ARCH exogenous variable example

Exogenous variable example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.0\n"
     ]
    }
   ],
   "source": [
    "import arch\n",
    "print arch.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import datetime as dt\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "import pandas_datareader.data as web\n",
    "\n",
    "from arch import arch_model\n",
    "\n",
    "start = dt.datetime(2000, 1, 1)\n",
    "end = dt.datetime(2014, 1, 1)\n",
    "sp500 = web.DataReader('^GSPC', 'yahoo', start=start, end=end)\n",
    "returns = 100 * sp500['Adj Close'].pct_change().dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mondays = np.array([1 if i.weekday() == 0 else 0 for i in sp500.index][1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:      1,   Func. Count:      6,   Neg. LLF: 5159.58323938\n",
      "Iteration:      2,   Func. Count:     16,   Neg. LLF: 5156.09760149\n",
      "Iteration:      3,   Func. Count:     24,   Neg. LLF: 5152.29989336\n",
      "Iteration:      4,   Func. Count:     31,   Neg. LLF: 5146.47531817\n",
      "Iteration:      5,   Func. Count:     38,   Neg. LLF: 5143.86337547\n",
      "Iteration:      6,   Func. Count:     45,   Neg. LLF: 5143.02096168\n",
      "Iteration:      7,   Func. Count:     52,   Neg. LLF: 5142.24105149\n",
      "Iteration:      8,   Func. Count:     60,   Neg. LLF: 5142.07138947\n",
      "Iteration:      9,   Func. Count:     67,   Neg. LLF: 5141.41665305\n",
      "Iteration:     10,   Func. Count:     73,   Neg. LLF: 5141.39212285\n",
      "Iteration:     11,   Func. Count:     79,   Neg. LLF: 5141.39023885\n",
      "Iteration:     12,   Func. Count:     85,   Neg. LLF: 5141.39023359\n",
      "Optimization terminated successfully.    (Exit mode 0)\n",
      "            Current function value: 5141.39023359\n",
      "            Iterations: 12\n",
      "            Function evaluations: 85\n",
      "            Gradient evaluations: 12\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Constant Mean - GARCH Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>Adj Close</td>     <th>  R-squared:         </th>  <td>  -0.001</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Mean Model:</th>       <td>Constant Mean</td>   <th>  Adj. R-squared:    </th>  <td>  -0.001</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Vol Model:</th>            <td>GARCH</td>       <th>  Log-Likelihood:    </th> <td>  -5141.39</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Distribution:</th>        <td>Normal</td>       <th>  AIC:               </th> <td>   10290.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>        <td>Maximum Likelihood</td> <th>  BIC:               </th> <td>   10315.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                        <td></td>          <th>  No. Observations:  </th>    <td>3520</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>           <td>Mon, Feb 20 2017</td>  <th>  Df Residuals:      </th>    <td>3516</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>               <td>18:22:11</td>      <th>  Df Model:          </th>      <td>4</td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Mean Model</caption>\n",
       "<tr>\n",
       "   <td></td>     <th>coef</th>     <th>std err</th>      <th>t</th>       <th>P>|t|</th>     <th>95.0% Conf. Int.</th>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>mu</th> <td>    0.0531</td> <td>1.487e-02</td> <td>    3.569</td> <td>3.581e-04</td> <td>[2.392e-02,8.220e-02]</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Volatility Model</caption>\n",
       "<tr>\n",
       "      <td></td>        <th>coef</th>     <th>std err</th>      <th>t</th>       <th>P>|t|</th>     <th>95.0% Conf. Int.</th>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>omega</th>    <td>    0.0156</td> <td>4.932e-03</td> <td>    3.155</td> <td>1.606e-03</td> <td>[5.892e-03,2.523e-02]</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[1]</th> <td>    0.0879</td> <td>1.140e-02</td> <td>    7.710</td> <td>1.260e-14</td>  <td>[6.554e-02,  0.110]</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>beta[1]</th>  <td>    0.9014</td> <td>1.183e-02</td> <td>   76.163</td>   <td>0.000</td>     <td>[  0.878,  0.925]</td>  \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                     Constant Mean - GARCH Model Results                      \n",
       "==============================================================================\n",
       "Dep. Variable:              Adj Close   R-squared:                      -0.001\n",
       "Mean Model:             Constant Mean   Adj. R-squared:                 -0.001\n",
       "Vol Model:                      GARCH   Log-Likelihood:               -5141.39\n",
       "Distribution:                  Normal   AIC:                           10290.8\n",
       "Method:            Maximum Likelihood   BIC:                           10315.4\n",
       "                                        No. Observations:                 3520\n",
       "Date:                Mon, Feb 20 2017   Df Residuals:                     3516\n",
       "Time:                        18:22:11   Df Model:                            4\n",
       "                                  Mean Model                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|        95.0% Conf. Int.\n",
       "------------------------------------------------------------------------------\n",
       "mu             0.0531  1.487e-02      3.569  3.581e-04   [2.392e-02,8.220e-02]\n",
       "                               Volatility Model                               \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|        95.0% Conf. Int.\n",
       "------------------------------------------------------------------------------\n",
