td>101.676034</td>\n",
       "      <td>30.781831</td>\n",
       "      <td>47.746814</td>\n",
       "      <td>48.685599</td>\n",
       "      <td>14.144676</td>\n",
       "      <td>15.915873</td>\n",
       "      <td>...</td>\n",
       "      <td>16.556145</td>\n",
       "      <td>NaN</td>\n",
       "      <td>45.01</td>\n",
       "      <td>7.194574</td>\n",
       "      <td>NaN</td>\n",
       "      <td>39.724403</td>\n",
       "      <td>95.280130</td>\n",
       "      <td>NaN</td>\n",
       "      <td>71.823160</td>\n",
       "      <td>110.660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-26</th>\n",
       "      <td>66.103865</td>\n",
       "      <td>13.090909</td>\n",
       "      <td>33.12</td>\n",
       "      <td>102.6</td>\n",
       "      <td>101.638345</td>\n",
       "      <td>30.910253</td>\n",
       "      <td>47.877896</td>\n",
       "      <td>49.350089</td>\n",
       "      <td>14.057871</td>\n",
       "      <td>15.899431</td>\n",
       "      <td>...</td>\n",
       "      <td>16.464421</td>\n",
       "      <td>NaN</td>\n",
       "      <td>44.30</td>\n",
       "      <td>7.140138</td>\n",
       "      <td>NaN</td>\n",
       "      <td>39.685760</td>\n",
       "      <td>96.335122</td>\n",
       "      <td>NaN</td>\n",
       "      <td>71.695100</td>\n",
       "      <td>110.910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-27</th>\n",
       "      <td>66.032013</td>\n",
       "      <td>12.926407</td>\n",
       "      <td>33.21</td>\n",
       "      <td>102.6</td>\n",
       "      <td>101.421632</td>\n",
       "      <td>30.949767</td>\n",
       "      <td>47.886089</td>\n",
       "      <td>49.920989</td>\n",
       "      <td>14.117264</td>\n",
       "      <td>16.285818</td>\n",
       "      <td>...</td>\n",
       "      <td>16.565318</td>\n",
       "      <td>NaN</td>\n",
       "      <td>43.52</td>\n",
       "      <td>7.180965</td>\n",
       "      <td>NaN</td>\n",
       "      <td>39.782366</td>\n",
       "      <td>93.179086</td>\n",
       "      <td>NaN</td>\n",
       "      <td>71.768277</td>\n",
       "      <td>111.110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-30</th>\n",
       "      <td>65.933217</td>\n",
       "      <td>12.995671</td>\n",
       "      <td>33.98</td>\n",
       "      <td>103.2</td>\n",
       "      <td>100.884561</td>\n",
       "      <td>30.831224</td>\n",
       "      <td>48.213795</td>\n",
       "      <td>48.601368</td>\n",
       "      <td>14.194931</td>\n",
       "      <td>16.046078</td>\n",
       "      <td>...</td>\n",
       "      <td>16.519456</td>\n",
       "      <td>NaN</td>\n",
       "      <td>43.07</td>\n",
       "      <td>7.149211</td>\n",
       "      <td>NaN</td>\n",
       "      <td>39.946597</td>\n",
       "      <td>94.108909</td>\n",
       "      <td>NaN</td>\n",
       "      <td>71.685953</td>\n",
       "      <td>109.420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-31</th>\n",
       "      <td>66.328403</td>\n",
       "      <td>13.160173</td>\n",
       "      <td>34.75</td>\n",
       "      <td>102.4</td>\n",
       "      <td>101.214341</td>\n",
       "      <td>31.176976</td>\n",
       "      <td>47.746814</td>\n",
       "      <td>49.492346</td>\n",
       "      <td>14.341130</td>\n",
       "      <td>16.153548</td>\n",
       "      <td>...</td>\n",
       "      <td>16.372698</td>\n",
       "      <td>NaN</td>\n",
       "      <td>43.47</td>\n",
       "      <td>7.167356</td>\n",
       "      <td>NaN</td>\n",
       "      <td>39.830669</td>\n",
       "      <td>94.269841</td>\n",
       "      <td>NaN</td>\n",
       "      <td>72.152456</td>\n",
       "      <td>109.930</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3021 rows × 727 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  IEX       NUAN    MOH   NVAX        SBNY        PWR  \\\n",
