{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## ARMA Modeling: Estimation\n",
    "\n",
    "**Functions**\n",
    "\n",
    "`tsa.SARIMAX`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-22T10:06:06.713846Z",
     "iopub.status.busy": "2021-09-22T10:06:06.713846Z",
     "iopub.status.idle": "2021-09-22T10:06:07.370849Z",
     "shell.execute_reply": "2021-09-22T10:06:07.371850Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "data = pd.read_hdf(\"data/term-premium.h5\", \"term_premium\")\n",
    "term = data.TERM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-22T10:06:07.375848Z",
     "iopub.status.busy": "2021-09-22T10:06:07.374849Z",
     "iopub.status.idle": "2021-09-22T10:06:08.250847Z",
     "shell.execute_reply": "2021-09-22T10:06:08.250847Z"
    },
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='DATE'>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "sns.set_style(\"darkgrid\")\n",
    "\n",
    "plt.rc(\"figure\", figsize=(16, 6))\n",
    "plt.rc(\"font\", size=14)\n",
    "\n",
    "term.plot.line()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### Exercise 65\n",
    "Estimate an AR(1) on the term premium, and compute standard errors for the parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-22T10:06:08.253850Z",
     "iopub.status.busy": "2021-09-22T10:06:08.253850Z",
     "iopub.status.idle": "2021-09-22T10:06:08.657846Z",
     "shell.execute_reply": "2021-09-22T10:06:08.657846Z"
    },
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "intercept    0.028037\n",
       "ar.L1        0.970624\n",
       "sigma2       0.064199\n",
       "dtype: float64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.tsa.api as tsa\n",
    "\n",
    "mod = tsa.SARIMAX(term, order=(1, 0, 0), trend=\"c\")\n",
    "res = mod.fit()\n",
    "res.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-22T10:06:08.661850Z",
     "iopub.status.busy": "2021-09-22T10:06:08.661850Z",
     "iopub.status.idle": "2021-09-22T10:06:08.673850Z",
     "shell.execute_reply": "2021-09-22T10:06:08.673850Z"
    },
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>SARIMAX Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>TERM</td>       <th>  No. Observations:  </th>   <td>821</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>SARIMAX(1, 0, 0)</td> <th>  Log Likelihood     </th> <td>-39.253</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Wed, 22 Sep 2021</td> <th>  AIC                </th> <td>84.506</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>11:06:08</td>     <th>  BIC                </th> <td>98.638</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>             <td>04-01-1953</td>    <th>  HQIC               </th> <td>89.928</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                   <td>- 08-01-2021</td>   <th>                     </th>    <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>        <td>opg</td>       <th>                     </th>    <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>intercept</th> <td>    0.0280</td> <td>    0.009</td> <td>    3.096</td> <td> 0.002</td> <td>    0.010</td> <td>    0.046</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1</th>     <td>    0.9706</td> <td>    0.006</td> <td>  154.969</td> <td> 0.000</td> <td>    0.958</td> <td>    0.983</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th>    <td>    0.0642</td> <td>    0.001</td> <td>   58.220</td> <td> 0.000</td> <td>    0.062</td> <td>    0.066</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Ljung-Box (L1) (Q):</th>     <td>75.51</td> <th>  Jarque-Bera (JB):  </th> <td>10071.40</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Q):</th>                <td>0.00</td>  <th>  Prob(JB):          </th>   <td>0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Heteroskedasticity (H):</th> <td>0.73</td>  <th>  Skew:              </th>   <td>0.91</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(H) (two-sided):</th>    <td>0.01</td>  <th>  Kurtosis:          </th>   <td>20.06</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using the outer product of gradients (complex-step)."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                               SARIMAX Results                                \n",
       "==============================================================================\n",
       "Dep. Variable:                   TERM   No. Observations:                  821\n",
       "Model:               SARIMAX(1, 0, 0)   Log Likelihood                 -39.253\n",
       "Date:                Wed, 22 Sep 2021   AIC                             84.506\n",
       "Time:                        11:06:08   BIC                             98.638\n",
       "Sample:                    04-01-1953   HQIC                            89.928\n",
       "                         - 08-01-2021                                         \n",
       "Covariance Type:                  opg                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "intercept      0.0280      0.009      3.096      0.002       0.010       0.046\n",
       "ar.L1          0.9706      0.006    154.969      0.000       0.958       0.983\n",
       "sigma2         0.0642      0.001     58.220      0.000       0.062       0.066\n",
       "===================================================================================\n",
       "Ljung-Box (L1) (Q):                  75.51   Jarque-Bera (JB):             10071.40\n",
       "Prob(Q):                              0.00   Prob(JB):                         0.00\n",
       "Heteroskedasticity (H):               0.73   Skew:                             0.91\n",
       "Prob(H) (two-sided):                  0.01   Kurtosis:                        20.06\n",
