FERM534 Assignment II.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ca59b836-c2fd-4cd8-a180-9bc5aeae87cb",
   "metadata": {},
   "source": [
    "# FERM534 Project II - Emir Eğilli"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "25eab9c6-2d82-4658-8457-3ac7d19a81ff",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\emir.e\\Anaconda3\\lib\\site-packages\\scipy\\__init__.py:177: UserWarning: A NumPy version >=1.18.5 and <1.26.0 is required for this version of SciPy (detected version 1.26.3\n",
      "  warnings.warn(f\"A NumPy version >={np_minversion} and <{np_maxversion}\"\n"
     ]
    }
   ],
   "source": [
    "import yfinance as yf\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "from statsmodels.tsa.stattools import adfuller\n",
    "from statsmodels.stats.diagnostic import acorr_ljungbox\n",
    "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf\n",
    "from arch import *\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7f46eb29-9ed4-44cb-86fd-7a8547667521",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n"
     ]
    }
   ],
   "source": [
    "AMZN = yf.download(\"AMZN\", start='2018-01-05', end='2024-01-05')['Adj Close']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "65ad5cd3-967d-4135-a8ae-c29878f4a1f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "rAMZN=(np.log(AMZN).diff().dropna())*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a6beab08-17c2-4f8e-9e99-3460c5cbec75",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(rAMZN)\n",
    "plt.xlabel('Year')\n",
    "plt.ylabel('Log Returns')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6ced64e2-22cc-480c-be9a-9c3b7c83639b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9882725926237924 0.3231778088806889\n"
     ]
    }
   ],
   "source": [
    "t_statistic, p_value = stats.ttest_1samp(rAMZN, 0)   # t-test for the mean. test value=0\n",
    "print(t_statistic , p_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3282c7b-afa4-495b-aa7e-02e8e854731a",
   "metadata": {},
   "source": [
    "#### Applying t-test for mean H0 shows statistical insignificance (0.32 > 0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66a41469-7599-4a73-adb9-60f954638a48",
   "metadata": {},
   "source": [
    "## Q1-) Show that there are ARCH effects in the data (AMAZON log-returns). Comment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ece8d2fa-bc53-4ac8-b4c1-0e805b6959b2",
   "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>lb_stat</th>\n",
       "      <th>lb_pvalue</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>17.510035</td>\n",
       "      <td>0.063813</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      lb_stat  lb_pvalue\n",
       "10  17.510035   0.063813"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acorr_ljungbox(rAMZN, lags=[10]) # Checked up to 10 lags"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3788a331-8637-4aaa-9fc1-52e868cff35e",
   "metadata": {},
   "source": [
    "#### With p-value 0.063813 (> 0.05) there's no significant autocorrelation in return series. However, for GARCH modeling, which focuses on volatility patterns rather than return levels, further analysis is needed. Specifically, examining autocorrelation in squared or absolute returns would be more indicative of the volatility clustering GARCH models aim to capture. Our current findings suggest a lack of autocorrelation in returns, but this does not directly translate to volatility patterns, which are central to GARCH modeling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b6486278-0557-49d5-b2b4-2f98d7578050",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Check for ACF on both returns and squared returns\n",
    "fig, axes = plt.subplots(2, 1)\n",
    "plot_acf(rAMZN, lags=24, ax=axes[0])\n",
    "plot_acf(rAMZN**2, lags=24, ax=axes[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7504721-924e-4664-bc4d-f5c93d22a3f9",
   "metadata": {},
   "source": [
    "#### We have no significant autocorrelation in lags 1-24 in both the returns and squared returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "42f9a5e1-bf46-49e0-a891-40f24836dd58",
   "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>lb_stat</th>\n",
       "      <th>lb_pvalue</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>17.510035</td>\n",
       "      <td>0.063813</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      lb_stat  lb_pvalue\n",
       "10  17.510035   0.063813"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_demeaned = rAMZN - np.mean(rAMZN)\n",
    "acorr_ljungbox(r_demeaned, lags=[10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f1cc8a8b-898c-4885-8583-e404d4c4886f",
   "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>lb_stat</th>\n",
       "      <th>lb_pvalue</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>148.898544</td>\n",
       "      <td>6.280103e-27</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       lb_stat     lb_pvalue\n",
       "10  148.898544  6.280103e-27"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acorr_ljungbox(r_demeaned**2, lags=[10])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb921ffd-7f61-4bb3-ac62-23bc4a7deb5a",
   "metadata": {},
   "source": [
    "#### The Ljung-Box test on Amazon's demeaned returns shows a p-value above 0.05, suggesting no significant autocorrelation in returns at the 5% level. However, the squared demeaned returns have a very low p-value, indicating strong autocorrelation in volatility. This supports using a GARCH model to capture the volatility clustering evident in Amazon's stock returns."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ee3e13f-bf09-434f-a8e7-009e4e95c575",
