7. The ARMA Model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing the relevant packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.graphics.tsaplots as sgt\n",
    "import statsmodels.tsa.stattools as sts\n",
    "from statsmodels.tsa.arima_model import ARMA\n",
    "from scipy.stats.distributions import chi2 \n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing the Data and Pre-processing "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "raw_csv_data = pd.read_csv(\"Index2018.csv\") \n",
    "df_comp=raw_csv_data.copy()\n",
    "df_comp.date = pd.to_datetime(df_comp.date, dayfirst = True)\n",
    "df_comp.set_index(\"date\", inplace=True)\n",
    "df_comp=df_comp.asfreq('b')\n",
    "df_comp=df_comp.fillna(method='ffill')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_comp['market_value']=df_comp.ftse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "del df_comp['spx']\n",
    "del df_comp['dax']\n",
    "del df_comp['ftse']\n",
    "del df_comp['nikkei']\n",
    "size = int(len(df_comp)*0.8)\n",
    "df, df_test = df_comp.iloc[:size], df_comp.iloc[size:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The LLR Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def LLR_test(mod_1, mod_2, DF = 1):\n",
    "    L1 = mod_1.fit().llf\n",
    "    L2 = mod_2.fit().llf\n",
    "    LR = (2*(L2-L1))    \n",
    "    p = chi2.sf(LR, DF).round(3)\n",
    "    return p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "df['returns'] = df.market_value.pct_change(1)*100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ARMA(1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(1, 1)</td>    <th>  Log Likelihood     </th> <td>-7916.500</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.171</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 08 Sep 2019</td> <th>  AIC                </th> <td>15841.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>17:37:33</td>     <th>  BIC                </th> <td>15867.085</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15850.140</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.013</td> <td>    1.446</td> <td> 0.148</td> <td>   -0.007</td> <td>    0.045</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.returns</th> <td>    0.7649</td> <td>    0.067</td> <td>   11.349</td> <td> 0.000</td> <td>    0.633</td> <td>    0.897</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.returns</th> <td>   -0.8141</td> <td>    0.061</td> <td>  -13.406</td> <td> 0.000</td> <td>   -0.933</td> <td>   -0.695</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>           1.3074</td> <td>          +0.0000j</td> <td>           1.3074</td> <td>           0.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>           1.2284</td> <td>          +0.0000j</td> <td>           1.2284</td> <td>           0.0000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   No. Observations:                 5020\n",
       "Model:                     ARMA(1, 1)   Log Likelihood               -7916.500\n",
       "Method:                       css-mle   S.D. of innovations              1.171\n",
       "Date:                Sun, 08 Sep 2019   AIC                          15841.000\n",
       "Time:                        17:37:33   BIC                          15867.085\n",
       "Sample:                    01-10-1994   HQIC                         15850.140\n",
       "                         - 04-05-2013                                         \n",
       "=================================================================================\n",
       "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "const             0.0189      0.013      1.446      0.148      -0.007       0.045\n",
       "ar.L1.returns     0.7649      0.067     11.349      0.000       0.633       0.897\n",
       "ma.L1.returns    -0.8141      0.061    -13.406      0.000      -0.933      -0.695\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1            1.3074           +0.0000j            1.3074            0.0000\n",
       "MA.1            1.2284           +0.0000j            1.2284            0.0000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ret_ar_1_ma_1 = ARMA(df.returns[1:], order=(1,1))\n",
    "results_ret_ar_1_ma_1 = model_ret_ar_1_ma_1.fit()\n",
    "results_ret_ar_1_ma_1.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "model_ret_ar_1 = ARMA(df.returns[1:], order = (1,0))\n",
    "model_ret_ma_1 = ARMA(df.returns[1:], order = (0,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "ARMA vs AR  0.0\n",
      "\n",
      "ARMA vs MA  0.0\n"
     ]
    }
   ],
   "source": [
    "print(\"\\nARMA vs AR \", LLR_test(model_ret_ar_1, model_ret_ar_1_ma_1))\n",
    "print(\"\\nARMA vs MA \", LLR_test(model_ret_ma_1, model_ret_ar_1_ma_1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Higher-Lag ARMA Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_ret_ar_3_ma_3 = ARMA(df.returns[1:], order=(3,3))\n",
    "results_ret_ar_3_ma_3 = model_ret_ar_3_ma_3.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LLR_test(model_ret_ar_1_ma_1, model_ret_ar_3_ma_3, DF = 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(3, 3)</td>    <th>  Log Likelihood     </th> <td>-7893.515</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.166</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 08 Sep 2019</td> <th>  AIC                </th> <td>15803.030</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>17:40:54</td>     <th>  BIC                </th> <td>15855.199</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15821.310</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.014</td> <td>    1.395</td> <td> 0.163</td> <td>   -0.008</td> <td>    0.045</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.returns</th> <td>   -0.1898</td> <td>    0.104</td> <td>   -1.827</td> <td> 0.068</td> <td>   -0.393</td> <td>    0.014</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.returns</th> <td>   -0.2942</td> <td>    0.087</td> <td>   -3.389</td> <td> 0.001</td> <td>   -0.464</td> <td>   -0.124</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L3.returns</th> <td>    0.4459</td> <td>    0.138</td> <td>    3.225</td> <td> 0.001</td> <td>    0.175</td> <td>    0.717</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.returns</th> <td>    0.1707</td> <td>    0.099</td> <td>    1.726</td> <td> 0.084</td> <td>   -0.023</td> <td>    0.365</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L2.returns</th> <td>    0.2277</td> <td>    0.084</td> <td>    2.701</td> <td> 0.007</td> <td>    0.062</td> <td>    0.393</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L3.returns</th> <td>   -0.5432</td> <td>    0.127</td> <td>   -4.270</td> <td> 0.000</td> <td>   -0.793</td> <td>   -0.294</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>          -0.5168</td> <td>          -1.0283j</td> <td>           1.1508</td> <td>          -0.3241</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th> <td>          -0.5168</td> <td>          +1.0283j</td> <td>           1.1508</td> <td>           0.3241</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.3</th> <td>           1.6932</td> <td>          -0.0000j</td> <td>           1.6932</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>          -0.5286</td> <td>          -0.9835j</td> <td>           1.1166</td> <td>          -0.3285</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.2</th> <td>          -0.5286</td> <td>          +0.9835j</td> <td>           1.1166</td> <td>           0.3285</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.3</th> <td>           1.4764</td> <td>          -0.0000j</td> <td>           1.4764</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   No. Observations:                 5020\n",
       "Model:                     ARMA(3, 3)   Log Likelihood               -7893.515\n",
       "Method:                       css-mle   S.D. of innovations              1.166\n",
       "Date:                Sun, 08 Sep 2019   AIC                          15803.030\n",
       "Time:                        17:40:54   BIC                          15855.199\n",
       "Sample:                    01-10-1994   HQIC                         15821.310\n",
       "                         - 04-05-2013                                         \n",
       "=================================================================================\n",
       "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "const             0.0189      0.014      1.395      0.163      -0.008       0.045\n",
       "ar.L1.returns    -0.1898      0.104     -1.827      0.068      -0.393       0.014\n",
       "ar.L2.returns    -0.2942      0.087     -3.389      0.001      -0.464      -0.124\n",
       "ar.L3.returns     0.4459      0.138      3.225      0.001       0.175       0.717\n",
       "ma.L1.returns     0.1707      0.099      1.726      0.084      -0.023       0.365\n",
       "ma.L2.returns     0.2277      0.084      2.701      0.007       0.062       0.393\n",
       "ma.L3.returns    -0.5432      0.127     -4.270      0.000      -0.793      -0.294\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1           -0.5168           -1.0283j            1.1508           -0.3241\n",
       "AR.2           -0.5168           +1.0283j            1.1508            0.3241\n",
       "AR.3            1.6932           -0.0000j            1.6932           -0.0000\n",
       "MA.1           -0.5286           -0.9835j            1.1166           -0.3285\n",
       "MA.2           -0.5286           +0.9835j            1.1166            0.3285\n",
       "MA.3            1.4764           -0.0000j            1.4764           -0.0000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results_ret_ar_3_ma_3.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(3, 2)</td>    <th>  Log Likelihood     </th> <td>-7895.747</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.166</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 08 Sep 2019</td> <th>  AIC                </th> <td>15805.495</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>17:43:23</td>     <th>  BIC                </th> <td>15851.143</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15821.491</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0188</td> <td>    0.015</td> <td>    1.251</td> <td> 0.211</td> <td>   -0.011</td> <td>    0.048</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.returns</th> <td>   -0.6785</td> <td>    0.087</td> <td>   -7.799</td> <td> 0.000</td> <td>   -0.849</td> <td>   -0.508</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.returns</th> <td>   -0.5088</td> <td>    0.139</td> <td>   -3.670</td> <td> 0.000</td> <td>   -0.780</td> <td>   -0.237</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L3.returns</th> <td>   -0.1141</td> <td>    0.015</td> <td>   -7.655</td> <td> 0.000</td> <td>   -0.143</td> <td>   -0.085</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.returns</th> <td>    0.6568</td> <td>    0.087</td> <td>    7.536</td> <td> 0.000</td> <td>    0.486</td> <td>    0.828</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L2.returns</th> <td>    0.4474</td> <td>    0.141</td> <td>    3.175</td> <td> 0.002</td> <td>    0.171</td> <td>    0.724</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>          -0.4929</td> <td>          -1.5100j</td> <td>           1.5884</td> <td>          -0.3002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th> <td>          -0.4929</td> <td>          +1.5100j</td> <td>           1.5884</td> <td>           0.3002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.3</th> <td>          -3.4749</td> <td>          -0.0000j</td> <td>           3.4749</td> <td>          -0.5000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>          -0.7340</td> <td>          -1.3025j</td> <td>           1.4951</td> <td>          -0.3317</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.2</th> <td>          -0.7340</td> <td>          +1.3025j</td> <td>           1.4951</td> <td>           0.3317</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   No. Observations:                 5020\n",