       "2002-01-02  11.232835   3.852814    NaN  272.4         NaN  15.865090   \n",
       "2002-01-03  11.397299   4.017316    NaN  266.0         NaN  15.489702   \n",
       "2002-01-04  11.420323   4.329004    NaN  263.0         NaN  15.628003   \n",
       "2002-01-07  11.364406   4.458874    NaN  263.0         NaN  15.786061   \n",
       "2002-01-08  11.486109   4.701299    NaN  264.8         NaN  15.282250   \n",
       "...               ...        ...    ...    ...         ...        ...   \n",
       "2013-12-24  65.672753  13.281385  33.51  101.6  101.676034  30.781831   \n",
       "2013-12-26  66.103865  13.090909  33.12  102.6  101.638345  30.910253   \n",
       "2013-12-27  66.032013  12.926407  33.21  102.6  101.421632  30.949767   \n",
       "2013-12-30  65.933217  12.995671  33.98  103.2  100.884561  30.831224   \n",
       "2013-12-31  66.328403  13.160173  34.75  102.4  101.214341  31.176976   \n",
       "\n",
       "                  WSM       FANG        BRO       STLD  ...        RES  LE  \\\n",
       "2002-01-02  14.170295        NaN   5.453000   1.985875  ...   1.702178 NaN   \n",
       "2002-01-03  14.335989        NaN   5.505086   1.968888  ...   1.726847 NaN   \n",
       "2002-01-04  14.525847        NaN   5.639308   1.999466  ...   1.717966 NaN   \n",
       "2002-01-07  14.553462        NaN   5.450997   2.038538  ...   1.697244 NaN   \n",
       "2002-01-08  14.646665        NaN   5.298745   2.106489  ...   1.726847 NaN   \n",
       "...               ...        ...        ...        ...  ...        ...  ..   \n",
       "2013-12-24  47.746814  48.685599  14.144676  15.915873  ...  16.556145 NaN   \n",
       "2013-12-26  47.877896  49.350089  14.057871  15.899431  ...  16.464421 NaN   \n",
       "2013-12-27  47.886089  49.920989  14.117264  16.285818  ...  16.565318 NaN   \n",
       "2013-12-30  48.213795  48.601368  14.194931  16.046078  ...  16.519456 NaN   \n",
       "2013-12-31  47.746814  49.492346  14.341130  16.153548  ...  16.372698 NaN   \n",
       "\n",
       "             APEI        FF  WK        PKI       ALGT  SAGE        OII  \\\n",
       "2002-01-02    NaN       NaN NaN  28.196012        NaN   NaN   4.741946   \n",
       "2002-01-03    NaN       NaN NaN  28.872910        NaN   NaN   4.810350   \n",
       "2002-01-04    NaN       NaN NaN  29.187184        NaN   NaN   4.843449   \n",
       "2002-01-07    NaN       NaN NaN  28.244362        NaN   NaN   4.836829   \n",
       "2002-01-08    NaN       NaN NaN  28.204070        NaN   NaN   4.841242   \n",
       "...           ...       ...  ..        ...        ...   ...        ...   \n",
       "2013-12-24  45.01  7.194574 NaN  39.724403  95.280130   NaN  71.823160   \n",
       "2013-12-26  44.30  7.140138 NaN  39.685760  96.335122   NaN  71.695100   \n",
       "2013-12-27  43.52  7.180965 NaN  39.782366  93.179086   NaN  71.768277   \n",
       "2013-12-30  43.07  7.149211 NaN  39.946597  94.108909   NaN  71.685953   \n",
       "2013-12-31  43.47  7.167356 NaN  39.830669  94.269841   NaN  72.152456   \n",
       "\n",
       "                DRQ  \n",
       "2002-01-02   11.250  \n",
       "2002-01-03   11.220  \n",
       "2002-01-04   11.095  \n",
       "2002-01-07   11.600  \n",
       "2002-01-08   11.550  \n",
       "...             ...  \n",
       "2013-12-24  110.660  \n",
       "2013-12-26  110.910  \n",
       "2013-12-27  111.110  \n",
       "2013-12-30  109.420  \n",
       "2013-12-31  109.930  \n",
       "\n",
       "[3021 rows x 727 columns]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('vbr0214.csv', index_col=0)\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddedfcd8",
   "metadata": {},
   "source": [