   "metadata": {},
   "source": [
    "## Q2-) Estimate an ARCH model for the data assuming normal distribution for the standardized residuals. As a comment, write down the fitted model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4112be9d-0258-40ef-b320-e3aa54de8205",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pacf(r_demeaned**2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "481cf33a-0a50-4101-b917-30932e7f896d",
   "metadata": {},
   "source": [
    "#### PACF shows significant spike in first lag, indicating there's autocorrelation between the squared returns after removing the effects of intervening lags. This further supports the use of GARCH-type models that can model the autocorrelation in volatility."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "52af05d6-6186-49c3-a808-d2c852be38da",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                      Constant Mean - ARCH Model Results                      \n",
      "==============================================================================\n",
      "Dep. Variable:              Adj Close   R-squared:                       0.000\n",
      "Mean Model:             Constant Mean   Adj. R-squared:                  0.000\n",
      "Vol Model:                       ARCH   Log-Likelihood:               -3285.87\n",
      "Distribution:                  Normal   AIC:                           6577.73\n",
      "Method:            Maximum Likelihood   BIC:                           6593.69\n",
      "                                        No. Observations:                 1508\n",
      "Date:                Mon, Jan 22 2024   Df Residuals:                     1507\n",
      "Time:                        11:47:20   Df Model:                            1\n",
      "                                 Mean Model                                \n",
      "===========================================================================\n",
      "                 coef    std err          t      P>|t|     95.0% Conf. Int.\n",
      "---------------------------------------------------------------------------\n",
      "mu             0.0846  5.329e-02      1.587      0.112 [-1.985e-02,  0.189]\n",
      "                            Volatility Model                            \n",
      "========================================================================\n",
      "                 coef    std err          t      P>|t|  95.0% Conf. Int.\n",
      "------------------------------------------------------------------------\n",
      "omega          3.4945      0.259     13.501  1.540e-41 [  2.987,  4.002]\n",
      "alpha[1]       0.3201  7.378e-02      4.339  1.432e-05 [  0.176,  0.465]\n",
      "========================================================================\n",
      "\n",
      "Covariance estimator: robust\n"
     ]
    }
   ],
   "source": [
    "AM1 = arch_model(rAMZN, p=1, q=0, rescale=False)  # ARCH(1) model estimation\n",
    "res1 = AM1.fit(update_freq=0, disp='off')\n",
    "print(res1.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f24637a3-27b8-4f9e-9e44-6e57cc9b52b0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                      Constant Mean - ARCH Model Results                      \n",
      "==============================================================================\n",
      "Dep. Variable:              Adj Close   R-squared:                       0.000\n",
      "Mean Model:             Constant Mean   Adj. R-squared:                  0.000\n",
      "Vol Model:                       ARCH   Log-Likelihood:               -3257.97\n",
      "Distribution:                  Normal   AIC:                           6523.93\n",
      "Method:            Maximum Likelihood   BIC:                           6545.21\n",
      "                                        No. Observations:                 1508\n",
      "Date:                Mon, Jan 22 2024   Df Residuals:                     1507\n",
      "Time:                        11:47:30   Df Model:                            1\n",
      "                                 Mean Model                                \n",
      "===========================================================================\n",
      "                 coef    std err          t      P>|t|     95.0% Conf. Int.\n",
      "---------------------------------------------------------------------------\n",
      "mu             0.0834  5.243e-02      1.590      0.112 [-1.938e-02,  0.186]\n",
      "                            Volatility Model                            \n",
      "========================================================================\n",
      "                 coef    std err          t      P>|t|  95.0% Conf. Int.\n",
      "------------------------------------------------------------------------\n",
      "omega          2.7409      0.263     10.417  2.070e-25 [  2.225,  3.257]\n",
      "alpha[1]       0.2896  7.366e-02      3.931  8.459e-05 [  0.145,  0.434]\n",
      "alpha[2]       0.1998  4.830e-02      4.137  3.516e-05 [  0.105,  0.294]\n",
      "========================================================================\n",
      "\n",
      "Covariance estimator: robust\n"
     ]
    }
   ],
   "source": [
    "AM2 = arch_model(rAMZN, p=2, q=0, rescale=False)  # ARCH(2) model estimation\n",