       "Model:                     ARMA(3, 2)   Log Likelihood               -7895.747\n",
       "Method:                       css-mle   S.D. of innovations              1.166\n",
       "Date:                Sun, 08 Sep 2019   AIC                          15805.495\n",
       "Time:                        17:43:23   BIC                          15851.143\n",
       "Sample:                    01-10-1994   HQIC                         15821.491\n",
       "                         - 04-05-2013                                         \n",
       "=================================================================================\n",
       "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "const             0.0188      0.015      1.251      0.211      -0.011       0.048\n",
       "ar.L1.returns    -0.6785      0.087     -7.799      0.000      -0.849      -0.508\n",
       "ar.L2.returns    -0.5088      0.139     -3.670      0.000      -0.780      -0.237\n",
       "ar.L3.returns    -0.1141      0.015     -7.655      0.000      -0.143      -0.085\n",
       "ma.L1.returns     0.6568      0.087      7.536      0.000       0.486       0.828\n",
       "ma.L2.returns     0.4474      0.141      3.175      0.002       0.171       0.724\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1           -0.4929           -1.5100j            1.5884           -0.3002\n",
       "AR.2           -0.4929           +1.5100j            1.5884            0.3002\n",
       "AR.3           -3.4749           -0.0000j            3.4749           -0.5000\n",
       "MA.1           -0.7340           -1.3025j            1.4951           -0.3317\n",
       "MA.2           -0.7340           +1.3025j            1.4951            0.3317\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ret_ar_3_ma_2 = ARMA(df.returns[1:], order=(3,2))\n",
    "results_ret_ar_3_ma_2 = model_ret_ar_3_ma_2.fit()\n",
    "results_ret_ar_3_ma_2.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(2, 3)</td>    <th>  Log Likelihood     </th> <td>-7895.587</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.166</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 08 Sep 2019</td> <th>  AIC                </th> <td>15805.174</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>17:43:54</td>     <th>  BIC                </th> <td>15850.823</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15821.170</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.015</td> <td>    1.276</td> <td> 0.202</td> <td>   -0.010</td> <td>    0.048</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.returns</th> <td>   -0.5605</td> <td>    0.090</td> <td>   -6.245</td> <td> 0.000</td> <td>   -0.736</td> <td>   -0.385</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.returns</th> <td>   -0.4187</td> <td>    0.193</td> <td>   -2.172</td> <td> 0.030</td> <td>   -0.797</td> <td>   -0.041</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.returns</th> <td>    0.5378</td> <td>    0.090</td> <td>    6.000</td> <td> 0.000</td> <td>    0.362</td> <td>    0.714</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L2.returns</th> <td>    0.3540</td> <td>    0.195</td> <td>    1.818</td> <td> 0.069</td> <td>   -0.028</td> <td>    0.736</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L3.returns</th> <td>   -0.1158</td> <td>    0.016</td> <td>   -7.369</td> <td> 0.000</td> <td>   -0.147</td> <td>   -0.085</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>          -0.6694</td> <td>          -1.3930j</td> <td>           1.5455</td> <td>          -0.3213</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th> <td>          -0.6694</td> <td>          +1.3930j</td> <td>           1.5455</td> <td>           0.3213</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>          -0.7270</td> <td>          -1.1772j</td> <td>           1.3836</td> <td>          -0.3381</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.2</th> <td>          -0.7270</td> <td>          +1.1772j</td> <td>           1.3836</td> <td>           0.3381</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.3</th> <td>           4.5096</td> <td>          -0.0000j</td> <td>           4.5096</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   No. Observations:                 5020\n",
       "Model:                     ARMA(2, 3)   Log Likelihood               -7895.587\n",
       "Method:                       css-mle   S.D. of innovations              1.166\n",
       "Date:                Sun, 08 Sep 2019   AIC                          15805.174\n",
       "Time:                        17:43:54   BIC                          15850.823\n",
       "Sample:                    01-10-1994   HQIC                         15821.170\n",
       "                         - 04-05-2013                                         \n",
       "=================================================================================\n",
       "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "const             0.0189      0.015      1.276      0.202      -0.010       0.048\n",
       "ar.L1.returns    -0.5605      0.090     -6.245      0.000      -0.736      -0.385\n",
       "ar.L2.returns    -0.4187      0.193     -2.172      0.030      -0.797      -0.041\n",
       "ma.L1.returns     0.5378      0.090      6.000      0.000       0.362       0.714\n",
       "ma.L2.returns     0.3540      0.195      1.818      0.069      -0.028       0.736\n",
       "ma.L3.returns    -0.1158      0.016     -7.369      0.000      -0.147      -0.085\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1           -0.6694           -1.3930j            1.5455           -0.3213\n",
       "AR.2           -0.6694           +1.3930j            1.5455            0.3213\n",
       "MA.1           -0.7270           -1.1772j            1.3836           -0.3381\n",
       "MA.2           -0.7270           +1.1772j            1.3836            0.3381\n",
       "MA.3            4.5096           -0.0000j            4.5096           -0.0000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ret_ar_2_ma_3 = ARMA(df.returns[1:], order=(2,3))\n",
    "results_ret_ar_2_ma_3 = model_ret_ar_2_ma_3.fit()\n",
    "results_ret_ar_2_ma_3.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.042"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LLR_test(model_ret_ar_2_ma_3, model_ret_ar_3_ma_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(3, 1)</td>    <th>  Log Likelihood     </th> <td>-7899.072</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.167</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 08 Sep 2019</td> <th>  AIC                </th> <td>15810.144</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>17:46:14</td>     <th>  BIC                </th> <td>15849.271</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15823.855</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.015</td> <td>    1.298</td> <td> 0.194</td> <td>   -0.010</td> <td>    0.047</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.returns</th> <td>   -0.5077</td> <td>    0.088</td> <td>   -5.769</td> <td> 0.000</td> <td>   -0.680</td> <td>   -0.335</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.returns</th> <td>   -0.0638</td> <td>    0.016</td> <td>   -4.023</td> <td> 0.000</td> <td>   -0.095</td> <td>   -0.033</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L3.returns</th> <td>   -0.1102</td> <td>    0.014</td> <td>   -7.850</td> <td> 0.000</td> <td>   -0.138</td> <td>   -0.083</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.returns</th> <td>    0.4839</td> <td>    0.088</td> <td>    5.500</td> <td> 0.000</td> <td>    0.311</td> <td>    0.656</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>          -1.5095</td> <td>          -0.0000j</td> <td>           1.5095</td> <td>          -0.5000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th> <td>           0.4653</td> <td>          -2.4076j</td> <td>           2.4521</td> <td>          -0.2196</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.3</th> <td>           0.4653</td> <td>          +2.4076j</td> <td>           2.4521</td> <td>           0.2196</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>          -2.0668</td> <td>          +0.0000j</td> <td>           2.0668</td> <td>           0.5000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   No. Observations:                 5020\n",
       "Model:                     ARMA(3, 1)   Log Likelihood               -7899.072\n",
       "Method:                       css-mle   S.D. of innovations              1.167\n",
       "Date:                Sun, 08 Sep 2019   AIC                          15810.144\n",
       "Time:                        17:46:14   BIC                          15849.271\n",
       "Sample:                    01-10-1994   HQIC                         15823.855\n",
       "                         - 04-05-2013                                         \n",
       "=================================================================================\n",
       "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "const             0.0189      0.015      1.298      0.194      -0.010       0.047\n",
       "ar.L1.returns    -0.5077      0.088     -5.769      0.000      -0.680      -0.335\n",
       "ar.L2.returns    -0.0638      0.016     -4.023      0.000      -0.095      -0.033\n",
       "ar.L3.returns    -0.1102      0.014     -7.850      0.000      -0.138      -0.083\n",
       "ma.L1.returns     0.4839      0.088      5.500      0.000       0.311       0.656\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1           -1.5095           -0.0000j            1.5095           -0.5000\n",
       "AR.2            0.4653           -2.4076j            2.4521           -0.2196\n",
       "AR.3            0.4653           +2.4076j            2.4521            0.2196\n",
       "MA.1           -2.0668           +0.0000j            2.0668            0.5000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ret_ar_3_ma_1 = ARMA(df.returns[1:], order=(3,1))\n",
    "results_ret_ar_3_ma_1 = model_ret_ar_3_ma_1.fit()\n",
    "results_ret_ar_3_ma_1.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.01"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LLR_test(model_ret_ar_3_ma_1, model_ret_ar_3_ma_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(2, 2)</td>    <th>  Log Likelihood     </th> <td>-7913.223</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.170</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 08 Sep 2019</td> <th>  AIC                </th> <td>15838.446</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>17:47:04</td>     <th>  BIC                </th> <td>15877.573</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15852.156</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.014</td> <td>    1.394</td> <td> 0.163</td> <td>   -0.008</td> <td>    0.045</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.returns</th> <td>    0.7820</td> <td>    0.238</td> <td>    3.284</td> <td> 0.001</td> <td>    0.315</td> <td>    1.249</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.returns</th> <td>   -0.1563</td> <td>    0.177</td> <td>   -0.884</td> <td> 0.377</td> <td>   -0.503</td> <td>    0.190</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.returns</th> <td>   -0.8105</td> <td>    0.239</td> <td>   -3.388</td> <td> 0.001</td> <td>   -1.279</td> <td>   -0.342</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L2.returns</th> <td>    0.1177</td> <td>    0.187</td> <td>    0.628</td> <td> 0.530</td> <td>   -0.250</td> <td>    0.485</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>           2.5017</td> <td>          -0.3737j</td> <td>           2.5295</td> <td>          -0.0236</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th> <td>           2.5017</td> <td>          +0.3737j</td> <td>           2.5295</td> <td>           0.0236</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>           1.6107</td> <td>          +0.0000j</td> <td>           1.6107</td> <td>           0.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.2</th> <td>           5.2740</td> <td>          +0.0000j</td> <td>           5.2740</td> <td>           0.0000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   No. Observations:                 5020\n",