       "omega          0.0156  4.932e-03      3.155  1.606e-03   [5.892e-03,2.523e-02]\n",
       "alpha[1]       0.0879  1.140e-02      7.710  1.260e-14     [6.554e-02,  0.110]\n",
       "beta[1]        0.9014  1.183e-02     76.163      0.000       [  0.878,  0.925]\n",
       "==============================================================================\n",
       "\n",
       "Covariance estimator: robust\n",
       "\"\"\""
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arch_model(returns, x=mondays).fit().summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "x must be nobs by n, where nobs is the same as the number of elements in y",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-31-f6829c130ccd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0march_model\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mreturns\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmondays\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmean\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'HARX'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msummary\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32mC:\\Program Files\\Miniconda2\\envs\\booth-econometrics2\\lib\\site-packages\\arch\\univariate\\mean.pyc\u001b[0m in \u001b[0;36march_model\u001b[0;34m(y, x, mean, lags, vol, p, o, q, power, dist, hold_back)\u001b[0m\n\u001b[1;32m   1159\u001b[0m         \u001b[0mam\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mConstantMean\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mhold_back\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mhold_back\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m   1160\u001b[0m     \u001b[1;32melif\u001b[0m \u001b[0mmean\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'harx'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1161\u001b[0;31m         \u001b[0mam\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mHARX\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlags\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mhold_back\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mhold_back\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1162\u001b[0m     \u001b[1;32melif\u001b[0m \u001b[0mmean\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'har'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m   1163\u001b[0m         \u001b[0mam\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mHARX\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mNone\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlags\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mhold_back\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mhold_back\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[0;32mC:\\Program Files\\Miniconda2\\envs\\booth-econometrics2\\lib\\site-packages\\arch\\univariate\\mean.pyc\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, y, x, lags, constant, use_rotated, hold_back, volatility, distribution)\u001b[0m\n\u001b[1;32m    167\u001b[0m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_hold_back\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmax_lags\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m    168\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m--> 169\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_init_model\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    170\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m    171\u001b[0m     \u001b[1;33m@\u001b[0m\u001b[0mproperty\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[0;32mC:\\Program Files\\Miniconda2\\envs\\booth-econometrics2\\lib\\site-packages\\arch\\univariate\\mean.pyc\u001b[0m in \u001b[0;36m_init_model\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    463\u001b[0m         \u001b[1;34m\"\"\"Should be called whenever the model is initialized or changed\"\"\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m    464\u001b[0m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_reformat_lags\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m--> 465\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_check_specification\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    466\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m    467\u001b[0m         \u001b[0mnobs_orig\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_y\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[0;32mC:\\Program Files\\Miniconda2\\envs\\booth-econometrics2\\lib\\site-packages\\arch\\univariate\\mean.pyc\u001b[0m in \u001b[0;36m_check_specification\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    391\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_x\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[1;36m2\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_x\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_y\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m    392\u001b[0m                 raise ValueError(\n\u001b[0;32m--> 393\u001b[0;31m                     \u001b[1;34m'x must be nobs by n, where nobs is the same as '\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    394\u001b[0m                     'the number of elements in y')\n\u001b[1;32m    395\u001b[0m             \u001b[0mdef_names\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;34m'x'\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mstr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_x\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: x must be nobs by n, where nobs is the same as the number of elements in y"
     ]
    }
   ],
   "source": [
    "arch_model(returns, x=mondays, mean='HARX').fit().summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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