    "res2 = AM2.fit(update_freq=0, disp='off')\n",
    "print(res2.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "3cb57b37-b15f-4355-8994-908bd80f7131",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                      Constant Mean - ARCH Model Results                      \n",
      "==============================================================================\n",
      "Dep. Variable:              Adj Close   R-squared:                       0.000\n",
      "Mean Model:             Constant Mean   Adj. R-squared:                  0.000\n",
      "Vol Model:                       ARCH   Log-Likelihood:               -3241.43\n",
      "Distribution:                  Normal   AIC:                           6492.86\n",
      "Method:            Maximum Likelihood   BIC:                           6519.45\n",
      "                                        No. Observations:                 1508\n",
      "Date:                Mon, Jan 22 2024   Df Residuals:                     1507\n",
      "Time:                        11:47:33   Df Model:                            1\n",
      "                                Mean Model                                \n",
      "==========================================================================\n",
      "                 coef    std err          t      P>|t|    95.0% Conf. Int.\n",
      "--------------------------------------------------------------------------\n",
      "mu             0.1139  5.179e-02      2.199  2.790e-02 [1.237e-02,  0.215]\n",
      "                             Volatility Model                             \n",
      "==========================================================================\n",
      "                 coef    std err          t      P>|t|    95.0% Conf. Int.\n",
      "--------------------------------------------------------------------------\n",
      "omega          2.2931      0.252      9.090  9.872e-20   [  1.799,  2.788]\n",
      "alpha[1]       0.2449  6.338e-02      3.863  1.118e-04   [  0.121,  0.369]\n",
      "alpha[2]       0.1665  4.686e-02      3.553  3.814e-04 [7.464e-02,  0.258]\n",
      "alpha[3]       0.1751  6.296e-02      2.781  5.419e-03 [5.170e-02,  0.299]\n",
      "==========================================================================\n",
      "\n",
      "Covariance estimator: robust\n"
     ]
    }
   ],
   "source": [
    "AM3 = arch_model(rAMZN, p=3, q=0, rescale=False)  # ARCH(3) model estimation\n",
    "res3 = AM3.fit(update_freq=0, disp='off')\n",
    "print(res3.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "61ca8da1-3aa7-4f3f-9b1a-886d9f101e3f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                      Constant Mean - ARCH Model Results                      \n",
      "==============================================================================\n",
      "Dep. Variable:              Adj Close   R-squared:                       0.000\n",
      "Mean Model:             Constant Mean   Adj. R-squared:                  0.000\n",
      "Vol Model:                       ARCH   Log-Likelihood:               -3222.84\n",
      "Distribution:                  Normal   AIC:                           6457.68\n",
      "Method:            Maximum Likelihood   BIC:                           6489.59\n",
      "                                        No. Observations:                 1508\n",
      "Date:                Mon, Jan 22 2024   Df Residuals:                     1507\n",
      "Time:                        11:47:36   Df Model:                            1\n",
      "                                Mean Model                                \n",
      "==========================================================================\n",
      "                 coef    std err          t      P>|t|    95.0% Conf. Int.\n",
      "--------------------------------------------------------------------------\n",
      "mu             0.1317  4.930e-02      2.671  7.570e-03 [3.504e-02,  0.228]\n",
      "                             Volatility Model                             \n",
      "==========================================================================\n",
      "                 coef    std err          t      P>|t|    95.0% Conf. Int.\n",
      "--------------------------------------------------------------------------\n",
      "omega          1.7841      0.220      8.096  5.675e-16   [  1.352,  2.216]\n",
      "alpha[1]       0.2354  6.215e-02      3.788  1.521e-04   [  0.114,  0.357]\n",
      "alpha[2]       0.1481  4.382e-02      3.380  7.238e-04 [6.225e-02,  0.234]\n",
      "alpha[3]       0.2091  6.598e-02      3.169  1.530e-03 [7.977e-02,  0.338]\n",
      "alpha[4]       0.1241  4.540e-02      2.733  6.277e-03 [3.509e-02,  0.213]\n",
      "==========================================================================\n",
      "\n",
      "Covariance estimator: robust\n"
     ]
    }
   ],
   "source": [
    "AM4 = arch_model(rAMZN, p=4, q=0, rescale=False)  # ARCH(4) model estimation\n",
    "res4 = AM4.fit(update_freq=0, disp='off')\n",
    "print(res4.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2a22c0b-8f6e-42fb-9eb4-ead42fea650d",
   "metadata": {},
   "source": [
    "#### We have tested for ARCH model through 1-4. AIC and BIC of ARCH(4) being less than ARCH(1), we selected ARCH(4)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "109294fd-2bed-4273-bdc9-2e77c8fb8549",
   "metadata": {},
   "source": [
    "#### Fitted model:\n",