       "Model:                     ARMA(2, 2)   Log Likelihood               -7913.223\n",
       "Method:                       css-mle   S.D. of innovations              1.170\n",
       "Date:                Sun, 08 Sep 2019   AIC                          15838.446\n",
       "Time:                        17:47:04   BIC                          15877.573\n",
       "Sample:                    01-10-1994   HQIC                         15852.156\n",
       "                         - 04-05-2013                                         \n",
       "=================================================================================\n",
       "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "const             0.0189      0.014      1.394      0.163      -0.008       0.045\n",
       "ar.L1.returns     0.7820      0.238      3.284      0.001       0.315       1.249\n",
       "ar.L2.returns    -0.1563      0.177     -0.884      0.377      -0.503       0.190\n",
       "ma.L1.returns    -0.8105      0.239     -3.388      0.001      -1.279      -0.342\n",
       "ma.L2.returns     0.1177      0.187      0.628      0.530      -0.250       0.485\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1            2.5017           -0.3737j            2.5295           -0.0236\n",
       "AR.2            2.5017           +0.3737j            2.5295            0.0236\n",
       "MA.1            1.6107           +0.0000j            1.6107            0.0000\n",
       "MA.2            5.2740           +0.0000j            5.2740            0.0000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ret_ar_2_ma_2 = ARMA(df.returns[1:], order=(2,2))\n",
    "results_ret_ar_2_ma_2 = model_ret_ar_2_ma_2.fit()\n",
    "results_ret_ar_2_ma_2.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(1, 3)</td>    <th>  Log Likelihood     </th> <td>-7896.838</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.167</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 08 Sep 2019</td> <th>  AIC                </th> <td>15805.676</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>17:47:41</td>     <th>  BIC                </th> <td>15844.803</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15819.386</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.014</td> <td>    1.332</td> <td> 0.183</td> <td>   -0.009</td> <td>    0.047</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.returns</th> <td>   -0.4699</td> <td>    0.096</td> <td>   -4.901</td> <td> 0.000</td> <td>   -0.658</td> <td>   -0.282</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.returns</th> <td>    0.4474</td> <td>    0.095</td> <td>    4.691</td> <td> 0.000</td> <td>    0.260</td> <td>    0.634</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L2.returns</th> <td>   -0.0637</td> <td>    0.015</td> <td>   -4.113</td> <td> 0.000</td> <td>   -0.094</td> <td>   -0.033</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L3.returns</th> <td>   -0.1182</td> <td>    0.014</td> <td>   -8.200</td> <td> 0.000</td> <td>   -0.146</td> <td>   -0.090</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>          -2.1282</td> <td>          +0.0000j</td> <td>           2.1282</td> <td>           0.5000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>          -1.4882</td> <td>          -1.1206j</td> <td>           1.8629</td> <td>          -0.3973</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.2</th> <td>          -1.4882</td> <td>          +1.1206j</td> <td>           1.8629</td> <td>           0.3973</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.3</th> <td>           2.4376</td> <td>          -0.0000j</td> <td>           2.4376</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   No. Observations:                 5020\n",
       "Model:                     ARMA(1, 3)   Log Likelihood               -7896.838\n",
       "Method:                       css-mle   S.D. of innovations              1.167\n",
       "Date:                Sun, 08 Sep 2019   AIC                          15805.676\n",
       "Time:                        17:47:41   BIC                          15844.803\n",
       "Sample:                    01-10-1994   HQIC                         15819.386\n",
       "                         - 04-05-2013                                         \n",
       "=================================================================================\n",
       "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "const             0.0189      0.014      1.332      0.183      -0.009       0.047\n",
       "ar.L1.returns    -0.4699      0.096     -4.901      0.000      -0.658      -0.282\n",
       "ma.L1.returns     0.4474      0.095      4.691      0.000       0.260       0.634\n",
       "ma.L2.returns    -0.0637      0.015     -4.113      0.000      -0.094      -0.033\n",
       "ma.L3.returns    -0.1182      0.014     -8.200      0.000      -0.146      -0.090\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1           -2.1282           +0.0000j            2.1282            0.5000\n",
       "MA.1           -1.4882           -1.1206j            1.8629           -0.3973\n",
       "MA.2           -1.4882           +1.1206j            1.8629            0.3973\n",
       "MA.3            2.4376           -0.0000j            2.4376           -0.0000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ret_ar_1_ma_3 = ARMA(df.returns[1:], order=(1,3))\n",
    "results_ret_ar_1_ma_3 = model_ret_ar_1_ma_3.fit()\n",
    "results_ret_ar_1_ma_3.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " ARMA(3,2): \tLL =  -7895.74745851493 \tAIC =  15805.49491702986\n",
      "\n",
      " ARMA(1,3): \tLL =  -7896.837893752797 \tAIC =  15805.675787505594\n"
     ]
    }
   ],
   "source": [
    "print(\"\\n ARMA(3,2): \\tLL = \", results_ret_ar_3_ma_2.llf, \"\\tAIC = \", results_ret_ar_3_ma_2.aic)\n",
    "print(\"\\n ARMA(1,3): \\tLL = \", results_ret_ar_1_ma_3.llf, \"\\tAIC = \", results_ret_ar_1_ma_3.aic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Residuals for Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['res_ret_ar_3_ma_2'] = results_ret_ar_3_ma_2.resid[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.res_ret_ar_3_ma_2.plot(figsize = (20,5))\n",
    "plt.title(\"Residuals of Returns\", size=24)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAETCAYAAAAs4pGmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvDW2N/gAAIABJREFUeJztnXucHFWV+L/d0zOZhMwkMDMhCSGBEDg8JIaHrj/eCuIuLj9kMWSB5aWI/FxFV5Zddnks4OIqu4gLgrICBhYiAroqStBFXiIioITI60gIScgLkiHJ5D2v/v1xqzI1nepndU9Xd5/v55P0VN1bVaduVd1z7znn3ptIp9MYhmEYRibJagtgGIZhxBNTEIZhGEYopiAMwzCMUExBGIZhGKGYgjAMwzBCMQVhGIZhhJKqtgAjjYh8DzjP2/ygqj5f4HF7ABcCfw7sD4wB3gNeBOYB96rqQMhxc4FzCxRvg6qOLzBv8BonAGcCRwMTcc91BfAb4E5VfTLP8ccD/wocDAwAT6rq/82R/zzgezlOOQhsBpYBTwDXqeqqAm+nrIjIEmAacLKq/qzAYx4ETgOuUdWrKyZc9utfDfwL8ENV/WSFrtEEXIn7FiYB64B/UNW7K3G9HHJcjbvXbAwAm4C3gPnA11V1QxmvPwqYrKpvleuc9URDKQgRGYP78H0uAPIqCBG5ALgZaMVVfiuAN4G9gI95/y4WkU+o6vIsp3kXeCPPpTbmkyVDrk7gHu/64CrlN4EmYB/gHOAcEfkRcK6qbgo5xz7Aw0ALsAZYivsYC2E78ELI/hSwB3CQ9+9MEfmQqv6pwPMaleefGaqYX8VVxMuqJw49wB9D9jfjvrNZ3r8zROSDqrom6gVF5KPArcB/At+Ker56pKEUBHAq0Ab8EjgR97J9WVU3ZztARL4O/APQB3wd+A9VXRtIPwn3gh0G/Mp7ecNaOPNV9bxy3YiITMD1EGYAy4HLgAdVdbuX3oJTEF8B/srtkmNVtTvjVJ/AKYc3gfep6rYixFitqkflkPFY4EGgE9fjOLKIc5eL43GVzNtVuHacOd37vU5Vr6iqJI4XVfW4bIki8lfAvThl8U3grDJc83Lc92NkodF8EOd4vw8AC3DK4vRsmUXkROBSXOvqTFW9LKgcAFT1YeBYYC2wH3B1+cUO5V7cy/0ycJiq3usrB0+uXlW9HTgC1yM4CLgl5Dxd3u/zRSqHvHimrS97m0eIyAHlPH+BMrypqq/nagQ0KP5z/3VVpSgQVf0R8FVvc7aItFdTnkahYRSEiEzCtSbB9SB+5P19QZb8SVz3MwHMVdUHs51bVVcCX/M2PyMiu5RF6CyIyJ8DJ+AU12xVfTeHbG8xdI9zPKUXxO9FbqcyzA/8PeIKwshKpZ97JfDfpWas5T8iNJKJ6Sycbf4lVV0mIg8A1+K1bFX1tYz8x+Ls+AA3FHD+uTg/w5Mj0Fr9f97vQ6r6er7MqvqYiDwFHANcBPwyxNF8roic6+VPlFHW4GRfO53XM5X9A3AyMBXYBvwB+HaYUhaRBPAp4G8AAXbDlfvTwI2ZQQe5nNQicirwJeD9npyPAf8UdhMichzwONCtqp0h6X8JPAQsVdW9MtLagc9597g/0I7zN/0R+G9cIMFg2HUzztMCfB7nR9sX1wNe6cl9QyHvgog8gXu3fR4XEYC7giZQz6TzWeADwC7AauBRnJN4mC8p4Gi+FOcHuxzowJktP6Gqi/LJVSD53qW9cabWE4HJuDJ+Fvde/CqQ7zjcs/S5WURuxgtKyBckICL/AVxCoMxEZC9cT/0VnFXiDuAQXCDLV1X1WyKSxpVPG/Bp3Ld4ANAPPAdcr6r/G3K944AvAjOBKcAG3DfyPVX9QbbCKgcN04MAzvZ+7wfwPqaXvH1hvYiPeL+rQpTHTqhqt6r+t6pW1NHn9Wz8D/yXRRz6E+/3RC+C5R2cD2OFt/9db/s35ZAzgB8UkCbDoS0ih+IqyUtwlfifgG5c2T8gInd6CiHIt4HbcWWwEWdiGwucAfxWRE4pRCgRuR7XizwG9xEvAU7Bfaj7FnWHua8zFRfp9m84P9VqT+Ym79rfxfVU850nAfwPrrHyQZxJ8zVgAu79/b2I/FkBIv0R94z7ve2Xve0/eddJisg9wA9xFe0mYCGwK04xv+QpjzBO8+5lAFeeY4HFBchUKP67tAVXEe9ARD6Gu7cLcWXyCrAV+DjwqIgEI6U24O65x9te7G2X49sdB/wCeB/O+T8e95yC/BfuuU8HXsfVwycAv8gsWxE5E/gVQ77Chbhe38eA+zxlVTEaQkGIyCyc9gW4L5D0fe/3HK91FmR/7/flSspWAtNwLyGER31kY4H3uwuwl6rO9xzMfnnMV9Wjcjmdi8GraD4B/Lu36z5VXRpIHwf8GPcx3w50qer7VXUGcBSuZXw+ruXkH3MQrlW7BjhYVUVVD8eFad6Kq3S/UYBsH8O1drfjTHTTVfUQnA9pGUPvSjm4EVcRPAXsqaoHedeaAPgf94UiMjHPeU7y/v0J2FtVD1TVQ3Et5R/jwq6/muN4AFT1C94z9gMpvuA9d//YK3C97Q24XtdUVf0AsLt3L63AvSLyvpDTfwjnQN5LVQ8ADi+kZ5QPEWn2Igkv9Xb9Z9Bf5rXe78e9218BdlXVQ1V1T5zS7wGu9t5HVPVFrwxe9E5xo1cGd0aVFdfC3wrs4z2fKbgens8uuPf6C0Cnqh6Gi/h7Etcr+krgvpK49zkJzFHVPVX1A959nYtrdP2dd/8VoVFMTL5z+neqGmzR3Idr2XXiXqQHAmn+eITMqJ9S2WHCycJPVPUTBZynI/D3e0VcP+in6MJ1/6MyUUSeDtm/Cy7axC/DX+Aq9iAXAnviPowLVXWH+UBVf+NVCA8D/yQit6hqH26cBsAzqvpKIP92EbkU1/JfKiJjw0J6A/yj9/u1oBlLVReLyGm4Fl9TrhsvBBFpBf4M9yF/Nhia6cl8Ga6iGIVrkKzOcTr/3ucHQ6lVdaOI/B2uzPOamPLIuwvw997mZ4MmOVXdCnxZRKbjvpUrgTkZp+gFrvSfZWZARx4OyfIuteFMvb5f7252HjdxKc5sd7eqXhVMUNWfeuV8q3fcj4uQqVT+w/cLqmrYN/pdVd0RVquqPSJyBS5g4EARaVfVHlwjYnfcGJVg3YSq3i0iR+B6aeOoEHWvIDxzyhneZrD3gKouFZHf4iJ9LmD4Q9ji/ZarjPKNg3i1wPMEK67eIq7fH/i7XD6GUWQPXV0D3Ak8oKqPhKT7A/HuCyqHAI/gPowJONPMswwptY97CuFeL0AAVd2CM4nkRETG4noo4MaQDENV3/D8NR/Od658eK3cKSIy2qtgM2nF3eNEXA8gF/69f0pEXgZ+5Fc+qrqEAu69AI7GVchryKiQAtyEUxB/ISJNOnxw6Mt5FHMu2sn+Li0D7sI972dC0k/2fr8fkgbuu78FmCUik7TygzZ/myf94ZB9Gvi7HdfrWYvrye0K3CEiN2Q0jC6KKmg+6l5B4D6cibgBbveHpH8fpyBOEJFpATOI35rbySFZIuUaB7Ei8PeuRRwX7HkU07LLxTCHrOeMPQcX0bUbsJ7sfpIDvd+LReRvsuTxzX4CPKuqz4vI/+DGs1wPXC8iC3E9lJ8BTxdg0piGi4LpJXsvaiFlUBA+qrrVMwMcgevl7I0LO57J0D3mM/f+BPgdrkfyXeA2EXked+8PqWrYgMVi2c/7XZijHP/g/bbhvqvg+xil4n1SvXEQnr+lExeMcSWuFf1WmHIQkTZcTxTgq15LPIwBXH23X0Q5CyHf+VeE7As2IJoAVLVfRK7CjbM6HzhfRN7GfVMPA494DaOK0QgKwjcvJYEVXsRGGEmcE87vvvqRGgeGZ98ZETkYeN0zh1SKVTjH4VhcBVPQVCG4SB1wPaNyOg534HWLvyUir+N6AF/GVcYXh2T349gLCX0NdqFn4yqOC3D3NNP7dynOvPRFVf3JzqfY6VxbsvRcwCm2suA5qf8T1+oO9txW4wYR/gUFKHpV7RWRD+Mc+ufiwjz/zPt3lYi8gjMLRQkyaPN+c43oD/YQ2jLSyjKOxnsua4BrvQrxTuDfRWRQVTN9TMHxEIcUcPqKmWMC5CuHfD3/He+Jqt4kIm/gvqXjcMrw096/jSJyvar+awRZc1LXTmqvRetHtazBae6wf/4Hcb7nGAL4ufc7wav4811rLC5K5z3PCVoRvC69XwGenCtvBn7eX2nInFHlRFUfxfl2AL4gIpm2anDhfuAcmYk8/24KnHtAVb+lqrNwYbHn43qBPbjewQ9F5LAc4q3zfseEREj5jM5xfLZjdjIRiZvaxY9AWYIL5/0IMElVJ6nqWRRRqarqVlX9V1XdF9er+hzOpr4N1yP5hbg5w0rFr/xzDUILVrClmpMKRlW/x5Ap8HrP7h4kGFLeWcC79NMiLl/ws64k6gJKPorrVZ2KM5ctwynor4jIF3MdH4W6VhDAJ3Ef+3ZAVHVK2D+GQmD3xJvXSF0YrO8X+HLmiUM4D2cuaAZ+X8Z7CMMfv3CyiORtNYnI4QzN13RbxaQazrUMRYDdKm7eqCC+PyZrD0JEjhOR/f0IMxFpF5EPisg0AFV9W1XnquqZOGXhh4/+dQ65luLehxay9w7DZPJ9OKOyHDMpZN8ncC39buADqvrvqvq4qq727qeV4aa/rIhIh4gcKSJdAKr6J1X9tqqe6l1jNc6RW0igQzZ8O/jMQEMpE1/5bsFFmo0EF+PurwmYK26CPQBUdT2u8QdZ3iURaRKRE0RkhueTzEcpz7rsiMgoEXmfF4WJqm5Q1R+r6udxZsq7vKzZTLSRqXcF4ZuXHlLVdTny/Zwhu2FwTMS1/nlEJNfsptOBa7zN7xYZvVE06gb9fB/3/H4gIpNzyDYZN9tsAnhMVX+eLW+ZZewDPoOL4NmNoZBOH1+OC8Na8iJyNG4w06u4ngE4v8PvCBnMpm7+K9/clrUS8Gy2/mCknca/eOX10ZBD/fdnFxGZEpIe9n7s5f0u053nwALXMPF9EPnMvffiBgN+OjNBVVcwFGsfJfrqaVxPrBNnygvjb73fXxXg7ykL3rf7JW9zX3Z+/r7TN5vT9izcM1+AM836+PJnvn/+s97JHu1ZJY7N3F8hTsWFss/L/Ea8svfDZyNH3GWjbhWE18o8xtu8K1deVe0P5DlZ3Ohe1I1SnIcrpx+JyLXBlrAX6/9XuA9rN5zf4p/LeiPZ+TxuoN++wO9E5K+DYzlEpEVE/pqhgV9LKM8EZwWjqs/i7MfgwnyPCSTfinOWH42L0NhhuvB6PH7E2U9U1e9tzPN+LxCRvwl+NOImBvQrteD0HmFci6scLhaRz/rn8ZTDD3HRRZm8zlBY8Q1e6x8RaRWRf2NoYGUQ3481U0R2mAMDcf3fDOQNu2YQ/94vl4zpUkRkNq4cBylu8OQwvAgkf9aA20Tk44FrtIrIN3CKsJfcU3SXHe9b9EdDXyYiwcGM1+PMbGeJyHX+s4Ed86n5IaXf1eETafomsmkMx3eGzxARXzEhIrvjAl2KCQ6Jws9w5u8DgBs9k6Uvy1SGQpLzve8lU7cKAtc6S+DCS8PCLDO5HdfabWb4+g3n44bN+/PnrxKRN7wIkrW4CmUSriL+sKoWNWV3qXghjkfhRgNPwfUo1orIiyKyAGfW+D5uEM7/Akf4po0R5jKGKtZvi0gzgBcnfhrOIXw+sFpEXvAccs/jBoAt9NLwjnkKN3CoCTdFxWoReV5E3sKtOzEW+C8Nma4giLrpOL6Iez++AywTkRdwUyXMYqiHETxmgKGJGE/HBTy8gDN9XEb4JI0/xpkbm4Cfisib3jHv4iKRtnr3iHe/ufhv3Ls2FudreNu79xW4SisFXKEFTLeRh+twynkc8DMRWSoiz3ky/x3OtHSeqr6Y4xyV4m9xymkUgYknVfVVnLVgO66B9q5XNktwUV5tuGlC/jHjfH7Zf8n7bv7JO9+LDM3VdqNXBi/i7P5HMzT4s6J4CvtsXL30Rdz7/qKIvIqLwDsY9359LftZolHPCsK3y83zegg5UdU3cZUMBLrx6mZFvQD4PzglsginEGbhXtaHcS3zI/yY/JFCVTep6mm4kMy7cR/xAbhBV+/gekXHq+qJIxD7nU3GtQyZBA5kqNXjV/gH46J83sY5WqfgutX/Ahzp2ZiD/D3O3/MErlKchas0HwE+qaqZA/KyyfUtXKv/EZyfaj/caOejGQrlzDzmZtzU6b/GmYb2w43G9ad8z8zfj4s8uRY39cNE3PNZhWupH8zQNBs5Aw68yJ4zcBXFszhH8izcN/w/uOf8b9nPUBieIjwTNwjuUVzlOhP3bt0KHKKq2cYbVBRVVYZ6OB8VkTMCaQ/gyuMOXINkJs5U9jzOPHWSqmZGD30N94304L6Z4Ojwv8ZFxr2MC7PdA6fwD2Woh1FxvIi8Y3EKa6Mn4x64d/Tvcd9IxRqliXQ6W6SfYRiG0cjUcw/CMAzDiIApCMMwDCMUUxCGYRhGKKYgDMMwjFBqcS6mUbhVrlbhJuAyDMMw8tOEi8B8ngKXmq1FBfEBamShdcMwjBhyNG5wb15qUUGsAli3bjODgzuH6HZ0jKW7u+JziJWEyVYaJltpmGylUa+yJZMJdt11FyhiuvNaVBADAIOD6VAF4afFFZOtNEy20jDZSqPOZSvYNG9OasMwDCMUUxCGYRhGKKYgDMMwjFBMQRiGYRih1KKT2jCMHAwOplm4uJvuBSvpGNvCzOkdJJPZVs80jOyYgjCMOmJwMM0NP1jA4pU99PYN0NLcxPTJ7VwyZ9aIKAlfOS17ZyNTd28z5VTjmIIwjDpi4eJuFq/sYXufi2Tc3jfA4pU9LFzczawZmcuCl5dqKyej/JgPwjDqiGXvbKS3b3iYe2/fAG+/U/mFDoPKKc1w5WTUJqYgDKOOmLp7Gy3Nw9ewb2luYs/d2yp+7WoqJ6MyRDIxiciZwBW4dZy/qaq3ZKTPwi3T2Y5bzvEiVe0XkaNxC7a34NYBPldV10WRxTAMmDm9g+mT23ntrXchkWJUS4rpk9uZOb2j4tf2ldP2gJIYKeVkVIaSexAisgdugfOjcGvBXigiB2Zkuwf4vKruh1sg/jPe/u8BZ6vqwcCruLVfjRIZHEyzYNFafvqbt1iwaG2spwkwKksymeCSObNg9RM0bXiJz55y0Ij5AHzlxGAfpNOM8nwQI6GcjMoQpQdxAvCYqr4HICIPAp/ELdCOiEwDRqvqs17+ucA1wLeBA1S1T0SacQtwL4wgR0NjjkEjk2QyQWLzclJ9qyvumM687iVzZnHBl/4ZWjr47EXnWRRTjRPFBzGZ4bMCrgKmFJLuKYeDgeXAh4H7IsjR0Jhj0IgTvnJKrHuJWTM6TTnUOFF6EEkgaMtIAIOFpqvqH4HdReSzwA+AI4q5eEfH2KxpXV3xtXmWW7buBStDHYPvbeot+lqNVG7lJI6ytbS4T7sashV67TiWm4/J5oiiIJbjFp7wmQiszEiflJkuIq3An6vqj7399wA3FHvx7u5Nobb2rq421qyJZ9REJWTrGNsS6hjcbWxLUddqtHIrF3GVrbe3n5aWVFVk6+3tB8h57biWG9SvbMlkImfDOvSYkq7keBQ4XkS6RGQMcBrwiJ+oqkuBbSJypLfrbGA+0AfcIiKHeftPp8DVjYydMcegUSwW1GAUSsk9CFVdISKXA4/jwlVvV9XnRORh4CpVfQE4C/iuiLQDfwBuUtUBEZkD/JeINAErgAsi30mDYo5BoxgsqMEohkjjIFR1HjAvY99Jgb9fAj4YctzTwGGZ+43S8B2DbF4+olErRu2RbSqOPy7uZta+5Xl3EgmABIlEboUTTM+TNS/pdO5eUHpHvuAxkCANCfd32su4rbefgcHBnfKHCRl+2cr1yLZ55ruRouHmYor6IuYj7EX06esfIJ1Ok2boZYS0y5tIBI4p/gXzj+jtH8zYX9i5Nm3pZXt/5kqEicjvejk+lZ7N29nWV/Aqie66JVw4PfRQ3DMKPp/MvP5/67awYUtvSGJlyXd//QNp6Btg3aZeL7874PVl64f5q8ApideWrWNy1y55z58mnff+evvcO7iqe/NO50t7b2TP9n56erZlnHuni+14f9PeAxlMB7YLIFe+Hd9GRp72zX1s6NmaQ7AQQfPuKQ8DiSSjm0p7v0uh4RREz5Y+1q7fmj9jDkp9ON2b+tjQs2XY2xOok4J/FP2CbdvuWhZLV/UM21/oedZv6WfDhmjlkpcSy23c1j42ZDyzQhVfoZT6TLf0DbJ+/ZayylIOevsHGATeCVTSAGNbUzSnkvQFGhLNqSRjW5vpXr+NctA34M69fuP2rHmaUik2bu7Nml5NBgbT9Gc0tOKCe+9HzhTYcAoCYHtvca3RctE/MEhfX2VePL9+GyjR4ZhOx3eh9nSaHS1HIxrTJ7UzqWMMS1eug2SKluYmJnWMYfqk9mqLZsQQm6zPMBqIZDLB6cfNoHf5Y/S/+3tOPmIvTj9uhjmojVBMQRg1y+BgmkUrNvDMy6tZtGJDbHtAcSOZTDC4cRn9a15kxh7jTDkYWWlIE5NR+wwOprn/iUWs6t5CX/8gzakkkzrGWGvYMMqI9SCMmmTxqp4dygGgr3+QVd1bWJzhpDcMo3RMQRg1ybvrtg6LxAGnJN5dV+FILMOoAr45df4zS1jwxsiNfjcTk1GTTNh1dGi45oRdR1dRKsMoP5nm1FEjOPrdehBGTeKHa6YH+kin0zt8EBauadQbmebUkZzS3xSEUZNYuKbRKISZU0dqrW9TEEbNYuGaRiPgm1ODjNRa36YgDMMwYkymOXUkp/Q3BWEYhhFjguZUul/kolMOGrHp2S2KyTAMI+b45lR6VzJr306bzdUwDCNODA6mWbyqh3fXbWXCrqOZPqm97v1ekRSEiJwJXAE0A99U1Vsy0mcBtwPtwFPARara7y1DeiNuJbpu4FPeEqWGYRixo1GndinZByEiewDXAUcBs4ALReTAjGz3AJ9X1f1wk5h/xtt/L3CBqs7y/r6pVDkMwzAqTaNO7RLFSX0C8Jiqvqeqm4EHgU/6iSIyDRitqs96u+YCs0VkFHCFqi709i8EpkaQwzCMBqFaM/g26tQuUUxMk4FVge1VDF9/Oix9iqpux/UsEJEkcDXw4whyGIbRAFTTzNOoU7tEURBJhi8imQAGC00XkRbgLk+GrxZ78Y6OsVnTurqyDyBJrNvC5t7qLSc4fvyYipw3lWqKfP5KyVYOsslWjvuOShzLLV+5VLLcCj13sdd+fcl7rM4w86zu3sK7PdvZf6/dShO2QNkObR/NS292s+jttZBIMcobqHboARNHzAfhl2tnZ+UHyO24ZoRjlwNHB7YnAisz0ieFpYvIWOCnOAf1KaraV+zFu7s3hXYvu7raWLMm+xD0jVv7qraG8PjxYyp27f5+t4xqqeevpGxRySVb1PuOSlzLrb9/gFSqqSrlVsi5Sym3xcvX05s55UT/IIuXr2fi+NbiBS1StlOP2pvrrr+fZGsHp80+nemT2unpGTkTU3//AKmmFGvXbiwpzDWZTORsWIceU/xldvAocLyIdInIGOA04BE/0YtK2uZFLAGcDcz3/r4HWATM8UxOhmEYOQmbcmIkzTyNOLVLyQpCVVcAlwOPAwuAear6nIg8LCKHe9nOAm4UkdeBscBNInIIcApwJPAHEVkgIg9HugvDMOoem8F35Ik0DkJV5wHzMvadFPj7JYY7rgFexPkjDMMwCsafcuK6678+zMzTCC35amFzMRmGUTM0opmnmpiCMAzDMEIxBWEYhmGEYgrCMAzDCMUUhGEYhhGKKQjDMAwjFFMQhmEYRii2YJBhGCOGv+hOz6Ju2kenbBxDzDEFYRjGiNCoi+7UMmZiMgxjRGjURXdqGVMQhmGMCI266E4tYwrCMIwRodqzsRrFYwrCMIwRwWZjrT1MQRiGMSL4s7H2Ln+MwbV/4OQj9jIHdcwxBWEYxojhz8Y62P2SzcZaA1iYq2FUAD/e/911W5mw62iL9zdqkkgKQkTOBK4AmoFvquotGemzgNuBduAp4CJV7Q+kfwUYUNWro8hhxJdGrCgt3t+oF0o2MYnIHsB1wFHALOBCETkwI9s9wOdVdT/cKnKf8Y4dJyJ3AJeUen0j/vgV5UPPLOHpP67ioWeWcP8TixgcLGHF9RrC4v2NeiGKD+IE4DFVfU9VNwMPAp/0E0VkGjBaVZ/1ds0FZnt/nwK8AdwQ4fpGzGnUitLi/Y16IYqCmAysCmyvAqYUkq6qd6vq14CBCNc3Yk6jVpQW72/UC1F8EEkgaCtIAINFpEeio2Ns1rSurrasaYl1W9jcWzYximb8+DEVOW8q1RT5/OWWbfqU8Tz32jv0BpRESyrJ9Cnji75WtvzluO+oZF770PbRvPRmN4veXguJFKOam9hz9zYOPWDiiPkg8pVLJcut0tceiWcex/fNv3ZnZ/b6rezXjHDscuDowPZEYGVG+qQc6ZHo7t4Uasvu6mpjzZqNWY/buLWP9eu3lEuMohg/fkzFrt3f7zpjpZ6/ErJNaB/FxI4xLF25DpIpWpqbmNgxhgnto4q6Vi7Zot53VLLJdupRe3Pd9feTbO3gtNmnM31SOz09I9dz6u8fIJVqqkq55Tt3Ptminj8qcX3f+vsHSDWlWLt2I+kS3HjJZCJnwzr0mOIvs4NHgeNFpEtExgCnAY/4iaq6FNgmIkd6u84G5ke4nlFjBAdG9b/7+4YaGOXH+/evedHi/Y2apWQFoaorgMuBx4EFwDxVfU5EHhaRw71sZwE3isjrwFjgpqgCG7WFVZSGUbtEGgehqvOAeRn7Tgr8/RLwwRzHXx3l+oZhGEblsKk2DMMwjFBsqg0jJ404EtowDIcpCCMrNmWEYRROPTamTEEYWck1EnrGHuOqLJ1RLeqxIoxKvTamTEEYWck1EtoURGNSrxVhVOq1MWVOaiMrNmWEkUmjzq+Vj3qdVsYUhJEVWyLSyKReK8Ko1GtjyhSEkZVGHglthFOvFWFU6rUxZQrCyImNhDaC1GtFGJV6bUyZgqhzBgfTLFqxgWdeXs2iFRvqfrEeo7LUa0VYDuqxMWVRTHW+eruEAAAZA0lEQVSMRZwYlcCvCAc3LmPGHp+ptjhGBbEeRB1jESeGYUTBFEQdYxEnhmFEwRREHWMRJ4ZhRMEURB1jESeGYUTBFEQdYxEnhmFEwRREnVOPoXeGYYwMkcJcReRM4AqgGfimqt6SkT4LuB1oB54CLlLVfhGZCtwDTAAUOEtVN0WRxTAMwygvJfcgRGQP4DrgKGAWcKGIHJiR7R7g86q6H5AA/KDpW4FbVXV/4AXgylLlKJTBwTQLFq3lF79bZgPGDMMwCiCRTpdWUYrIucAxqvppb/tKIKGq13rb04DHVHUfb/to4BrgY0A3sJvXm9gTeFJVpxd46b2At66781nW9WzfKbG5pYm+3oFh+9LpNMvXbGJr7wDptNNULc1NdI1vJZEYOZNLKpWkPyPstFwseetPAOy1935FpRUiWyHHlypbIVRStqiUKls6nWZb7wC9/YO0pJK0tjSV9V1c8tafSCQSTNtr36JlK/T82Y7Pd+58skW5djmI8r6VKlsh78OSt/5EMpFg//0PgBKq7V3bR3H5pz4EsDewpJBjopiYJgOrAturgA/mSZ8CdAI9qtqfsb8oUs1NNLc0haZl7u/Z3LtDOYAr297+AfoGBhnT2rwj35uLFIB9ZkjoeXOlRzm2HOkz9t0/dH++tKjnjnp8Je876vkrJVs6nWZ191a2bu8DEiSTCUY1NzGxY8ywSiGKbPnKpZLPtJrXznd8pd+3UmQr9H2Yse/+pJqSNDeH13v5SJVwXBQFkWS4HksAgwWkZ+4n47iCuOCkA0LNRF1dbaxZs3HYvp/+5i3eXj18XzoN++4xniPeN3HHvmt+eQMAsz99Uug1c6UXcmwq1VTSuQtJj0I+2Qo5HkqTLWq55WJwMM11v32AZGsHh8w4MnTls0o+02wsWrGBh9YsIZFwFt50GgYG0xy6b9ewxWWiyAYwfvwY1q/fUpRsxZw/Crlki3rtajzTKLIV+j4ATNtzPGOaEpRi+CklQCVKFNNyYFJgeyKwsoD0d4FxIuKrs0kZx5Wdqbu30ZKhPW3AWH3jz0PVMuUjpCYcxkPPLOH+JxbFwvdkI9yNIHF+H6IoiEeB40WkS0TGAKcBj/iJqroU2CYiR3q7zgbmq2of8Gtgjrf/HGB+BDnyMnN6B9MntzPKUxI2YKz+8eehSjQ1k0gkYjUPlY1wN4LE+X0o2cSkqitE5HLgcaAFuF1VnxORh4GrVPUF4CzguyLSDvwBuMk7/HPAXSJyBbAMOCPKTeQjmUxwyZxZLFzczaIVG2htbtrJ3DA4mCbZNpVkaweLVmywhdhrnDivp+2PcM+cZdcaLI1JnN+HSOMgVHUeMC9j30mBv19iuOPa378UOC7KtYslmUwwa0Yn++wxjhXvDh9yETRHkEzx0DNLbFrsGsdvlQWVRFxaZf4I98Wrenh33VYm7DraGiQNTJzfB1sPguHmCBg+LXa1W5tGacS5VQauUpixxzh7vwwgvu+DKQjibY4wSiPOrTLDqBVMQRBvc4RROnFtlRlGrWCT9TFkjvAjCeJmjjAMw6gG1oMg/uYIi7AyjNqnFr9jUxAecTVHWISVYdQ+tfodm4kp5sR5wJdhGIVRq9+xKYiYE+dh+IZhFEatfsemIGJOnIfhR8W3yaa6DrE1Ooy6pla/Y1MQMadeI6ziPJmeYZSbWv2OzUkdc+IeYVUqNnrdaCRq9Ts2BVEDxDXCKgo2et1oNGrxOzYTk1EVatUmGwfMd2OMFKYgjKpQqzbZamO+G2MkMROTURVq1SZbbcx3Y4wkpiCMqlGLNtlqY74bYyQpWUGIyFTgHmACoMBZqropI08LcAdwOLAVOFNVXw+kHwzcp6oHlSqHYTQSNvOwMZJE8UHcCtyqqvsDLwBXhuS5GNisqgcAXwLm+gkicg5uDetdIshg1DE7JjfreL85Yz3Md2OMJCX1IESkGTgG+IS3ay7wJPCPGVk/DlwFoKpPiUiX1/PYAJyCW4v67lJkMOqbWp3crNKY78YYSUo1MXUCPara722vAqaE5JvspRHMp6rLgNNEZK8Sr2/UOXF3xu7o3YzpHPGpm813Y4wUeRWEiMwGbszY/QaQ2d8fZGeSGfkSWfIVTUfH2KxpXV1tWdMS67awubc0EVKpJgDGjx9TVFo50itJ1GtXQvaeRd2hztiebf1lvU4pz3RwMM33fvYKLXt+BBIpfvbMEvbcvY3z//KgsiqJcpRrnJ5pJpX6Fir5ncaBzs7s9Vu5yasgVPUB4IHgPs/E1C0iTao6AEwCVoYcvtxLe9PbnpglX9F0d28KtUl3dbWxZs3GrMdt3NrH+vVbSrpmf/8AQOjxudL89FSqKWd6ruMrST7ZCjkeyit7++hUqDO2vTVV1uuU8kwXrdjAsnc2kki63k1v/yDL3tnIH15bXdZWfdRyHT9+TKyeaZBcskW9diW/02ozrq2FtWs3ki7BHZdMJnI2rEOPKf4yoKp9wK+BOd6uc4D5IVkf9tIQkaOAbZ55yTByEmdnbK1O3WwYxRJlHMTngLtE5ApgGc7hjIhcBExW1auAm4HbROQVYDtwdkR5jTJTTVt6LoLO2J5t/bS3pmIjm4WaGo1CyQpCVZcCx4Xs/07g723AuTnOsQTYq1QZjGiUI1Kokuvs+s7YKKaSSuD3blZ1b6GvfzBWvRvDKCc2krpAanHB8XxEjRRq1FDUOPduDKOcmIIogHqtCKNO2xD3UNRKEtfejWGUE5vNtQBqdcHxfESdctuctYZR35iCKIB6rQijRgrZmg6GUd+YiakA6jVqJaot3Zy1hlHfmIIogHquCKPY0m1eIMOob0xBFIBVhNmxeYEMo34xBVEgVhEahtFomJPaMAzDCMUUhGEYhhGKKQjDiCH+yP1U1yG2mp5RNcwHYRgxo15H7hu1h/UgDCNm1OvIfaP2MAVhGDGjXkfuG7WHKQjDiBk2hYkRF0xBGEbMiPNqekZjUbKTWkSmAvcAEwAFzlLVTRl5WoA7gMOBrcCZqvq6iIwF7gT2BxLAdap6X6my1Dr1uNaEUTo2ct+IC1F6ELcCt6rq/sALwJUheS4GNqvqAcCXgLne/suAZao6Ezge+IaI7B5BlpolGLGSmnAYDz2zhPufWGRhjQ2OP3L/iPdNZMYe40w5jAA7Gmod77fQYo+SFISINAPHAA96u+YCs0Oyfhy4F0BVnwK6vJ7Hk8BN3v53gfeAiaXIUutYxIphVJ9gQy3Zeag11DxK7UF0Aj2q2u9trwKmhOSb7KURzKeq/6uqywBE5HRgFPBKibLUNBaxYhjVxxpq4eT1QYjIbODGjN1vAJmqdZCdSWbkSwTzeef+T+DPA8qmIDo6xmZN6+pqy5qWWLeFzb1hokYjlWoCYPz4MUWlT58ynudee4fegJJoSSWZPmV81nNVipG+XjFUSrZczy3fM/Wpx3Ir9N6jUOy3UiilPNOeRd2hDbWebf2xe76dndnrt3KTV0Go6gPAA8F9nompW0SaVHUAmASsDDl8uZf2prc90c8nIl8ALgVOVNU/Fit4d/em0O5fV1cba9ZszHrcxq19FVlDuL9/ACDrufv7B0ilmnZKn9A+iokZa01M7BjDhPZRI7rWcZzXVq6kbLmeW75nWmnZohJFtkLuPQq5ZIt67VKeafvoVOiiYO2tqVg933FtLaxdu5F0CZavZDKRs2EdRklRTKraJyK/BuYA84BzgPkhWR/20p4WkaOAbaq6TEQ+AfwdcKSqvl2KDPWCRawYcaMRo+rqeVGwKESZi+lzwF0icgWwDDgDQEQuAiar6lXAzcBtIvIKsB042zv2GmA08JCI+Oe7QFVfiCBPzWJrTRhxoVHngYq6/G69UrKCUNWlwHEh+78T+HsbcG5InveXel3DMCpH0FkLDHPW1nsDJsryu/WKjaQ2DGMHFlVnBDEFYRjGDmweKCOIKQjDCKFRF+yxeaCMILZgkGFk0KiOWrCoOmM4piAMI4NGdtSCRdUZQ5iJyTAyMEetYThMQRhGBuaoNQyHKQjDyMActYbhMB+EYWRgjlrDcJiCKAONOHdNvWOOWsMwBRGZRg6JNAyjvjEfRERsoRHDMOoVUxARsZBIwzDqFVMQEbGQSMMw6pWG80EkEgnGjmkp2/lm7tPJgjfWsnzNJnr7B2lJJdmjaxfeN71jyAeRTtOUTJBMQOuopmGrQYWtDJXeaTVXdl7gtUjyHd6UTJBKhbQXYjAFUVMyQaqpMH9OqLg57sE/a1MyMZQtHf4MSlnFyzBqmYZTEG2jm2kf01zWc15x7uEsfLObZe9sZOrubczcp2MnB3VrS4rm5iamT3ZRMelAbZNmqPIJVkKJHakFknDHByu6jD+yMn7XXVi/buh1KLkyTJTmmM91vV3Hj2ZdQc+s+Eq9tcXd89RJ3jq/aacoEqQZPj9f5tLqjrb2Vtpbi/2MImiaROGHt7WPpq21yWUf+m94AyUgTjqksHbKm5FYiCjpwIn8/O1to2gKXcaeHT3y3ca1esek3eGBb2SQ7IKlkknSwNhdWoYp+3TaNQQAxrSmGEzvXB7+9Vuamwq4s3AKK5XSSDCygS8NpyDS6XRFWoIz9+lg5j4dO7YzZ//0P75ss4L6j33n+rW4F2LY8Ymd/shKa0uKpmQ8LY6jW5vZ1LStgJzFfzx+eY1KlVYh7NrWSv+2vpKOrTS7tbcysD0esmW+152dbYzK8rq1eApi92Fm2sKf7agW9yynTth5/WW/QbBXxqDHoHLcdbexrHuvObSaz1d3VLqXudtuu7B+3ebKXiRAyQpCRKYC9wATAAXOUtVNGXlagDuAw4GtwJmq+rqIjAXuAvYFBoBLVfXRUmUxDCPehJpSs1SmYb3pYnpduRpj+Rpq4JkbsyTnU1MldqALJtPfWWmiXO1W4FZV3R94AbgyJM/FwGZVPQD4EjDX238J8IaqzsStZX13BDkMwzCMClCSghCRZuAY4EFv11xgdkjWjwP3AqjqU0CXiExV1WuAK7w8ewPrSpHDMAzDqBylmpg6gR5V7fe2VwFTQvJN9tLIyLdMVftF5BfA8cCFxQrQ0bGzfdGnq6ut2NNVnBbP9hlH2XwaUbZyPJdGLLdykE22KM9kYDBN07hppFt24601mzls/913OKaLOXctllslyKsgRGQ2cGPG7jfY2SgYFpKQzMiXCOZT1Y+JyDTgGRH5raq+VpDUQHf3plA7YldXG2vWbCz0NCNGb28/LS2pWMoG8S03qKxsvb2ujVPq+Ru13KKSS7ZSn8ngYJobfrCA/s6jIZHi+rtfYPrkdi6ZM2tHVGEh567VcstHMpnI2bAOPSZfBlV9QFWnBP8BJwLjRMQP/ZgErAw5fLmX5jMRWCkix4rIJO/8S4FngIOKktwwDCPAwsXdLF7ZA8lmSCTY3jfA4pU9LFzcXW3RapaSfBCq2gf8Gpjj7ToHmB+S9WEvDRE5CtimqstwvonLvP2TgA8Az5cii2EYBsCydzbS2zcwbF9v3wBvvxPP3kAtECWK6XPAhSLyKnA0ntNZRC4SkWu9PDcDo0TkFeAm4Gxv/1eASSLyR5wS+ZLXkzAMwyiJqbu37TTAraW5iT13j68/Ie6UPA7Cq9CPC9n/ncDf24BzQ/JsBE4v9dqGYRiZzJzewfTJ7Sxe2UNv3wAtzU1Mn9zOzOkd+Q82Qmm4kdSGYdQnyWSCS+bMYuHibt5+ZyN77t7GzOk7T3tjFI4pCMMw6oZkMsGsGZ3MmtFZbVHqgnhOvmMYhmFUHVMQhmEYRiimIAzDMIxQTEEYhmEYoZiCMAzDMEIxBWEYhmGEYgrCMAzDCMUUhGEYhhGKKQjDMAwjFFMQhmE0BIODadK7TCG92/