    "## Prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "af6b68f4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing years 2002-2003\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 465/465 [26:01<00:00,  3.36s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing years 2004-2005\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 495/495 [23:42<00:00,  2.87s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing years 2006-2007\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 525/525 [20:27<00:00,  2.34s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing years 2008-2009\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 575/575 [21:07<00:00,  2.20s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing years 2010-2011\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 596/596 [23:33<00:00,  2.37s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing years 2012-2013\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  3%|▎         | 19/628 [00:46<31:27,  3.10s/it]"
     ]
    }
   ],
   "source": [
    "start_years = [2002, 2004, 2006, 2008, 2010, 2012]\n",
    "columns = ['AIC_AR', 'AIC_RW', 'AIC_PAR', 'rho', 'sigma_M', 'sigma_R', '$R^2_{MR}$']\n",
    "results = {}\n",
    "\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter('ignore')\n",
    "    \n",
    "    for sy in start_years:\n",
    "        print(f'Processing years {sy}-{sy+1}')\n",
    "        data_tmp = data.loc[f'{sy}-01-01':f'{sy+2}-01-01']\n",
    "        data_tmp = data_tmp.dropna(axis=1)\n",
    "        results_df = pd.DataFrame(columns=columns, index=data_tmp.columns)\n",
    "\n",
    "        for s in tqdm(data_tmp.columns):\n",
    "            X = data_tmp[s].values\n",
    "\n",
    "            # fit PAR\n",
    "            rho_par, sigmaM_par, sigmaR_par = mle_fit(X, mode='PAR')\n",
    "            ll_par = log_like(X, rho_par, sigmaM_par, sigmaR_par)\n",
    "            aic_par = 2*3 - 2*ll_par\n",
    "\n",
    "            # fit AR\n",
    "            rho_ar, sigmaM_ar = mle_fit(X, mode='AR')\n",
    "            ll_ar = log_like(X, rho_ar, sigmaM_ar, 0)\n",
    "            aic_ar = 2*2 - 2*ll_ar\n",
    "\n",
    "            # fit RW\n",
    "            sigmaR_rw = mle_fit(X, mode='RW')\n",
    "            ll_rw = log_like(X, 0, 0, sigmaR_rw)\n",
    "            aic_rw = 2*1 - 2*ll_rw\n",
    "\n",
    "            # calculate R^2\n",
    "            r_sq = calculate_Rsq(rho_par, sigmaM_par, sigmaR_par)\n",
    "\n",
    "            results_df.loc[s] = [aic_ar, aic_rw, aic_par, rho_par, sigmaM_par, sigmaR_par, r_sq]\n",
    "\n",
    "        results[sy] = results_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "7e10970b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>N</th>\n",
       "      <th>P_ar</th>\n",
       "      <th>P_rw</th>\n",
       "      <th>P_par</th>\n",
       "      <th>$\\overline{\\rho}$</th>\n",
       "      <th>$\\overline{R}^2_{MR}$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2002-2003</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004-2005</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-2007</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-2009</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-2011</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-2013</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             N P_ar P_rw P_par $\\overline{\\rho}$ $\\overline{R}^2_{MR}$\n",
       "2002-2003  NaN  NaN  NaN   NaN               NaN                   NaN\n",
       "2004-2005  NaN  NaN  NaN   NaN               NaN                   NaN\n",
       "2006-2007  NaN  NaN  NaN   NaN               NaN                   NaN\n",
       "2008-2009  NaN  NaN  NaN   NaN               NaN                   NaN\n",
       "2010-2011  NaN  NaN  NaN   NaN               NaN                   NaN\n",
       "2012-2013  NaN  NaN  NaN   NaN               NaN                   NaN"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_ind = ['2002-2003', '2004-2005', '2006-2007', '2008-2009', '2010-2011', '2012-2013']\n",