    "### $$ y = 0.1317 + \\epsilon_t $$\n",
    "### $$ \\sigma_t^2 = 1.7841 + 0.2354 * \\epsilon_{(t-1)}^2 + 0.1481 * \\epsilon_{(t-2)}^2 + 0.2091 * \\epsilon_{(t-3)}^2 + 0.1241 * \\epsilon_{(t-4)}^2 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c508bce-7de6-416e-8408-213785aed0fe",
   "metadata": {},
   "source": [
    "## Q3-) Check the model. Answer the following questions.\n",
    " - Is the normality assumption for the standardized residuals appropriate?\n",
    " - Is the mean equation adequate?\n",
    " - Is the variance equation adequate?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bd39a27e-287d-47dc-86c1-19c57bfcf71d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot: xlabel='Date'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.concat([res1.conditional_volatility, res4.conditional_volatility], axis=1) # estimated conditional volatilities\n",
    "df.columns = [\"ARCH(1)\", \"ARCH(4)\"]\n",
    "df.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "8cf35aa3-0b99-434d-8e06-6d171f21469a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "std_resi = res4.resid/res4.conditional_volatility\n",
    "tdx = pd.date_range(start='2018-01-05', periods=len(rAMZN), freq='D')\n",
    "plt.plot(tdx, std_resi)\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "ebf6da73-d9a3-4b40-8445-56a621d4cbbd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res4.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "af312868-a3d7-4266-a818-4363898044c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ACF and PACF for squared standardized residuals\n",
    "fig, axes = plt.subplots(2, 1)\n",
    "plot_acf(std_resi, lags=20, ax=axes[0])\n",
    "plot_pacf(std_resi**2, lags=20, ax=axes[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "fbe090f6-d9cc-48c8-8ed4-736cfabe7b6e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import shapiro"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "88ffd44a-5c4d-44ee-88c9-e2e8309ca4e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ShapiroResult(statistic=0.9757030010223389, pvalue=2.8079144319062424e-15)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shapiro(res1.std_resid) # Shapiro-Wilk test for normality of the standardized residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "b2c0bf78-7e53-4b12-9115-360b9d67f80a",
   "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>lb_stat</th>\n",
       "      <th>lb_pvalue</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>4.194965</td>\n",
       "      <td>0.938123</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     lb_stat  lb_pvalue\n",
       "10  4.194965   0.938123"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acorr_ljungbox(std_resi, lags=[10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "7d304b48-b797-4160-87cc-928fb34845fa",
   "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>lb_stat</th>\n",
       "      <th>lb_pvalue</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>16.618262</td>\n",
       "      <td>0.083249</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      lb_stat  lb_pvalue\n",
       "10  16.618262   0.083249"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acorr_ljungbox(std_resi**2, lags=[10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c4c3bb76-eed3-427d-9053-881170a81229",
   "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>lb_stat</th>\n",
       "      <th>lb_pvalue</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>16.618262</td>\n",
       "      <td>0.083249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>22.352651</td>\n",
       "      <td>0.098885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>32.430070</td>\n",
       "      <td>0.019544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>40.361084</td>\n",
       "      <td>0.002933</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>41.020816</td>\n",
       "      <td>0.003702</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      lb_stat  lb_pvalue\n",
       "10  16.618262   0.083249\n",
       "15  22.352651   0.098885\n",
       "18  32.430070   0.019544\n",
       "19  40.361084   0.002933\n",
       "20  41.020816   0.003702"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acorr_ljungbox(res4.std_resid**2, lags=['10', '15', '18', '19', '20'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "3e0bfb18-238b-4a15-a7f2-d135fb7fb89b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ARCH-LM Test\n",
       "H0: Standardized residuals are homoskedastic.\n",
       "ARCH-LM Test\n",
       "H1: Standardized residuals are conditionally heteroskedastic.\n",
       "Statistic: 16.8290\n",
       "P-value: 0.0782\n",
       "Distributed: chi2(10)\n",
       "WaldTestStatistic, id: 0x212307e76a0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res4.arch_lm_test(lags=10, standardized=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "748f21fc-0674-4135-9c39-957df6cfaada",
   "metadata": {},
   "source": [
    "#### A) Found pvalue=2.8079144319062424e-15 (<0.05) on Shapiro test. We reject the null hypothesis and accept HAlternative that the standardized residuals are not normally distributed. We should change the distribution to student-t or skewed student-t."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01f17826-38ab-454c-b779-4e549712ae4c",
   "metadata": {},
   "source": [
    "#### B) Ljung-box test shows 0.938123 (>0.05) meaning standardized residuals are statistically insignificant. Therefore we don't have autocorrelation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e317e63-5c9c-4fbd-acdc-f4e6c33f06e7",
