Statsmodels example: Out of sample prediction

example_predict.ipynb

{
 "metadata": {
  "name": "example_predict"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Out of sample prediction"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import statsmodels.api as sm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Artificial data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nsample = 50\n",
      "sig = 0.25\n",
      "x1 = np.linspace(0, 20, nsample)\n",
      "X = np.c_[x1, np.sin(x1), (x1-5)**2, np.ones(nsample)]\n",
      "beta = [0.5, 0.5, -0.02, 5.]\n",
      "y_true = np.dot(X, beta)\n",
      "y = y_true + sig * np.random.normal(size=nsample)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Estimation "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "olsmod = sm.OLS(y, X)\n",
      "olsres = olsmod.fit()\n",
      "print olsres.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                            OLS Regression Results                            \n",
        "==============================================================================\n",
        "Dep. Variable:                      y   R-squared:                       0.987\n",
        "Model:                            OLS   Adj. R-squared:                  0.986\n",
        "Method:                 Least Squares   F-statistic:                     1135.\n",
        "Date:                Sun, 26 Aug 2012   Prob (F-statistic):           4.03e-43\n",
        "Time:                        20:53:07   Log-Likelihood:                 5.3984\n",
        "No. Observations:                  50   AIC:                            -2.797\n",
        "Df Residuals:                      46   BIC:                             4.851\n",
        "Df Model:                           3                                         \n",
        "==============================================================================\n",
        "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------\n",
        "x1             0.5167      0.012     43.406      0.000         0.493     0.541\n",
        "x2             0.4541      0.047      9.705      0.000         0.360     0.548\n",
        "x3            -0.0215      0.001    -20.550      0.000        -0.024    -0.019\n",
        "const          4.8695      0.077     63.089      0.000         4.714     5.025\n",
        "==============================================================================\n",
        "Omnibus:                        1.333   Durbin-Watson:                   2.195\n",
        "Prob(Omnibus):                  0.514   Jarque-Bera (JB):                1.220\n",
        "Skew:                           0.231   Prob(JB):                        0.543\n",
        "Kurtosis:                       2.390   Cond. No.                         221.\n",
        "==============================================================================\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## In-sample prediction"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ypred = olsres.predict(X)\n",
      "print ypred"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[  4.33259464   4.80783601   5.24630515   5.62325195   5.92285846\n",
        "   6.1408378    6.28513842   6.3746382    6.43604293   6.49949852\n",
        "   6.5936382    6.74087813   6.95373448   7.23276706   7.56648738\n",
        "   7.93324611   8.30479007   8.65090411   8.94437538   9.16546434\n",
        "   9.30514787   9.36660181   9.3646791    9.32346955   9.27234192\n",
        "   9.24111872   9.25517645   9.33127633   9.47481046   9.67891594\n",
        "   9.9256024   10.18870775  10.4381966   10.64509493  10.78625047\n",
        "  10.84813654  10.82907443  10.73950927  10.60029383  10.43926257\n",
        "  10.28665841  10.17016402  10.11035353  10.11731232  10.18898002\n",
        "  10.31148898  10.46144275  10.60975997  10.72645244  10.78555203]\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Create a new sample of explanatory variables Xnew, predict and plot"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x1n = np.linspace(20.5,25, 10)\n",
      "Xnew = np.c_[x1n, np.sin(x1n), (x1n-5)**2, np.ones(10)]\n",
      "ynewpred =  olsres.predict(Xnew) # predict out of sample\n",
      "print ypred"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[  4.33259464   4.80783601   5.24630515   5.62325195   5.92285846\n",
        "   6.1408378    6.28513842   6.3746382    6.43604293   6.49949852\n",
        "   6.5936382    6.74087813   6.95373448   7.23276706   7.56648738\n",
        "   7.93324611   8.30479007   8.65090411   8.94437538   9.16546434\n",
        "   9.30514787   9.36660181   9.3646791    9.32346955   9.27234192\n",
        "   9.24111872   9.25517645   9.33127633   9.47481046   9.67891594\n",
        "   9.9256024   10.18870775  10.4381966   10.64509493  10.78625047\n",
        "  10.84813654  10.82907443  10.73950927  10.60029383  10.43926257\n",
        "  10.28665841  10.17016402  10.11035353  10.11731232  10.18898002\n",
        "  10.31148898  10.46144275  10.60975997  10.72645244  10.78555203]\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Plot comparison"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "plt.figure()\n",
      "plt.plot(x1, y, 'o', x1, y_true, 'b-')\n",
      "plt.plot(np.hstack((x1, x1n)), np.hstack((ypred, ynewpred)),'r')\n",
      "plt.title('OLS prediction, blue: true and data, fitted/predicted values:red')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<matplotlib.text.Text at 0x48a6b10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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GxsZKbyIAMGLECOzbtw+HDh2CVCpFXl4eoqKicP/+fdSvXx9t2rTB/PnzUVhYiJMnT8o/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\nMjIwaNAgNG3aFM2aNcPZs2dVnYRSJ0/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      }
     ],
     "prompt_number": 6
    }
   ],
   "metadata": {}
  }
 ]
}