    "sum_col = ['N', 'P_ar', 'P_rw', 'P_par', '$\\overline{\\rho}$', '$\\overline{R}^2_{MR}$']\n",
    "sum_df = pd.DataFrame(index=sum_ind, columns=sum_col)\n",
    "sum_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "5f7a695c",
   "metadata": {},
   "outputs": [],
   "source": [
    "for sy in start_years:\n",
    "    res = results[sy]\n",
    "    N = len(res)\n",
    "    cond_ar = (res['AIC_AR'] == res[['AIC_AR', 'AIC_RW', 'AIC_PAR']].min(axis=1))\n",
    "    cond_rw = (res['AIC_RW'] == res[['AIC_AR', 'AIC_RW', 'AIC_PAR']].min(axis=1))\n",
    "    cond_par = (res['AIC_PAR'] == res[['AIC_AR', 'AIC_RW', 'AIC_PAR']].min(axis=1))\n",
    "    P_ar = len(res[cond_ar]) / N\n",
    "    P_rw = len(res[cond_rw]) / N\n",
    "    P_par = len(res[cond_par]) / N\n",
    "    rho_bar = res[cond_par]['rho'].mean()\n",
    "    rsq_bar = res[cond_par]['$R^2_{MR}$'].mean()\n",
    "    sum_df.loc[f'{sy}-{sy+1}'] = [N, P_ar, P_rw, P_par, rho_bar, rsq_bar]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "472ca3b6",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "    .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>N</th>\n",
       "      <th>P_ar</th>\n",
       "      <th>P_rw</th>\n",
       "      <th>P_par</th>\n",
       "      <th>$\\overline{\\rho}$</th>\n",
       "      <th>$\\overline{R}^2_{MR}$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2002-2003</th>\n",
       "      <td>465</td>\n",
       "      <td>0.027957</td>\n",
       "      <td>0.584946</td>\n",
       "      <td>0.387097</td>\n",
       "      <td>0.065974</td>\n",
       "      <td>0.37766</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004-2005</th>\n",
       "      <td>495</td>\n",
       "      <td>0.028283</td>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.305051</td>\n",
       "      <td>0.136103</td>\n",
       "      <td>0.368734</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-2007</th>\n",
       "      <td>525</td>\n",
       "      <td>0.028571</td>\n",
       "      <td>0.592381</td>\n",
       "      <td>0.379048</td>\n",
       "      <td>0.464074</td>\n",
       "      <td>0.504158</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-2009</th>\n",
       "      <td>575</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.41913</td>\n",
       "      <td>0.46087</td>\n",
       "      <td>0.201295</td>\n",
       "      <td>0.422426</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-2011</th>\n",
       "      <td>596</td>\n",
       "      <td>0.010067</td>\n",
       "      <td>0.528523</td>\n",
       "      <td>0.461409</td>\n",
       "      <td>-0.129947</td>\n",
       "      <td>0.303954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-2013</th>\n",
       "      <td>628</td>\n",
       "      <td>0.004777</td>\n",
       "      <td>0.845541</td>\n",
       "      <td>0.149682</td>\n",
       "      <td>-0.021865</td>\n",
       "      <td>0.301145</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             N      P_ar      P_rw     P_par $\\overline{\\rho}$  \\\n",
       "2002-2003  465  0.027957  0.584946  0.387097          0.065974   \n",
       "2004-2005  495  0.028283  0.666667  0.305051          0.136103   \n",
       "2006-2007  525  0.028571  0.592381  0.379048          0.464074   \n",
       "2008-2009  575      0.12   0.41913   0.46087          0.201295   \n",
       "2010-2011  596  0.010067  0.528523  0.461409         -0.129947   \n",
       "2012-2013  628  0.004777  0.845541  0.149682         -0.021865   \n",
       "\n",
       "          $\\overline{R}^2_{MR}$  \n",
       "2002-2003               0.37766  \n",
       "2004-2005              0.368734  \n",
       "2006-2007              0.504158  \n",
       "2008-2009              0.422426  \n",
       "2010-2011              0.303954  \n",