   "metadata": {},
   "source": [
    "#### C) Applying Ljung-box to square of standardized residuals shows 0.083249 (>0.05) statistical insignificance again."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "312eefb3-d87e-4960-8292-e6d40346bded",
   "metadata": {},
   "source": [
    "## Q4-) Estimate alternative ARCH models assuming student-t and skewed student-t distributions for the standardized residuals. Interpret shape and skew coefficient estimates. Which model would you prefer? Justify your choice based on coefficient estimates and on information criteria."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "10a4e375-2122-47e3-b5c6-5c0c3d33b48f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "641150e3-952f-4dcb-9a63-5281334d47d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# q-q plot\n",
    "fig = sm.qqplot(res4.std_resid, line='45')\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "7d6f9d7e-e5db-4427-8464-334dce4337ba",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                         Constant Mean - ARCH Model Results                         \n",
      "====================================================================================\n",
      "Dep. Variable:                    Adj Close   R-squared:                       0.000\n",
      "Mean Model:                   Constant Mean   Adj. R-squared:                  0.000\n",
      "Vol Model:                             ARCH   Log-Likelihood:               -3182.95\n",
      "Distribution:      Standardized Student's t   AIC:                           6379.91\n",
      "Method:                  Maximum Likelihood   BIC:                           6417.14\n",
      "                                              No. Observations:                 1508\n",
      "Date:                      Mon, Jan 22 2024   Df Residuals:                     1507\n",
      "Time:                              13:28:30   Df Model:                            1\n",
      "                                Mean Model                                \n",
      "==========================================================================\n",
      "                 coef    std err          t      P>|t|    95.0% Conf. Int.\n",
      "--------------------------------------------------------------------------\n",
      "mu             0.1222  4.433e-02      2.757  5.829e-03 [3.534e-02,  0.209]\n",
      "                             Volatility Model                             \n",
      "==========================================================================\n",
      "                 coef    std err          t      P>|t|    95.0% Conf. Int.\n",
      "--------------------------------------------------------------------------\n",
      "omega          1.8671      0.234      7.986  1.394e-15   [  1.409,  2.325]\n",
      "alpha[1]       0.2007  6.141e-02      3.268  1.084e-03 [8.031e-02,  0.321]\n",
      "alpha[2]       0.2030  5.015e-02      4.047  5.177e-05   [  0.105,  0.301]\n",
      "alpha[3]       0.1918  5.799e-02      3.308  9.385e-04 [7.819e-02,  0.305]\n",
      "alpha[4]       0.1227  4.592e-02      2.672  7.549e-03 [3.268e-02,  0.213]\n",
      "                              Distribution                              \n",
      "========================================================================\n",
      "                 coef    std err          t      P>|t|  95.0% Conf. Int.\n",
      "------------------------------------------------------------------------\n",
      "nu             5.3828      0.731      7.365  1.774e-13 [  3.950,  6.815]\n",
      "========================================================================\n",
      "\n",
      "Covariance estimator: robust\n"
     ]
    }
   ],
   "source": [
    "AM4s = arch_model(rAMZN, p=4, q=0, dist=\"StudentsT\", rescale=False)    # ARCH(4) with student-t distributed residuals\n",
    "res4s = AM4s.fit(update_freq=10, disp='off')\n",
    "print(res4s.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "8c34e59e-c9f9-46d7-8746-fc31b5c20406",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            Constant Mean - ARCH Model Results                           \n",
      "=========================================================================================\n",
      "Dep. Variable:                         Adj Close   R-squared:                       0.000\n",
      "Mean Model:                        Constant Mean   Adj. R-squared:                  0.000\n",
      "Vol Model:                                  ARCH   Log-Likelihood:               -3182.41\n",
      "Distribution:      Standardized Skew Student's t   AIC:                           6380.83\n",
      "Method:                       Maximum Likelihood   BIC:                           6423.38\n",
      "                                                   No. Observations:                 1508\n",
      "Date:                           Mon, Jan 22 2024   Df Residuals:                     1507\n",
      "Time:                                   13:28:59   Df Model:                            1\n",
      "                                Mean Model                                \n",
      "==========================================================================\n",
      "                 coef    std err          t      P>|t|    95.0% Conf. Int.\n",
      "--------------------------------------------------------------------------\n",