tZsGhtznWpDYcpCMMw6h5/MSEmHge7HcJtP3mFG36wwJREHkxBGIZR99hiQqVhCsIwjLrHFhMqDVMQhmHUPbaYUGmUPN23iEwF7gEmAAqcpaqbMvK0AHcAhwNbgTNV9fVAegq3dOltqjq3VFkMw6gPfEcyozpYsGht2dZzsMWESiPKehC3Areq6n0iciVwJfCPGXkuBjar6gEicgwwF/hQIP0qYL8IMhiGUScMcyQnUtz2k1eYPrmdS+bMiqwkbDGh0ijJxCQizcAxwIPerrnA7JCsHwfuBVDVp4Aur+eBiBwBvB94qBQZDMOoLyrtSPYXEzr5yL2ZNaPTlEMBlOqD6AR6VLXf214FTAnJN9lLI5hPRNqBG4ELS7y+YRh1hjmS40deE5OIzMZV5kHeADIDiAdDDk9m5Et4+W4Bvqqq74hI4dIG6OgYmzWtqyt+jqeWFlfUcZTNpxFlK8dzacRyKweZsh283wQe+d0ytvUOKYlRLU28b78JI34ftVRulSSvglDVB4AHgvs8E1O3iDSp6gAwCVgZcvhyL+1Nb3sirhdxPHCwiFwDTAU+IiJ9qnpvoYJ3d28KHeTS1dXGmjXxa3H09vbT0pKKpWwQ33KDysrW2+s6waWev1HLLSphsk3rGMPek4Y7kvee1M60jjEjeh+1Vm6FkkwmcjaswyjJSa2qfSLya2AOMA84B5gfkvVhL+1pETkK2KaqS3GmJwBEZC7wRDHKwTCM+sMcyfEjShTT54C7ROQKYBlwBoCIXARMVtWrgJuB20TkFWA7cHZEeQ3DqGN8R/KsGZ3VFsUggoLwegLHhez/TuDvbcC5ec5zXqkyGIZhGJXDRlIbhmEYoZiCGAH80aH94w62aYYNw6gZTEFUmODo0IFx77dphg3DqBlMQVQYm2bYMIxaxRREhbHRoYZh1CqmICqMTTNsGEatYgqiwvjTDI9qbiIBjLJphmODrVFsGLmJMlDOKIDg6ND3NvWy29gWGx0aAyo5tbRh1AumIEYAf3RonOd4aTSGBQ/AsOABG8VrGA4zMRkNiQUPGEZ+TEEYDYkFDxhGfkxBGA2JBQ8YRn7MB2E0JDa1tGHkxxSE0bDY1NKGkRszMRmGYRihmIIwDMMwQjEFYRiGYYRiCsIwDMMIpRad1E1AzmiTOEeimGylYbKVhslWGvUoW+C4plz5giTS6ZqboOwo4NfVFsIwDKNGORp4upCMtaggRgEfAFYBA3nyGoZhGI4mYBLwPLC9kANqUUEYhmEYI4A5qQ3DMIxQTEEYhmEYoZiCMAzDMEIxBWEYhmGEYgrCMAzDCMUUhGEYhhGKKQjDMAwjlFqcaiMrInImcAXQDHxTVW+pskg7EJHHgQlAn7frs6r6uyrK0w48A/ylqi4RkROAbwCjgR+o6hUxku17uBH0m70s16jq/1RBrn8BTvc2f66q/xCXcssiWyzKzZPvWuCTQBq4Q1W/EaOyC5MtTmX3H0Cnqp4nIrOA24F24CngIlXtr9S160ZBiMgewHXAYbhRgs+IyOOq+mp1JQMRSQD7AdMq+TCLkOfPgO/iZEJERgN3AscCbwM/F5G/UNX51ZbN43DgGFVdNdLy+HiV2YnAIbiK5BEROQP4OlUutyyynUoMys2T71jgI8BMXOPtVRH5FTF457LI9nPiU3bHA+cCP/d23QNcoKrPisgdwGeAb1fq+vVkYjoBeExV31PVzcCDuFZBHBDv95ci8pKIfL6q0riX6m+Bld72B4E3VPUtT4HdA8yOg2wiMgaYCtwpIgtF5BoRqcZ7uwq4RFV7VbUPeA2nxOJQbmGyTSUe5YaqPgl82CujCbiG6XhiUHZZZNtKDMpORHbDNXq/6m1PA0ar6rNelrlUuMzqSUFMxn0oPquAKVWSJZNdgV8BpwLHAxeJyEerJYyqXqCqwQkPY1N2IbJNBB4DPgV8CDfR2KerINcr/ocpIvvizDmDxKDcssj2CDEot4CMfSJyDfAq7luI0zuXKVsz8Si724DLgXXe9oiXWT0piCSue+2TwH3AVUdVf6uq56jqBlVdC9wBnFRtuQLEuewWq+qpqrpKVbcAN1PFshORg4D/BS4FFhOjcgvKpo7YlBuAqv4L0AXsiet9xabsMmQ7vtplJyIXAG+r6q8Cu0f8O60nBbEcN1Ohz0SGTChVRUSO8myJPgmGnNVxIM5ld7CInBbYVbWyE5EjcS3My1T1LmJUbpmyxazc9vecq3gV7o+A44hB2WWRbU4Mym4OcKKILACuBf4vcAEjXGZ146QGHgWuFpEuXOTBacCF1RVpB+OBa0XkCFz39VzgouqKNIzfASIiM4C3gDNxDsQ4kAC+KSKPAZtwz/SukRZCRPYEfgzMUdXHvN2xKLcsssWi3DymA9eIyFG4FvApOPPJv1e77LLI9iRVLjtV3WGCFpHzgONU9XwReVlEjlTV3wBnAxV16tdND0JVV+DsdY8DC4B5qvpcdaVyqOrPcFEILwK/B+5U1d9WV6ohVHUbcB7wQ5wd9nWck7/qqOpC4N+A3+BkW6Cq36+CKH8PtALfEJEFXsvuPOJRbmGyHUE8yg1VfZjh7/8zqnofMSi7LLJdS0zKLoSzgBtF5HVgLHBTJS9m60EYhmEYodRND8IwDMMoL6YgDMMwjFBMQRiGYRihmIIwDMMwQjEFYRiGYYRiCsIwDMMIxRSEYRiGEYopCMMwDCOU/w9Vg4aM+o4jdQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sgt.plot_acf(df.res_ret_ar_3_ma_2[2:], zero = False, lags = 40)\n",
    "plt.title(\"ACF Of Residuals for Returns\",size=24)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reevaluating Model Selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(5, 5)</td>    <th>  Log Likelihood     </th> <td>-7882.160</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.163</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 08 Sep 2019</td> <th>  AIC                </th> <td>15788.321</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>17:52:26</td>     <th>  BIC                </th> <td>15866.575</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15815.742</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.013</td> <td>    1.402</td> <td> 0.161</td> <td>   -0.008</td> <td>    0.045</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.returns</th> <td>   -0.0684</td> <td>    0.140</td> <td>   -0.490</td> <td> 0.624</td> <td>   -0.342</td> <td>    0.205</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.returns</th> <td>   -0.6722</td> <td>    0.146</td> <td>   -4.603</td> <td> 0.000</td> <td>   -0.958</td> <td>   -0.386</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L3.returns</th> <td>   -0.1152</td> <td>    0.141</td> <td>   -0.817</td> <td> 0.414</td> <td>   -0.392</td> <td>    0.161</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L4.returns</th> <td>    0.1779</td> <td>    0.129</td> <td>    1.381</td> <td> 0.167</td> <td>   -0.075</td> <td>    0.430</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L5.returns</th> <td>    0.1215</td> <td>    0.107</td> <td>    1.132</td> <td> 0.258</td> <td>   -0.089</td> <td>    0.332</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.returns</th> <td>    0.0443</td> <td>    0.138</td> <td>    0.322</td> <td> 0.748</td> <td>   -0.226</td> <td>    0.314</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L2.returns</th> <td>    0.6223</td> <td>    0.144</td> <td>    4.321</td> <td> 0.000</td> <td>    0.340</td> <td>    0.905</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L3.returns</th> <td>    0.0107</td> <td>    0.136</td> <td>    0.079</td> <td> 0.937</td> <td>   -0.256</td> <td>    0.277</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L4.returns</th> <td>   -0.1753</td> <td>    0.122</td> <td>   -1.436</td> <td> 0.151</td> <td>   -0.415</td> <td>    0.064</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L5.returns</th> <td>   -0.2240</td> <td>    0.104</td> <td>   -2.148</td> <td> 0.032</td> <td>   -0.428</td> <td>   -0.020</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>           0.0870</td> <td>          -1.0364j</td> <td>           1.0401</td> <td>          -0.2367</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th> <td>           0.0870</td> <td>          +1.0364j</td> <td>           1.0401</td> <td>           0.2367</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.3</th> <td>           1.7715</td> <td>          -0.0000j</td> <td>           1.7715</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.4</th> <td>          -1.7050</td> <td>          -1.1784j</td> <td>           2.0726</td> <td>          -0.4038</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.5</th> <td>          -1.7050</td> <td>          +1.1784j</td> <td>           2.0726</td> <td>           0.4038</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>           0.1033</td> <td>          -1.0434j</td> <td>           1.0485</td> <td>          -0.2343</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.2</th> <td>           0.1033</td> <td>          +1.0434j</td> <td>           1.0485</td> <td>           0.2343</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.3</th> <td>           1.4855</td> <td>          -0.0000j</td> <td>           1.4855</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.4</th> <td>          -1.2373</td> <td>          -1.0965j</td> <td>           1.6532</td> <td>          -0.3846</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.5</th> <td>          -1.2373</td> <td>          +1.0965j</td> <td>           1.6532</td> <td>           0.3846</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   No. Observations:                 5020\n",
       "Model:                     ARMA(5, 5)   Log Likelihood               -7882.160\n",
       "Method:                       css-mle   S.D. of innovations              1.163\n",
       "Date:                Sun, 08 Sep 2019   AIC                          15788.321\n",
       "Time:                        17:52:26   BIC                          15866.575\n",
       "Sample:                    01-10-1994   HQIC                         15815.742\n",
       "                         - 04-05-2013                                         \n",
       "=================================================================================\n",
       "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "const             0.0189      0.013      1.402      0.161      -0.008       0.045\n",
       "ar.L1.returns    -0.0684      0.140     -0.490      0.624      -0.342       0.205\n",
       "ar.L2.returns    -0.6722      0.146     -4.603      0.000      -0.958      -0.386\n",
       "ar.L3.returns    -0.1152      0.141     -0.817      0.414      -0.392       0.161\n",
       "ar.L4.returns     0.1779      0.129      1.381      0.167      -0.075       0.430\n",
       "ar.L5.returns     0.1215      0.107      1.132      0.258      -0.089       0.332\n",
       "ma.L1.returns     0.0443      0.138      0.322      0.748      -0.226       0.314\n",
       "ma.L2.returns     0.6223      0.144      4.321      0.000       0.340       0.905\n",
       "ma.L3.returns     0.0107      0.136      0.079      0.937      -0.256       0.277\n",
       "ma.L4.returns    -0.1753      0.122     -1.436      0.151      -0.415       0.064\n",
       "ma.L5.returns    -0.2240      0.104     -2.148      0.032      -0.428      -0.020\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1            0.0870           -1.0364j            1.0401           -0.2367\n",
       "AR.2            0.0870           +1.0364j            1.0401            0.2367\n",
       "AR.3            1.7715           -0.0000j            1.7715           -0.0000\n",
       "AR.4           -1.7050           -1.1784j            2.0726           -0.4038\n",
       "AR.5           -1.7050           +1.1784j            2.0726            0.4038\n",
       "MA.1            0.1033           -1.0434j            1.0485           -0.2343\n",
       "MA.2            0.1033           +1.0434j            1.0485            0.2343\n",
       "MA.3            1.4855           -0.0000j            1.4855           -0.0000\n",
       "MA.4           -1.2373           -1.0965j            1.6532           -0.3846\n",
       "MA.5           -1.2373           +1.0965j            1.6532            0.3846\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ret_ar_5_ma_5 = ARMA(df.returns[1:], order=(5,5))\n",
    "results_ret_ar_5_ma_5 = model_ret_ar_5_ma_5.fit()\n",
    "results_ret_ar_5_ma_5.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(5, 1)</td>    <th>  Log Likelihood     </th> <td>-7889.311</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.165</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 08 Sep 2019</td> <th>  AIC                </th> <td>15794.623</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>17:52:51</td>     <th>  BIC                </th> <td>15846.792</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15812.903</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.013</td> <td>    1.407</td> <td> 0.159</td> <td>   -0.007</td> <td>    0.045</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.returns</th> <td>    0.3440</td> <td>    0.131</td> <td>    2.624</td> <td> 0.009</td> <td>    0.087</td> <td>    0.601</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.returns</th> <td>   -0.0458</td> <td>    0.015</td> <td>   -3.005</td> <td> 0.003</td> <td>   -0.076</td> <td>   -0.016</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L3.returns</th> <td>   -0.0652</td> <td>    0.016</td> <td>   -4.010</td> <td> 0.000</td> <td>   -0.097</td> <td>   -0.033</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L4.returns</th> <td>    0.0741</td> <td>    0.018</td> <td>    4.068</td> <td> 0.000</td> <td>    0.038</td> <td>    0.110</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L5.returns</th> <td>   -0.0813</td> <td>    0.014</td> <td>   -5.688</td> <td> 0.000</td> <td>   -0.109</td> <td>   -0.053</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.returns</th> <td>   -0.3673</td> <td>    0.131</td> <td>   -2.801</td> <td> 0.005</td> <td>   -0.624</td> <td>   -0.110</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>          -1.6158</td> <td>          -0.0000j</td> <td>           1.6158</td> <td>          -0.5000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th> <td>           1.3793</td> <td>          -0.8613j</td> <td>           1.6261</td> <td>          -0.0888</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.3</th> <td>           1.3793</td> <td>          +0.8613j</td> <td>           1.6261</td> <td>           0.0888</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.4</th> <td>          -0.1156</td> <td>          -1.6929j</td> <td>           1.6968</td> <td>          -0.2608</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.5</th> <td>          -0.1156</td> <td>          +1.6929j</td> <td>           1.6968</td> <td>           0.2608</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>           2.7223</td> <td>          +0.0000j</td> <td>           2.7223</td> <td>           0.0000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   No. Observations:                 5020\n",