       "===================================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
       "\"\"\""
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### Exercise 66\n",
    "Estimate an MA(5) on the term premium, and compute standard errors for the parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-22T10:06:08.676848Z",
     "iopub.status.busy": "2021-09-22T10:06:08.676848Z",
     "iopub.status.idle": "2021-09-22T10:06:09.144847Z",
     "shell.execute_reply": "2021-09-22T10:06:09.144847Z"
    },
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\git\\statsmodels\\statsmodels\\tsa\\statespace\\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.\n",
      "  warn('Non-invertible starting MA parameters found.'\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "intercept    0.963095\n",
       "ma.L1        1.514383\n",
       "ma.L2        1.430350\n",
       "ma.L3        1.189689\n",
       "ma.L4        0.744114\n",
       "ma.L5        0.292505\n",
       "sigma2       0.082917\n",
       "dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mod = tsa.SARIMAX(term, order=(0, 0, 5), trend=\"c\")\n",
    "res = mod.fit()\n",
    "res.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-22T10:06:09.148847Z",
     "iopub.status.busy": "2021-09-22T10:06:09.147846Z",
     "iopub.status.idle": "2021-09-22T10:06:09.159847Z",
     "shell.execute_reply": "2021-09-22T10:06:09.159847Z"
    },
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>SARIMAX Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>TERM</td>       <th>  No. Observations:  </th>    <td>821</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>SARIMAX(0, 0, 5)</td> <th>  Log Likelihood     </th> <td>-144.216</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Wed, 22 Sep 2021</td> <th>  AIC                </th>  <td>302.432</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>11:06:09</td>     <th>  BIC                </th>  <td>335.406</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>             <td>04-01-1953</td>    <th>  HQIC               </th>  <td>315.084</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                   <td>- 08-01-2021</td>   <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>        <td>opg</td>       <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>intercept</th> <td>    0.9631</td> <td>    0.064</td> <td>   14.942</td> <td> 0.000</td> <td>    0.837</td> <td>    1.089</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1</th>     <td>    1.5144</td> <td>    0.016</td> <td>   94.801</td> <td> 0.000</td> <td>    1.483</td> <td>    1.546</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L2</th>     <td>    1.4304</td> <td>    0.029</td> <td>   49.179</td> <td> 0.000</td> <td>    1.373</td> <td>    1.487</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L3</th>     <td>    1.1897</td> <td>    0.035</td> <td>   33.652</td> <td> 0.000</td> <td>    1.120</td> <td>    1.259</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L4</th>     <td>    0.7441</td> <td>    0.035</td> <td>   21.283</td> <td> 0.000</td> <td>    0.676</td> <td>    0.813</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L5</th>     <td>    0.2925</td> <td>    0.024</td> <td>   12.170</td> <td> 0.000</td> <td>    0.245</td> <td>    0.340</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th>    <td>    0.0829</td> <td>    0.003</td> <td>   31.785</td> <td> 0.000</td> <td>    0.078</td> <td>    0.088</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Ljung-Box (L1) (Q):</th>     <td>12.90</td> <th>  Jarque-Bera (JB):  </th> <td>688.53</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Q):</th>                <td>0.00</td>  <th>  Prob(JB):          </th>  <td>0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Heteroskedasticity (H):</th> <td>1.03</td>  <th>  Skew:              </th>  <td>-0.32</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(H) (two-sided):</th>    <td>0.81</td>  <th>  Kurtosis:          </th>  <td>7.44</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using the outer product of gradients (complex-step)."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                               SARIMAX Results                                \n",
       "==============================================================================\n",
       "Dep. Variable:                   TERM   No. Observations:                  821\n",
       "Model:               SARIMAX(0, 0, 5)   Log Likelihood                -144.216\n",
       "Date:                Wed, 22 Sep 2021   AIC                            302.432\n",
       "Time:                        11:06:09   BIC                            335.406\n",
       "Sample:                    04-01-1953   HQIC                           315.084\n",
       "                         - 08-01-2021                                         \n",
       "Covariance Type:                  opg                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "intercept      0.9631      0.064     14.942      0.000       0.837       1.089\n",
       "ma.L1          1.5144      0.016     94.801      0.000       1.483       1.546\n",
       "ma.L2          1.4304      0.029     49.179      0.000       1.373       1.487\n",
       "ma.L3          1.1897      0.035     33.652      0.000       1.120       1.259\n",
       "ma.L4          0.7441      0.035     21.283      0.000       0.676       0.813\n",
       "ma.L5          0.2925      0.024     12.170      0.000       0.245       0.340\n",
       "sigma2         0.0829      0.003     31.785      0.000       0.078       0.088\n",
       "===================================================================================\n",