      "mu             0.1045  4.839e-02      2.158  3.090e-02 [9.603e-03,  0.199]\n",
      "                             Volatility Model                             \n",
      "==========================================================================\n",
      "                 coef    std err          t      P>|t|    95.0% Conf. Int.\n",
      "--------------------------------------------------------------------------\n",
      "omega          1.8731      0.235      7.987  1.386e-15   [  1.413,  2.333]\n",
      "alpha[1]       0.2002  6.098e-02      3.283  1.029e-03 [8.065e-02,  0.320]\n",
      "alpha[2]       0.2015  5.028e-02      4.007  6.147e-05   [  0.103,  0.300]\n",
      "alpha[3]       0.1900  5.729e-02      3.317  9.105e-04 [7.773e-02,  0.302]\n",
      "alpha[4]       0.1217  4.589e-02      2.652  8.000e-03 [3.176e-02,  0.212]\n",
      "                                 Distribution                                \n",
      "=============================================================================\n",
      "                 coef    std err          t      P>|t|       95.0% Conf. Int.\n",
      "-----------------------------------------------------------------------------\n",
      "eta            5.3852      0.729      7.386  1.509e-13      [  3.956,  6.814]\n",
      "lambda        -0.0349  3.205e-02     -1.088      0.277 [-9.768e-02,2.795e-02]\n",
      "=============================================================================\n",
      "\n",
      "Covariance estimator: robust\n"
     ]
    }
   ],
   "source": [
    "AM4ss = arch_model(rAMZN, p=4, q=0, dist='skewstudent', rescale=False)    #ARCH(4) with skewed student-t distributed residuals\n",
    "res4ss = AM4ss.fit(update_freq=10, disp='off')\n",
    "print(res4ss.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9a3c6eb-998b-4e77-94aa-f61b8e7e182b",
   "metadata": {},
   "source": [
    "#### In our ARCH(4) model, the shape parameter \"nu\" = 5.3828 and \"eta\" = 5.3852 both indicate leptokurtosis (kurtosis > 3.0). Skewness parameter \"lambda\" is slightly negative, suggesting skewness to the left that's not statistically significant. \n",
    "#### Since the ARCH terms are significant in both Student-t and skewed Student-t models, and considering the lower AIC and BIC values, we chose the \"ARCH(4) with Student-t distributed residuals\" model for its parsimony and better fit, as it accounts for heavy tails without unnecessary skewness parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07a3c9c6-68a6-4fcb-8ce3-a79c48cf6489",
   "metadata": {},
   "source": [
    "## Q5-) Estimate a GARCH (1,1) model for the data. Specify an appropriate distribution for the standardized residuals. Write down the fitted model as a comment. Compare this model with the ARCH model that you have chosen in question 4. Which model would you prefer? Comment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "fe64080f-d667-4185-9952-0a80de87dc22",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                     Constant Mean - GARCH Model Results                      \n",
      "==============================================================================\n",
      "Dep. Variable:              Adj Close   R-squared:                       0.000\n",
      "Mean Model:             Constant Mean   Adj. R-squared:                  0.000\n",
      "Vol Model:                      GARCH   Log-Likelihood:               -3203.58\n",
      "Distribution:                  Normal   AIC:                           6415.15\n",
      "Method:            Maximum Likelihood   BIC:                           6436.43\n",
      "                                        No. Observations:                 1508\n",
      "Date:                Mon, Jan 22 2024   Df Residuals:                     1507\n",
      "Time:                        13:39:21   Df Model:                            1\n",
      "                                Mean Model                                \n",
      "==========================================================================\n",
      "                 coef    std err          t      P>|t|    95.0% Conf. Int.\n",
      "--------------------------------------------------------------------------\n",
      "mu             0.1279  4.624e-02      2.766  5.677e-03 [3.727e-02,  0.219]\n",
      "                             Volatility Model                             \n",
      "==========================================================================\n",
      "                 coef    std err          t      P>|t|    95.0% Conf. Int.\n",
      "--------------------------------------------------------------------------\n",
      "omega          0.2169  8.541e-02      2.540  1.110e-02 [4.950e-02,  0.384]\n",
      "alpha[1]       0.1613  4.169e-02      3.870  1.087e-04 [7.963e-02,  0.243]\n",
      "beta[1]        0.8042  4.453e-02     18.058  6.883e-73   [  0.717,  0.891]\n",
      "==========================================================================\n",
      "\n",
      "Covariance estimator: robust\n"
     ]
    }
   ],
   "source": [
    "# Standard GARCH(1,1) model\n",
    "SGM = arch_model(rAMZN)\n",
    "resSGM = SGM.fit(update_freq=10, disp='off')\n",
    "print(resSGM.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "ba342854-5794-4a6a-a007-310a3e224551",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                        Constant Mean - GARCH Model Results                         \n",