       "Model:                     ARMA(5, 1)   Log Likelihood               -7889.311\n",
       "Method:                       css-mle   S.D. of innovations              1.165\n",
       "Date:                Sun, 08 Sep 2019   AIC                          15794.623\n",
       "Time:                        17:52:51   BIC                          15846.792\n",
       "Sample:                    01-10-1994   HQIC                         15812.903\n",
       "                         - 04-05-2013                                         \n",
       "=================================================================================\n",
       "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "const             0.0189      0.013      1.407      0.159      -0.007       0.045\n",
       "ar.L1.returns     0.3440      0.131      2.624      0.009       0.087       0.601\n",
       "ar.L2.returns    -0.0458      0.015     -3.005      0.003      -0.076      -0.016\n",
       "ar.L3.returns    -0.0652      0.016     -4.010      0.000      -0.097      -0.033\n",
       "ar.L4.returns     0.0741      0.018      4.068      0.000       0.038       0.110\n",
       "ar.L5.returns    -0.0813      0.014     -5.688      0.000      -0.109      -0.053\n",
       "ma.L1.returns    -0.3673      0.131     -2.801      0.005      -0.624      -0.110\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1           -1.6158           -0.0000j            1.6158           -0.5000\n",
       "AR.2            1.3793           -0.8613j            1.6261           -0.0888\n",
       "AR.3            1.3793           +0.8613j            1.6261            0.0888\n",
       "AR.4           -0.1156           -1.6929j            1.6968           -0.2608\n",
       "AR.5           -0.1156           +1.6929j            1.6968            0.2608\n",
       "MA.1            2.7223           +0.0000j            2.7223            0.0000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ret_ar_5_ma_1 = ARMA(df.returns[1:], order=(5,1))\n",
    "results_ret_ar_5_ma_1 = model_ret_ar_5_ma_1.fit()\n",
    "results_ret_ar_5_ma_1.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(1, 5)</td>    <th>  Log Likelihood     </th> <td>-7890.973</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.165</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 08 Sep 2019</td> <th>  AIC                </th> <td>15797.947</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>17:53:13</td>     <th>  BIC                </th> <td>15850.116</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15816.228</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.013</td> <td>    1.419</td> <td> 0.156</td> <td>   -0.007</td> <td>    0.045</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.returns</th> <td>    0.3285</td> <td>    0.152</td> <td>    2.159</td> <td> 0.031</td> <td>    0.030</td> <td>    0.627</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.returns</th> <td>   -0.3534</td> <td>    0.152</td> <td>   -2.332</td> <td> 0.020</td> <td>   -0.650</td> <td>   -0.056</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L2.returns</th> <td>   -0.0404</td> <td>    0.015</td> <td>   -2.624</td> <td> 0.009</td> <td>   -0.071</td> <td>   -0.010</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L3.returns</th> <td>   -0.0679</td> <td>    0.017</td> <td>   -4.022</td> <td> 0.000</td> <td>   -0.101</td> <td>   -0.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L4.returns</th> <td>    0.0742</td> <td>    0.020</td> <td>    3.771</td> <td> 0.000</td> <td>    0.036</td> <td>    0.113</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L5.returns</th> <td>   -0.0683</td> <td>    0.015</td> <td>   -4.660</td> <td> 0.000</td> <td>   -0.097</td> <td>   -0.040</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>           3.0443</td> <td>          +0.0000j</td> <td>           3.0443</td> <td>           0.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>          -1.1897</td> <td>          -1.1548j</td> <td>           1.6580</td> <td>          -0.3774</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.2</th> <td>          -1.1897</td> <td>          +1.1548j</td> <td>           1.6580</td> <td>           0.3774</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.3</th> <td>           1.5041</td> <td>          -0.0000j</td> <td>           1.5041</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.4</th> <td>           0.9809</td> <td>          -1.6057j</td> <td>           1.8815</td> <td>          -0.1627</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.5</th> <td>           0.9809</td> <td>          +1.6057j</td> <td>           1.8815</td> <td>           0.1627</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   No. Observations:                 5020\n",
       "Model:                     ARMA(1, 5)   Log Likelihood               -7890.973\n",
       "Method:                       css-mle   S.D. of innovations              1.165\n",
       "Date:                Sun, 08 Sep 2019   AIC                          15797.947\n",
       "Time:                        17:53:13   BIC                          15850.116\n",
       "Sample:                    01-10-1994   HQIC                         15816.228\n",
       "                         - 04-05-2013                                         \n",
       "=================================================================================\n",
       "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "const             0.0189      0.013      1.419      0.156      -0.007       0.045\n",
       "ar.L1.returns     0.3285      0.152      2.159      0.031       0.030       0.627\n",
       "ma.L1.returns    -0.3534      0.152     -2.332      0.020      -0.650      -0.056\n",
       "ma.L2.returns    -0.0404      0.015     -2.624      0.009      -0.071      -0.010\n",
       "ma.L3.returns    -0.0679      0.017     -4.022      0.000      -0.101      -0.035\n",
       "ma.L4.returns     0.0742      0.020      3.771      0.000       0.036       0.113\n",
       "ma.L5.returns    -0.0683      0.015     -4.660      0.000      -0.097      -0.040\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1            3.0443           +0.0000j            3.0443            0.0000\n",
       "MA.1           -1.1897           -1.1548j            1.6580           -0.3774\n",
       "MA.2           -1.1897           +1.1548j            1.6580            0.3774\n",
       "MA.3            1.5041           -0.0000j            1.5041           -0.0000\n",
       "MA.4            0.9809           -1.6057j            1.8815           -0.1627\n",
       "MA.5            0.9809           +1.6057j            1.8815            0.1627\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ret_ar_1_ma_5 = ARMA(df.returns[1:], order=(1,5))\n",
    "results_ret_ar_1_ma_5 = model_ret_ar_1_ma_5.fit()\n",
    "results_ret_ar_1_ma_5.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARMA(5,1):  \t LL =  -7889.311282945815 \t AIC =  15794.62256589163\n",
      "ARMA(1,5):  \t LL =  -7890.9734602094495 \t AIC =  15797.946920418899\n"
     ]
    }
   ],
   "source": [
    "print(\"ARMA(5,1):  \\t LL = \",results_ret_ar_5_ma_1.llf,\"\\t AIC = \",results_ret_ar_5_ma_1.aic)\n",
    "print(\"ARMA(1,5):  \\t LL = \",results_ret_ar_1_ma_5.llf,\"\\t AIC = \",results_ret_ar_1_ma_5.aic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARMA(3,2):  \t LL =  -7895.74745851493 \t AIC =  15805.49491702986\n"
     ]
    }
   ],
   "source": [
    "print(\"ARMA(3,2):  \\t LL = \",results_ret_ar_3_ma_2.llf,\"\\t AIC = \",results_ret_ar_3_ma_2.aic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Residuals for the New Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['res_ret_ar_5_ma_1'] = results_ret_ar_5_ma_1.resid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sgt.plot_acf(df.res_ret_ar_5_ma_1[1:], zero = False, lags = 40)\n",
    "plt.title(\"ACF of Residuals for Returns\",size=24)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ARMA Models for Prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sgt.plot_acf(df.market_value, unbiased=True, zero = False, lags = 40)\n",
    "plt.title(\"Autocorrelation Function for Prices\",size=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sgt.plot_pacf(df.market_value, lags = 40, alpha = 0.05, zero = False , method = ('ols'))\n",
    "plt.title(\"Partial Autocorrelation Function for Prices\",size=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>   <td>market_value</td>   <th>  No. Observations:  </th>    <td>5021</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(1, 1)</td>    <th>  Log Likelihood     </th> <td>-27621.789</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>59.248</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 08 Sep 2019</td> <th>  AIC                </th>  <td>55251.579</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>17:57:05</td>     <th>  BIC                </th>  <td>55277.664</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-07-1994</td>    <th>  HQIC               </th>  <td>55260.719</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>              <td> 5089.6411</td> <td>  496.827</td> <td>   10.244</td> <td> 0.000</td> <td> 4115.879</td> <td> 6063.403</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.market_value</th> <td>    0.9985</td> <td>    0.001</td> <td> 1323.212</td> <td> 0.000</td> <td>    0.997</td> <td>    1.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.market_value</th> <td>   -0.0190</td> <td>    0.015</td> <td>   -1.274</td> <td> 0.203</td> <td>   -0.048</td> <td>    0.010</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>           1.0015</td> <td>          +0.0000j</td> <td>           1.0015</td> <td>           0.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>          52.5188</td> <td>          +0.0000j</td> <td>          52.5188</td> <td>           0.0000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:           market_value   No. Observations:                 5021\n",
       "Model:                     ARMA(1, 1)   Log Likelihood              -27621.789\n",
       "Method:                       css-mle   S.D. of innovations             59.248\n",
       "Date:                Sun, 08 Sep 2019   AIC                          55251.579\n",
       "Time:                        17:57:05   BIC                          55277.664\n",
       "Sample:                    01-07-1994   HQIC                         55260.719\n",
       "                         - 04-05-2013                                         \n",
       "======================================================================================\n",
       "                         coef    std err          z      P>|z|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------\n",
       "const               5089.6411    496.827     10.244      0.000    4115.879    6063.403\n",
       "ar.L1.market_value     0.9985      0.001   1323.212      0.000       0.997       1.000\n",
       "ma.L1.market_value    -0.0190      0.015     -1.274      0.203      -0.048       0.010\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1            1.0015           +0.0000j            1.0015            0.0000\n",