       "2012-2013              0.301145  "
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "7c59056b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "N                        547.333333\n",
       "P_ar                       0.036609\n",
       "P_rw                       0.606198\n",
       "P_par                      0.357193\n",
       "$\\overline{\\rho}$          0.119272\n",
       "$\\overline{R}^2_{MR}$      0.379680\n",
       "dtype: float64"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_df.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "714641b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "per_col = ['$N$', '$A_{t}$', '$A_{t-1}$', '$A_{t}|A_{t-1}$', '$p_t$', '$p_{t|t-1}$']\n",
    "per_ind = sum_ind[1:]\n",
    "\n",
    "per_df = pd.DataFrame(index=per_ind, columns=per_col)\n",
    "\n",
    "for i in range(1,len(start_years)):\n",
    "    cur_res = results[start_years[i]]\n",
    "    prev_res = results[start_years[i-1]]\n",
    "    N = len(cur_res)\n",
    "    \n",
    "    # calculate A_t\n",
    "    cond = (cur_res['AIC_PAR'] == cur_res[['AIC_AR', 'AIC_RW', 'AIC_PAR']].min(axis=1))\n",
    "    cur_symbols = cur_res[cond].index # stocks that are PAR in current period\n",
    "    at0 = len(cur_symbols)\n",
    "    \n",
    "    # calculaye A_{t-1}\n",
    "    cond = (prev_res['AIC_PAR'] == prev_res[['AIC_AR', 'AIC_RW', 'AIC_PAR']].min(axis=1))\n",
    "    prev_symbols = prev_res[cond].index # stocks that are PAR in previous period\n",
    "    at1 = len(prev_symbols)\n",
    "    \n",
    "    # calculate A_{t}|A_{t-1}\n",
    "    symbols_is = set(cur_symbols).intersection(set(prev_symbols))\n",
    "    at_is = len(symbols_is)\n",
    "    \n",
    "    p0 = at0 / N\n",
    "    p1 = at_is / at1\n",
    "    \n",
    "    sy = start_years[i]\n",
    "    per_df.loc[f'{sy}-{sy+1}'] = [N, at0, at1, at_is, p0, p1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "f498791e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           $N$ $A_{t}$ $A_{t-1}$ $A_{t}|A_{t-1}$     $p_t$ $p_{t|t-1}$\n",
      "2004-2005  495     151       180              88  0.305051    0.488889\n",
      "2006-2007  525     199       151              92  0.379048    0.609272\n",
      "2008-2009  575     265       199             133   0.46087    0.668342\n",
      "2010-2011  596     275       265             170  0.461409    0.641509\n",
      "2012-2013  628      94       275              60  0.149682    0.218182\n"
     ]
    }
   ],
   "source": [
    "print(per_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0eae275a",
   "metadata": {},
   "source": [
    "## Log prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "1924bb68",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing years 2002-2003\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 465/465 [40:05<00:00,  5.17s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing years 2004-2005\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 495/495 [45:25<00:00,  5.51s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing years 2006-2007\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 525/525 [48:40<00:00,  5.56s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing years 2008-2009\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 575/575 [48:50<00:00,  5.10s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing years 2010-2011\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 596/596 [54:07<00:00,  5.45s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing years 2012-2013\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 628/628 [58:49<00:00,  5.62s/it]\n"
     ]
    }
   ],
   "source": [
    "results_log = {}\n",
    "\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter('ignore')\n",
    "    \n",
    "    for sy in start_years:\n",
    "        print(f'Processing years {sy}-{sy+1}')\n",