      "====================================================================================\n",
      "Dep. Variable:                    Adj Close   R-squared:                       0.000\n",
      "Mean Model:                   Constant Mean   Adj. R-squared:                  0.000\n",
      "Vol Model:                            GARCH   Log-Likelihood:               -3160.98\n",
      "Distribution:      Standardized Student's t   AIC:                           6331.97\n",
      "Method:                  Maximum Likelihood   BIC:                           6358.56\n",
      "                                              No. Observations:                 1508\n",
      "Date:                      Mon, Jan 22 2024   Df Residuals:                     1507\n",
      "Time:                              13:39:51   Df Model:                            1\n",
      "                                Mean Model                                \n",
      "==========================================================================\n",
      "                 coef    std err          t      P>|t|    95.0% Conf. Int.\n",
      "--------------------------------------------------------------------------\n",
      "mu             0.1207  4.309e-02      2.801  5.094e-03 [3.624e-02,  0.205]\n",
      "                              Volatility Model                             \n",
      "===========================================================================\n",
      "                 coef    std err          t      P>|t|     95.0% Conf. Int.\n",
      "---------------------------------------------------------------------------\n",
      "omega          0.1141  6.334e-02      1.801  7.163e-02 [-1.004e-02,  0.238]\n",
      "alpha[1]       0.1183  4.364e-02      2.711  6.705e-03  [3.278e-02,  0.204]\n",
      "beta[1]        0.8665  4.740e-02     18.282  1.148e-74    [  0.774,  0.959]\n",
      "                              Distribution                              \n",
      "========================================================================\n",
      "                 coef    std err          t      P>|t|  95.0% Conf. Int.\n",
      "------------------------------------------------------------------------\n",
      "nu             5.6759      0.821      6.912  4.786e-12 [  4.066,  7.285]\n",
      "========================================================================\n",
      "\n",
      "Covariance estimator: robust\n"
     ]
    }
   ],
   "source": [
    "#GARCH(1,1) with student-t distributed residuals\n",
    "GM = arch_model(rAMZN, p=1, q=1, dist='studentst')\n",
    "resGM = GM.fit(update_freq=10, disp='off')\n",
    "print(resGM.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "01e50d05-7775-4c22-af95-503ee97585ac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           Constant Mean - GARCH Model Results                           \n",
      "=========================================================================================\n",
      "Dep. Variable:                         Adj Close   R-squared:                       0.000\n",
      "Mean Model:                        Constant Mean   Adj. R-squared:                  0.000\n",
      "Vol Model:                                 GARCH   Log-Likelihood:               -3160.24\n",
      "Distribution:      Standardized Skew Student's t   AIC:                           6332.47\n",
      "Method:                       Maximum Likelihood   BIC:                           6364.38\n",
      "                                                   No. Observations:                 1508\n",
      "Date:                           Mon, Jan 22 2024   Df Residuals:                     1507\n",
      "Time:                                   13:49:21   Df Model:                            1\n",
      "                                Mean Model                                \n",
      "==========================================================================\n",
      "                 coef    std err          t      P>|t|    95.0% Conf. Int.\n",
      "--------------------------------------------------------------------------\n",
      "mu             0.1005  4.719e-02      2.129  3.324e-02 [7.984e-03,  0.193]\n",
      "                              Volatility Model                             \n",
      "===========================================================================\n",
      "                 coef    std err          t      P>|t|     95.0% Conf. Int.\n",
      "---------------------------------------------------------------------------\n",
      "omega          0.1079  6.490e-02      1.662  9.649e-02 [-1.933e-02,  0.235]\n",
      "alpha[1]       0.1135  4.479e-02      2.534  1.129e-02  [2.569e-02,  0.201]\n",
      "beta[1]        0.8717  4.940e-02     17.647  1.078e-69    [  0.775,  0.969]\n",
      "                               Distribution                               \n",
      "==========================================================================\n",
      "                 coef    std err          t      P>|t|    95.0% Conf. Int.\n",
      "--------------------------------------------------------------------------\n",
      "eta            5.6866      0.820      6.932  4.137e-12   [  4.079,  7.294]\n",
      "lambda        -0.0426  3.464e-02     -1.230      0.219 [ -0.110,2.528e-02]\n",
      "==========================================================================\n",
      "\n",
      "Covariance estimator: robust\n"
     ]
    }
   ],
   "source": [