       "MA.1           52.5188           +0.0000j           52.5188            0.0000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ar_1_ma_1 = ARMA(df.market_value, order=(1,1))\n",
    "results_ar_1_ma_1 = model_ar_1_ma_1.fit()\n",
    "results_ar_1_ma_1.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['res_ar_1_ma_1'] = results_ar_1_ma_1.resid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sgt.plot_acf(df.res_ar_1_ma_1, zero = False, lags = 40)\n",
    "plt.title(\"ACF Of Residuals of Prices\",size=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>   <td>market_value</td>   <th>  No. Observations:  </th>    <td>5021</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(6, 6)</td>    <th>  Log Likelihood     </th> <td>-27587.932</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>58.849</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 08 Sep 2019</td> <th>  AIC                </th>  <td>55203.864</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>17:59:06</td>     <th>  BIC                </th>  <td>55295.164</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-07-1994</td>    <th>  HQIC               </th>  <td>55235.856</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>              <td> 5089.6487</td> <td>  568.236</td> <td>    8.957</td> <td> 0.000</td> <td> 3975.926</td> <td> 6203.372</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.market_value</th> <td>    1.9277</td> <td>    0.032</td> <td>   59.829</td> <td> 0.000</td> <td>    1.865</td> <td>    1.991</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.market_value</th> <td>   -1.7361</td> <td>    0.040</td> <td>  -43.307</td> <td> 0.000</td> <td>   -1.815</td> <td>   -1.657</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L3.market_value</th> <td>    1.2675</td> <td>    0.035</td> <td>   36.722</td> <td> 0.000</td> <td>    1.200</td> <td>    1.335</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L4.market_value</th> <td>   -0.2373</td> <td>    0.157</td> <td>   -1.509</td> <td> 0.131</td> <td>   -0.546</td> <td>    0.071</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L5.market_value</th> <td>   -0.4064</td> <td>    0.165</td> <td>   -2.470</td> <td> 0.014</td> <td>   -0.729</td> <td>   -0.084</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L6.market_value</th> <td>    0.1842</td> <td>    0.049</td> <td>    3.768</td> <td> 0.000</td> <td>    0.088</td> <td>    0.280</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.market_value</th> <td>   -0.9488</td> <td>    0.035</td> <td>  -27.006</td> <td> 0.000</td> <td>   -1.018</td> <td>   -0.880</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L2.market_value</th> <td>    0.7800</td> <td>    0.032</td> <td>   24.160</td> <td> 0.000</td> <td>    0.717</td> <td>    0.843</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L3.market_value</th> <td>   -0.5083</td> <td>    0.031</td> <td>  -16.305</td> <td> 0.000</td> <td>   -0.569</td> <td>   -0.447</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L4.market_value</th> <td>   -0.1561</td> <td>    0.158</td> <td>   -0.988</td> <td> 0.323</td> <td>   -0.466</td> <td>    0.154</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L5.market_value</th> <td>    0.0955</td> <td>    0.057</td> <td>    1.682</td> <td> 0.093</td> <td>   -0.016</td> <td>    0.207</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L6.market_value</th> <td>    0.0670</td> <td>    0.024</td> <td>    2.808</td> <td> 0.005</td> <td>    0.020</td> <td>    0.114</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>           0.0856</td> <td>          -1.0503j</td> <td>           1.0538</td> <td>          -0.2371</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th> <td>           0.0856</td> <td>          +1.0503j</td> <td>           1.0538</td> <td>           0.2371</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.3</th> <td>          -2.0249</td> <td>          -0.0000j</td> <td>           2.0249</td> <td>          -0.5000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.4</th> <td>           1.0011</td> <td>          -0.0000j</td> <td>           1.0011</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.5</th> <td>           1.5294</td> <td>          -0.2695j</td> <td>           1.5529</td> <td>          -0.0278</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.6</th> <td>           1.5294</td> <td>          +0.2695j</td> <td>           1.5529</td> <td>           0.0278</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>           0.1027</td> <td>          -1.0613j</td> <td>           1.0662</td> <td>          -0.2346</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.2</th> <td>           0.1027</td> <td>          +1.0613j</td> <td>           1.0662</td> <td>           0.2346</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.3</th> <td>           1.3618</td> <td>          -0.2805j</td> <td>           1.3904</td> <td>          -0.0323</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.4</th> <td>           1.3618</td> <td>          +0.2805j</td> <td>           1.3904</td> <td>           0.0323</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.5</th> <td>          -2.1772</td> <td>          -1.4332j</td> <td>           2.6066</td> <td>          -0.4073</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.6</th> <td>          -2.1772</td> <td>          +1.4332j</td> <td>           2.6066</td> <td>           0.4073</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:           market_value   No. Observations:                 5021\n",
       "Model:                     ARMA(6, 6)   Log Likelihood              -27587.932\n",
       "Method:                       css-mle   S.D. of innovations             58.849\n",
       "Date:                Sun, 08 Sep 2019   AIC                          55203.864\n",
       "Time:                        17:59:06   BIC                          55295.164\n",
       "Sample:                    01-07-1994   HQIC                         55235.856\n",
       "                         - 04-05-2013                                         \n",
       "======================================================================================\n",
       "                         coef    std err          z      P>|z|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------\n",
       "const               5089.6487    568.236      8.957      0.000    3975.926    6203.372\n",
       "ar.L1.market_value     1.9277      0.032     59.829      0.000       1.865       1.991\n",
       "ar.L2.market_value    -1.7361      0.040    -43.307      0.000      -1.815      -1.657\n",
       "ar.L3.market_value     1.2675      0.035     36.722      0.000       1.200       1.335\n",
       "ar.L4.market_value    -0.2373      0.157     -1.509      0.131      -0.546       0.071\n",
       "ar.L5.market_value    -0.4064      0.165     -2.470      0.014      -0.729      -0.084\n",
       "ar.L6.market_value     0.1842      0.049      3.768      0.000       0.088       0.280\n",
       "ma.L1.market_value    -0.9488      0.035    -27.006      0.000      -1.018      -0.880\n",
       "ma.L2.market_value     0.7800      0.032     24.160      0.000       0.717       0.843\n",
       "ma.L3.market_value    -0.5083      0.031    -16.305      0.000      -0.569      -0.447\n",
       "ma.L4.market_value    -0.1561      0.158     -0.988      0.323      -0.466       0.154\n",
       "ma.L5.market_value     0.0955      0.057      1.682      0.093      -0.016       0.207\n",
       "ma.L6.market_value     0.0670      0.024      2.808      0.005       0.020       0.114\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1            0.0856           -1.0503j            1.0538           -0.2371\n",
       "AR.2            0.0856           +1.0503j            1.0538            0.2371\n",
       "AR.3           -2.0249           -0.0000j            2.0249           -0.5000\n",
       "AR.4            1.0011           -0.0000j            1.0011           -0.0000\n",
       "AR.5            1.5294           -0.2695j            1.5529           -0.0278\n",
       "AR.6            1.5294           +0.2695j            1.5529            0.0278\n",
       "MA.1            0.1027           -1.0613j            1.0662           -0.2346\n",
       "MA.2            0.1027           +1.0613j            1.0662            0.2346\n",
       "MA.3            1.3618           -0.2805j            1.3904           -0.0323\n",
       "MA.4            1.3618           +0.2805j            1.3904            0.0323\n",
       "MA.5           -2.1772           -1.4332j            2.6066           -0.4073\n",
       "MA.6           -2.1772           +1.4332j            2.6066            0.4073\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ar_6_ma_6 = ARMA(df.market_value, order=(6,6))\n",
    "results_ar_6_ma_6 = model_ar_6_ma_6.fit(start_ar_lags = 11)\n",
    "results_ar_6_ma_6.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>   <td>market_value</td>   <th>  No. Observations:  </th>    <td>5021</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(5, 6)</td>    <th>  Log Likelihood     </th> <td>-27587.863</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>58.849</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 08 Sep 2019</td> <th>  AIC                </th>  <td>55201.726</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>17:59:37</td>     <th>  BIC                </th>  <td>55286.504</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-07-1994</td>    <th>  HQIC               </th>  <td>55231.433</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>              <td> 5089.6485</td> <td>  580.944</td> <td>    8.761</td> <td> 0.000</td> <td> 3951.020</td> <td> 6228.277</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.market_value</th> <td>    1.3585</td> <td>    0.177</td> <td>    7.661</td> <td> 0.000</td> <td>    1.011</td> <td>    1.706</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.market_value</th> <td>   -1.1290</td> <td>    0.237</td> <td>   -4.767</td> <td> 0.000</td> <td>   -1.593</td> <td>   -0.665</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L3.market_value</th> <td>    0.9148</td> <td>    0.228</td> <td>    4.006</td> <td> 0.000</td> <td>    0.467</td> <td>    1.362</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L4.market_value</th> <td>    0.0158</td> <td>    0.203</td> <td>    0.078</td> <td> 0.938</td> <td>   -0.383</td> <td>    0.415</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L5.market_value</th> <td>   -0.1613</td> <td>    0.119</td> <td>   -1.353</td> <td> 0.176</td> <td>   -0.395</td> <td>    0.072</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.market_value</th> <td>   -0.3797</td> <td>    0.178</td> <td>   -2.135</td> <td> 0.033</td> <td>   -0.728</td> <td>   -0.031</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L2.market_value</th> <td>    0.7294</td> <td>    0.125</td> <td>    5.835</td> <td> 0.000</td> <td>    0.484</td> <td>    0.974</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L3.market_value</th> <td>   -0.2198</td> <td>    0.153</td> <td>   -1.439</td> <td> 0.150</td> <td>   -0.519</td> <td>    0.080</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L4.market_value</th> <td>   -0.1387</td> <td>    0.114</td> <td>   -1.216</td> <td> 0.224</td> <td>   -0.362</td> <td>    0.085</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L5.market_value</th> <td>   -0.0879</td> <td>    0.017</td> <td>   -5.325</td> <td> 0.000</td> <td>   -0.120</td> <td>   -0.056</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L6.market_value</th> <td>    0.0265</td> <td>    0.023</td> <td>    1.129</td> <td> 0.259</td> <td>   -0.020</td> <td>    0.073</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>           0.0917</td> <td>          -1.0418j</td> <td>           1.0458</td> <td>          -0.2360</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th> <td>           0.0917</td> <td>          +1.0418j</td> <td>           1.0458</td> <td>           0.2360</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.3</th> <td>           1.0010</td> <td>          -0.0000j</td> <td>           1.0010</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.4</th> <td>           1.8978</td> <td>          -0.0000j</td> <td>           1.8978</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.5</th> <td>          -2.9842</td> <td>          -0.0000j</td> <td>           2.9842</td> <td>          -0.5000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>           0.1071</td> <td>          -1.0487j</td> <td>           1.0542</td> <td>          -0.2338</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.2</th> <td>           0.1071</td> <td>          +1.0487j</td> <td>           1.0542</td> <td>           0.2338</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.3</th> <td>          -1.5352</td> <td>          -1.5157j</td> <td>           2.1574</td> <td>          -0.3760</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.4</th> <td>          -1.5352</td> <td>          +1.5157j</td> <td>           2.1574</td> <td>           0.3760</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.5</th> <td>           1.5918</td> <td>          -0.0000j</td> <td>           1.5918</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.6</th> <td>           4.5771</td> <td>          -0.0000j</td> <td>           4.5771</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:           market_value   No. Observations:                 5021\n",