       "Ljung-Box (L1) (Q):                  12.90   Jarque-Bera (JB):               688.53\n",
       "Prob(Q):                              0.00   Prob(JB):                         0.00\n",
       "Heteroskedasticity (H):               1.03   Skew:                            -0.32\n",
       "Prob(H) (two-sided):                  0.81   Kurtosis:                         7.44\n",
       "===================================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
       "\"\"\""
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### Exercise 67\n",
    "Estimate an ARMA(1,1) on the term premium, and compute standard errors for the parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-22T10:06:09.162847Z",
     "iopub.status.busy": "2021-09-22T10:06:09.162847Z",
     "iopub.status.idle": "2021-09-22T10:06:09.397847Z",
     "shell.execute_reply": "2021-09-22T10:06:09.397847Z"
    },
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "intercept    0.048289\n",
       "ar.L1        0.949604\n",
       "ma.L1        0.416127\n",
       "sigma2       0.056261\n",
       "dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mod = tsa.SARIMAX(term, order=(1, 0, 1), trend=\"c\")\n",
    "res = mod.fit()\n",
    "res.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-22T10:06:09.401848Z",
     "iopub.status.busy": "2021-09-22T10:06:09.400849Z",
     "iopub.status.idle": "2021-09-22T10:06:09.413848Z",
     "shell.execute_reply": "2021-09-22T10:06:09.413848Z"
    },
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>SARIMAX Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>TERM</td>       <th>  No. Observations:  </th>   <td>821</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>SARIMAX(1, 0, 1)</td> <th>  Log Likelihood     </th> <td>14.765</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Wed, 22 Sep 2021</td> <th>  AIC                </th> <td>-21.531</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>11:06:09</td>     <th>  BIC                </th> <td>-2.689</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>             <td>04-01-1953</td>    <th>  HQIC               </th> <td>-14.301</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                   <td>- 08-01-2021</td>   <th>                     </th>    <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>        <td>opg</td>       <th>                     </th>    <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>intercept</th> <td>    0.0483</td> <td>    0.012</td> <td>    4.054</td> <td> 0.000</td> <td>    0.025</td> <td>    0.072</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1</th>     <td>    0.9496</td> <td>    0.008</td> <td>  117.547</td> <td> 0.000</td> <td>    0.934</td> <td>    0.965</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1</th>     <td>    0.4161</td> <td>    0.012</td> <td>   33.983</td> <td> 0.000</td> <td>    0.392</td> <td>    0.440</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th>    <td>    0.0563</td> <td>    0.001</td> <td>   43.175</td> <td> 0.000</td> <td>    0.054</td> <td>    0.059</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Ljung-Box (L1) (Q):</th>     <td>0.60</td> <th>  Jarque-Bera (JB):  </th> <td>3843.17</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Q):</th>                <td>0.44</td> <th>  Prob(JB):          </th>  <td>0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Heteroskedasticity (H):</th> <td>0.71</td> <th>  Skew:              </th>  <td>0.61</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(H) (two-sided):</th>    <td>0.00</td> <th>  Kurtosis:          </th>  <td>13.53</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using the outer product of gradients (complex-step)."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                               SARIMAX Results                                \n",
       "==============================================================================\n",
       "Dep. Variable:                   TERM   No. Observations:                  821\n",
       "Model:               SARIMAX(1, 0, 1)   Log Likelihood                  14.765\n",
       "Date:                Wed, 22 Sep 2021   AIC                            -21.531\n",
       "Time:                        11:06:09   BIC                             -2.689\n",
       "Sample:                    04-01-1953   HQIC                           -14.301\n",
       "                         - 08-01-2021                                         \n",
       "Covariance Type:                  opg                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "intercept      0.0483      0.012      4.054      0.000       0.025       0.072\n",
       "ar.L1          0.9496      0.008    117.547      0.000       0.934       0.965\n",
       "ma.L1          0.4161      0.012     33.983      0.000       0.392       0.440\n",
       "sigma2         0.0563      0.001     43.175      0.000       0.054       0.059\n",
       "===================================================================================\n",
       "Ljung-Box (L1) (Q):                   0.60   Jarque-Bera (JB):              3843.17\n",
       "Prob(Q):                              0.44   Prob(JB):                         0.00\n",
       "Heteroskedasticity (H):               0.71   Skew:                             0.61\n",
       "Prob(H) (two-sided):                  0.00   Kurtosis:                        13.53\n",
       "===================================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
       "\"\"\""
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.summary()"
   ]
  }
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