    "        data_tmp = data.loc[f'{sy}-01-01':f'{sy+2}-01-01']\n",
    "        data_tmp = data_tmp.dropna(axis=1)\n",
    "        results_df = pd.DataFrame(columns=columns, index=data_tmp.columns)\n",
    "\n",
    "        for s in tqdm(data_tmp.columns):\n",
    "            X = np.log(data_tmp[s].values)\n",
    "\n",
    "            # fit PAR\n",
    "            rho_par, sigmaM_par, sigmaR_par = mle_fit(X, mode='PAR')\n",
    "            ll_par = log_like(X, rho_par, sigmaM_par, sigmaR_par)\n",
    "            aic_par = 2*3 - 2*ll_par\n",
    "\n",
    "            # fit AR\n",
    "            rho_ar, sigmaM_ar = mle_fit(X, mode='AR')\n",
    "            ll_ar = log_like(X, rho_ar, sigmaM_ar, 0)\n",
    "            aic_ar = 2*2 - 2*ll_ar\n",
    "\n",
    "            # fit RW\n",
    "            sigmaR_rw = mle_fit(X, mode='RW')\n",
    "            ll_rw = log_like(X, 0, 0, sigmaR_rw)\n",
    "            aic_rw = 2*1 - 2*ll_rw\n",
    "\n",
    "            # calculate R^2\n",
    "            r_sq = calculate_Rsq(rho_par, sigmaM_par, sigmaR_par)\n",
    "\n",
    "            results_df.loc[s] = [aic_ar, aic_rw, aic_par, rho_par, sigmaM_par, sigmaR_par, r_sq]\n",
    "\n",
    "        results_log[sy] = results_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "aa813249",
   "metadata": {},
   "outputs": [],
   "source": [
    "logsum_df = pd.DataFrame(index=sum_ind, columns=sum_col)\n",
    "logsum_df\n",
    "\n",
    "for sy in start_years:\n",
    "    res = results_log[sy]\n",
    "    N = len(res)\n",
    "    cond_ar = (res['AIC_AR'] == res[['AIC_AR', 'AIC_RW', 'AIC_PAR']].min(axis=1))\n",
    "    cond_rw = (res['AIC_RW'] == res[['AIC_AR', 'AIC_RW', 'AIC_PAR']].min(axis=1))\n",
    "    cond_par = (res['AIC_PAR'] == res[['AIC_AR', 'AIC_RW', 'AIC_PAR']].min(axis=1))\n",
    "    P_ar = len(res[cond_ar]) / N\n",
    "    P_rw = len(res[cond_rw]) / N\n",
    "    P_par = len(res[cond_par]) / N\n",
    "    rho_bar = res[cond_par]['rho'].mean()\n",
    "    rsq_bar = res[cond_par]['$R^2_{MR}$'].mean()\n",
    "    logsum_df.loc[f'{sy}-{sy+1}'] = [N, P_ar, P_rw, P_par, rho_bar, rsq_bar]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "33df1884",
   "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>N</th>\n",
       "      <th>P_ar</th>\n",
       "      <th>P_rw</th>\n",
       "      <th>P_par</th>\n",
       "      <th>$\\overline{\\rho}$</th>\n",
       "      <th>$\\overline{R}^2_{MR}$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2002-2003</th>\n",
       "      <td>465</td>\n",
       "      <td>0.015054</td>\n",
       "      <td>0.604301</td>\n",
       "      <td>0.380645</td>\n",
       "      <td>-0.056082</td>\n",
       "      <td>0.343914</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004-2005</th>\n",
       "      <td>495</td>\n",
       "      <td>0.012121</td>\n",
       "      <td>0.715152</td>\n",
       "      <td>0.272727</td>\n",
       "      <td>0.124042</td>\n",
       "      <td>0.37866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-2007</th>\n",
       "      <td>525</td>\n",
       "      <td>0.011429</td>\n",
       "      <td>0.659048</td>\n",
       "      <td>0.329524</td>\n",
       "      <td>0.41393</td>\n",
       "      <td>0.457518</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-2009</th>\n",
       "      <td>575</td>\n",
       "      <td>0.010435</td>\n",
       "      <td>0.546087</td>\n",
       "      <td>0.443478</td>\n",
       "      <td>0.189164</td>\n",
       "      <td>0.412758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-2011</th>\n",
       "      <td>596</td>\n",
       "      <td>0.006711</td>\n",
       "      <td>0.543624</td>\n",
       "      <td>0.449664</td>\n",
       "      <td>-0.192785</td>\n",
       "      <td>0.277766</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-2013</th>\n",