       "Model:                     ARMA(5, 6)   Log Likelihood              -27587.863\n",
       "Method:                       css-mle   S.D. of innovations             58.849\n",
       "Date:                Sun, 08 Sep 2019   AIC                          55201.726\n",
       "Time:                        17:59:37   BIC                          55286.504\n",
       "Sample:                    01-07-1994   HQIC                         55231.433\n",
       "                         - 04-05-2013                                         \n",
       "======================================================================================\n",
       "                         coef    std err          z      P>|z|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------\n",
       "const               5089.6485    580.944      8.761      0.000    3951.020    6228.277\n",
       "ar.L1.market_value     1.3585      0.177      7.661      0.000       1.011       1.706\n",
       "ar.L2.market_value    -1.1290      0.237     -4.767      0.000      -1.593      -0.665\n",
       "ar.L3.market_value     0.9148      0.228      4.006      0.000       0.467       1.362\n",
       "ar.L4.market_value     0.0158      0.203      0.078      0.938      -0.383       0.415\n",
       "ar.L5.market_value    -0.1613      0.119     -1.353      0.176      -0.395       0.072\n",
       "ma.L1.market_value    -0.3797      0.178     -2.135      0.033      -0.728      -0.031\n",
       "ma.L2.market_value     0.7294      0.125      5.835      0.000       0.484       0.974\n",
       "ma.L3.market_value    -0.2198      0.153     -1.439      0.150      -0.519       0.080\n",
       "ma.L4.market_value    -0.1387      0.114     -1.216      0.224      -0.362       0.085\n",
       "ma.L5.market_value    -0.0879      0.017     -5.325      0.000      -0.120      -0.056\n",
       "ma.L6.market_value     0.0265      0.023      1.129      0.259      -0.020       0.073\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1            0.0917           -1.0418j            1.0458           -0.2360\n",
       "AR.2            0.0917           +1.0418j            1.0458            0.2360\n",
       "AR.3            1.0010           -0.0000j            1.0010           -0.0000\n",
       "AR.4            1.8978           -0.0000j            1.8978           -0.0000\n",
       "AR.5           -2.9842           -0.0000j            2.9842           -0.5000\n",
       "MA.1            0.1071           -1.0487j            1.0542           -0.2338\n",
       "MA.2            0.1071           +1.0487j            1.0542            0.2338\n",
       "MA.3           -1.5352           -1.5157j            2.1574           -0.3760\n",
       "MA.4           -1.5352           +1.5157j            2.1574            0.3760\n",
       "MA.5            1.5918           -0.0000j            1.5918           -0.0000\n",
       "MA.6            4.5771           -0.0000j            4.5771           -0.0000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ar_5_ma_6 = ARMA(df.market_value, order=(5,6))\n",
    "results_ar_5_ma_6 = model_ar_5_ma_6.fit(start_ar_lags = 7)\n",
    "results_ar_5_ma_6.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>   <td>market_value</td>   <th>  No. Observations:  </th>    <td>5021</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(6, 1)</td>    <th>  Log Likelihood     </th> <td>-27594.195</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>58.923</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 08 Sep 2019</td> <th>  AIC                </th>  <td>55206.389</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>18:00:05</td>     <th>  BIC                </th>  <td>55265.082</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-07-1994</td>    <th>  HQIC               </th>  <td>55226.956</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 04-05-2013</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>const</th>              <td> 5089.6424</td> <td>  586.490</td> <td>    8.678</td> <td> 0.000</td> <td> 3940.143</td> <td> 6239.142</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.market_value</th> <td>    1.3921</td> <td>    0.058</td> <td>   23.930</td> <td> 0.000</td> <td>    1.278</td> <td>    1.506</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.market_value</th> <td>   -0.4369</td> <td>    0.059</td> <td>   -7.400</td> <td> 0.000</td> <td>   -0.553</td> <td>   -0.321</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L3.market_value</th> <td>   -0.0101</td> <td>    0.025</td> <td>   -0.409</td> <td> 0.683</td> <td>   -0.059</td> <td>    0.038</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L4.market_value</th> <td>    0.1126</td> <td>    0.025</td> <td>    4.527</td> <td> 0.000</td> <td>    0.064</td> <td>    0.161</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L5.market_value</th> <td>   -0.1158</td> <td>    0.025</td> <td>   -4.717</td> <td> 0.000</td> <td>   -0.164</td> <td>   -0.068</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L6.market_value</th> <td>    0.0573</td> <td>    0.014</td> <td>    4.067</td> <td> 0.000</td> <td>    0.030</td> <td>    0.085</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.market_value</th> <td>   -0.4127</td> <td>    0.060</td> <td>   -6.925</td> <td> 0.000</td> <td>   -0.529</td> <td>   -0.296</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th> <td>           1.0010</td> <td>          -0.0000j</td> <td>           1.0010</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th> <td>          -1.7608</td> <td>          -0.0000j</td> <td>           1.7608</td> <td>          -0.5000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.3</th> <td>          -0.0803</td> <td>          -1.8407j</td> <td>           1.8425</td> <td>          -0.2569</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.4</th> <td>          -0.0803</td> <td>          +1.8407j</td> <td>           1.8425</td> <td>           0.2569</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.5</th> <td>           1.4694</td> <td>          -0.8691j</td> <td>           1.7072</td> <td>          -0.0850</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.6</th> <td>           1.4694</td> <td>          +0.8691j</td> <td>           1.7072</td> <td>           0.0850</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>           2.4233</td> <td>          +0.0000j</td> <td>           2.4233</td> <td>           0.0000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:           market_value   No. Observations:                 5021\n",
       "Model:                     ARMA(6, 1)   Log Likelihood              -27594.195\n",
       "Method:                       css-mle   S.D. of innovations             58.923\n",
       "Date:                Sun, 08 Sep 2019   AIC                          55206.389\n",
       "Time:                        18:00:05   BIC                          55265.082\n",
       "Sample:                    01-07-1994   HQIC                         55226.956\n",
       "                         - 04-05-2013                                         \n",
       "======================================================================================\n",
       "                         coef    std err          z      P>|z|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------\n",
       "const               5089.6424    586.490      8.678      0.000    3940.143    6239.142\n",
       "ar.L1.market_value     1.3921      0.058     23.930      0.000       1.278       1.506\n",
       "ar.L2.market_value    -0.4369      0.059     -7.400      0.000      -0.553      -0.321\n",
       "ar.L3.market_value    -0.0101      0.025     -0.409      0.683      -0.059       0.038\n",
       "ar.L4.market_value     0.1126      0.025      4.527      0.000       0.064       0.161\n",
       "ar.L5.market_value    -0.1158      0.025     -4.717      0.000      -0.164      -0.068\n",
       "ar.L6.market_value     0.0573      0.014      4.067      0.000       0.030       0.085\n",
       "ma.L1.market_value    -0.4127      0.060     -6.925      0.000      -0.529      -0.296\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1            1.0010           -0.0000j            1.0010           -0.0000\n",
       "AR.2           -1.7608           -0.0000j            1.7608           -0.5000\n",
       "AR.3           -0.0803           -1.8407j            1.8425           -0.2569\n",
       "AR.4           -0.0803           +1.8407j            1.8425            0.2569\n",
       "AR.5            1.4694           -0.8691j            1.7072           -0.0850\n",
       "AR.6            1.4694           +0.8691j            1.7072            0.0850\n",
       "MA.1            2.4233           +0.0000j            2.4233            0.0000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ar_6_ma_1 = ARMA(df.market_value, order=(6,1))\n",
    "results_ar_6_ma_1 = model_ar_6_ma_1.fit(start_ar_lags = 7)\n",
    "results_ar_6_ma_1.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARMA(5,6):  \t LL =  -27587.862948301117 \t AIC =  55201.725896602235\n",
      "ARMA(6,1):  \t LL =  -27594.194571066146 \t AIC =  55206.38914213229\n"
     ]
    }
   ],
   "source": [
    "print(\"ARMA(5,6):  \\t LL = \", results_ar_5_ma_6.llf, \"\\t AIC = \", results_ar_5_ma_6.aic)\n",
    "print(\"ARMA(6,1):  \\t LL = \", results_ar_6_ma_1.llf, \"\\t AIC = \", results_ar_6_ma_1.aic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df['res_ar_5_ma_6'] = results_ar_5_ma_6.resid\n",
    "sgt.plot_acf(df.res_ar_5_ma_6, zero = False, lags = 40)\n",
    "plt.title(\"ACF Of Residuals of Prices\",size=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ARMA for Returns vs ARMA for Prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARMA(5,6):  \t LL =  -27587.862948301117 \t AIC =  55201.725896602235\n",
      "ARMA(5,1):  \t LL =  -7889.311282945815 \t AIC =  15794.62256589163\n"
     ]
    }
   ],
   "source": [
    "print(\"ARMA(5,6):  \\t LL = \", results_ar_5_ma_6.llf, \"\\t AIC = \", results_ar_5_ma_6.aic)\n",
    "print(\"ARMA(5,1):  \\t LL = \", results_ret_ar_5_ma_1.llf, \"\\t AIC = \", results_ret_ar_5_ma_1.aic)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}