    "#GARCH(1,1) with skewed student-t distributed residuals\n",
    "sGM = arch_model(rAMZN, p=1, q=1, dist='skewstudent')\n",
    "ressGM = sGM.fit(update_freq=10, disp='off')\n",
    "print(ressGM.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "aab84f38-5266-4331-8f6d-8adc156069da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "resGM.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae46de26-596c-4bab-b0b3-ee99a9a69d5e",
   "metadata": {},
   "source": [
    "#### Among the estimated models, the \"GARCH(1,1) with Student-t distributed residuals\" demonstrates the lowest AIC and BIC scores, indicating a superior fit to the data while efficiently penalizing complexity. The significance of the alpha and beta parameters at the 5% level further justifies our selection. So the model's mean and variance equations will be as below:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb630a40-6e09-47db-afbb-6a7543d199e1",
   "metadata": {},
   "source": [
    "### $$  y = 0.1207 + \\epsilon_t $$\n",
    "### $$  \\sigma_t^2 = 0.1141 + 0.1183 * \\epsilon_{(t-1)}^2 + 0.8665 * \\sigma_{(t-1)}^2 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1eb4772-f818-415e-ae9d-df22c77647fc",
   "metadata": {},
   "source": [
    "####  This GARCH(1,1) model is preferred over the \"ARCH(4) with Student-t distributed residuals\" due to its parsimonious representation of volatility dynamics as reflected in its statistical criteria."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a6d8297-d08d-488c-a014-60d26a6a4de9",
   "metadata": {},
   "source": [
    "## Q6-) Estimate a GJR-GARCH (1,1) model for the data. Assume normal distribution for the standardized residuals. Interpret the leverage parameter in detail."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "7098c4d9-30c3-4598-9bfa-fc17a7a6ecff",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                   Constant Mean - GJR-GARCH Model Results                    \n",
      "==============================================================================\n",
      "Dep. Variable:              Adj Close   R-squared:                       0.000\n",
      "Mean Model:             Constant Mean   Adj. R-squared:                  0.000\n",
      "Vol Model:                  GJR-GARCH   Log-Likelihood:               -3198.16\n",
      "Distribution:                  Normal   AIC:                           6406.32\n",
      "Method:            Maximum Likelihood   BIC:                           6432.91\n",
      "                                        No. Observations:                 1508\n",
      "Date:                Mon, Jan 22 2024   Df Residuals:                     1507\n",
      "Time:                        13:51:35   Df Model:                            1\n",
      "                                 Mean Model                                \n",
      "===========================================================================\n",
      "                 coef    std err          t      P>|t|     95.0% Conf. Int.\n",
      "---------------------------------------------------------------------------\n",
      "mu             0.0859  4.641e-02      1.850  6.429e-02 [-5.096e-03,  0.177]\n",
      "                             Volatility Model                             \n",
      "==========================================================================\n",
      "                 coef    std err          t      P>|t|    95.0% Conf. Int.\n",
      "--------------------------------------------------------------------------\n",
      "omega          0.2140  7.843e-02      2.729  6.359e-03 [6.029e-02,  0.368]\n",
      "alpha[1]       0.0944  3.704e-02      2.549  1.081e-02 [2.181e-02,  0.167]\n",
      "gamma[1]       0.1130  4.725e-02      2.391  1.679e-02 [2.038e-02,  0.206]\n",
      "beta[1]        0.8127  4.083e-02     19.904  3.749e-88   [  0.733,  0.893]\n",
      "==========================================================================\n",
      "\n",
      "Covariance estimator: robust\n"
     ]
    }
   ],
   "source": [
    "#GJR-GARCH(1,1) model estimation\n",
    "gjr = arch_model(rAMZN, mean='Constant', p=1, o=1, q=1, dist='normal')\n",
    "gjr = gjr.fit(update_freq=0, disp='off')\n",
    "print(gjr.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b284b0a3-2c4d-468d-a06a-abe08c787d2c",
   "metadata": {},
   "source": [
    "#### In our GJR-GARCH model, the positive coefficient of the leverage parameter, gamma (0.1130), with a p-value below 5%, signifies a statistically significant leverage effect. This result implies that the model effectively captures the asymmetric impact of shocks on volatility, where negative shocks lead to a greater increase in future volatility compared to positive shocks of the same magnitude. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5eb8d2aa-afb7-45fd-ae71-1b7edb32ecfa",
   "metadata": {},
   "source": [
    "#### P-values of both omega, alpha, gamma and beta are statistically significant (<0.05). Fitted model's mean and variance equations:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92c8bcd0-8394-4a4d-83af-1fe45b2d44fc",
   "metadata": {},
   "source": [
    "####  r(t)=0.012+a(t) a(t)=s(t)z(t), z(t)~N(0,1) \n",
    "#### s^2(t)=0.00067443+0.0882a^2(t-1)-0.028 * D * a^2(t-1)+0.8781(s^2(t-1)) where D=1 if a(t-1)<0.\n"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "id": "cf2fc40a-13f1-4684-857c-99450c3226b9",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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