       "      <td>628</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.866242</td>\n",
       "      <td>0.133758</td>\n",
       "      <td>0.05412</td>\n",
       "      <td>0.311417</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             N      P_ar      P_rw     P_par $\\overline{\\rho}$  \\\n",
       "2002-2003  465  0.015054  0.604301  0.380645         -0.056082   \n",
       "2004-2005  495  0.012121  0.715152  0.272727          0.124042   \n",
       "2006-2007  525  0.011429  0.659048  0.329524           0.41393   \n",
       "2008-2009  575  0.010435  0.546087  0.443478          0.189164   \n",
       "2010-2011  596  0.006711  0.543624  0.449664         -0.192785   \n",
       "2012-2013  628       0.0  0.866242  0.133758           0.05412   \n",
       "\n",
       "          $\\overline{R}^2_{MR}$  \n",
       "2002-2003              0.343914  \n",
       "2004-2005               0.37866  \n",
       "2006-2007              0.457518  \n",
       "2008-2009              0.412758  \n",
       "2010-2011              0.277766  \n",
       "2012-2013              0.311417  "
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logsum_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "ec3affae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "N                        547.333333\n",
       "P_ar                       0.009292\n",
       "P_rw                       0.655742\n",
       "P_par                      0.334966\n",
       "$\\overline{\\rho}$          0.088731\n",
       "$\\overline{R}^2_{MR}$      0.363672\n",
       "dtype: float64"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logsum_df.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "d4ffc6a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "logper_col = ['$N$', '$A_{t}$', '$A_{t-1}$', '$A_{t}|A_{t-1}$', '$p_t$', '$p_{t|t-1}$']\n",
    "logper_ind = sum_ind[1:]\n",
    "\n",
    "logper_df = pd.DataFrame(index=per_ind, columns=per_col)\n",
    "\n",
    "for i in range(1,len(start_years)):\n",
    "    cur_res = results_log[start_years[i]]\n",
    "    prev_res = results_log[start_years[i-1]]\n",
    "    N = len(cur_res)\n",
    "    \n",
    "    # calculate A_t\n",
    "    cond = (cur_res['AIC_PAR'] == cur_res[['AIC_AR', 'AIC_RW', 'AIC_PAR']].min(axis=1))\n",
    "    cur_symbols = cur_res[cond].index # stocks that are PAR in current period\n",
    "    at0 = len(cur_symbols)\n",
    "    \n",
    "    # calculaye A_{t-1}\n",
    "    cond = (prev_res['AIC_PAR'] == prev_res[['AIC_AR', 'AIC_RW', 'AIC_PAR']].min(axis=1))\n",
    "    prev_symbols = prev_res[cond].index # stocks that are PAR in previous period\n",
    "    at1 = len(prev_symbols)\n",
    "    \n",
    "    # calculate A_{t}|A_{t-1}\n",
    "    symbols_is = set(cur_symbols).intersection(set(prev_symbols))\n",
    "    at_is = len(symbols_is)\n",
    "    \n",
    "    p0 = at0 / N\n",
    "    p1 = at_is / at1\n",
    "    \n",
    "    sy = start_years[i]\n",
    "    logper_df.loc[f'{sy}-{sy+1}'] = [N, at0, at1, at_is, p0, p1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "77a96acc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           $N$ $A_{t}$ $A_{t-1}$ $A_{t}|A_{t-1}$     $p_t$ $p_{t|t-1}$\n",
      "2004-2005  495     135       177              81  0.272727    0.457627\n",
      "2006-2007  525     173       135              82  0.329524    0.607407\n",
      "2008-2009  575     255       173             114  0.443478     0.65896\n",
      "2010-2011  596     268       255             170  0.449664    0.666667\n",
      "2012-2013  628      84       268              54  0.133758    0.201493\n"
     ]
    }
   ],
   "source": [
    "print(logper_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3f0735a1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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