Python - Econometric Modeling

cee_monetary.ipynb

local_linear_trend.ipynb

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   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "from dismalpy.ssm.model import Model, StatespaceResults\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Local Linear Trend model\n",
      "\n",
      "The Local Linear Trend model has the form (see Durbin and Koopman 2012, Chapter 3.2 for all notation and details):\n",
      "\n",
      "$$\n",
      "\\begin{align}\n",
      "y_t & = \\mu_t + \\varepsilon_t \\qquad & \\varepsilon_t \\sim\n",
      "    N(0, \\sigma_\\varepsilon^2) \\\\\n",
      "\\mu_{t+1} & = \\mu_t + \\nu_t + \\xi_t & \\xi_t \\sim N(0, \\sigma_\\xi^2) \\\\\n",
      "\\nu_{t+1} & = \\nu_t + \\zeta_t & \\zeta_t \\sim N(0, \\sigma_\\zeta^2)\n",
      "\\end{align}\n",
      "$$\n",
      "\n",
      "It is easy to see that this can be cast into state space form as:\n",
      "\n",
      "$$\n",
      "\\begin{align}\n",
      "y_t & = \\begin{pmatrix} 1 & 0 \\end{pmatrix} \\begin{pmatrix} \\mu_t \\\\ \\nu_t \\end{pmatrix} + \\varepsilon_t \\\\\n",
      "\\begin{pmatrix} \\mu_{t+1} \\\\ \\nu_{t+1} \\end{pmatrix} & = \\begin{bmatrix} 1 & 1 \\\\ 0 & 1 \\end{bmatrix} \\begin{pmatrix} \\mu_t \\\\ \\nu_t \\end{pmatrix} + \\begin{pmatrix} \\xi_t \\\\ \\zeta_t \\end{pmatrix}\n",
      "\\end{align}\n",
      "$$\n",
      "\n",
      "Notice that much of the state space representation is composed of known values; in fact the only parts in which parameters to be estimated appear are in the variance / covariance matrices:\n",
      "\n",
      "$$\n",
      "\\begin{align}\n",
      "H_t & = \\begin{bmatrix} \\sigma_\\varepsilon^2 \\end{bmatrix} \\\\\n",
      "Q_t & = \\begin{bmatrix} \\sigma_\\xi^2 & 0 \\\\ 0 & \\sigma_\\zeta^2 \\end{bmatrix}\n",
      "\\end{align}\n",
      "$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\"\"\"\n",
      "Univariate Local Linear Trend Model\n",
      "\"\"\"\n",
      "class LocalLinearTrend(Model):\n",
      "    def __init__(self, endog, *args, **kwargs):\n",
      "        # Model order\n",
      "        k_states = k_posdef = 2\n",
      "\n",
      "        # Initialize the statespace\n",
      "        super(LocalLinearTrend, self).__init__(\n",
      "            endog, k_states=k_states, k_posdef=k_posdef, *args, **kwargs\n",
      "        )\n",
      "\n",
      "        # Initialize the matrices\n",
      "        self['design'] = np.array([1, 0])\n",
      "        self['transition'] = np.array([[1, 1],\n",
      "                                       [0, 1]])\n",
      "        self['selection'] = np.eye(k_states)\n",
      "\n",
      "        # Initialize the state space model as approximately diffuse\n",
      "        self.initialize_approximate_diffuse()\n",
      "        # Because of the diffuse initialization, burn first two loglikelihoods\n",
      "        self.loglikelihood_burn = 2\n",
      "        \n",
      "        # Cache some indices\n",
      "        self._state_cov_idx = ('state_cov',) + np.diag_indices(k_posdef)\n",
      "\n",
      "    _names = ['sigma2.measurement', 'sigma2.level', 'sigma2.trend']\n",
      "    def _get_model_names(self, latex=False):\n",
      "        return self._names\n",
      "\n",
      "    @property\n",
      "    def start_params(self):\n",
      "        return np.r_[0.1, 0.1, 0.1]\n",
      "\n",
      "    def transform_params(self, unconstrained):\n",
      "        return unconstrained**2\n",
      "\n",
      "    def untransform_params(self, constrained):\n",
      "        return constrained**0.5\n",
      "\n",
      "    def update(self, params, *args, **kwargs):\n",
      "        params = super(LocalLinearTrend, self).update(params, *args, **kwargs)\n",
      "        \n",
      "        # Observation covariance\n",
      "        self['obs_cov',0,0] = params[0]\n",
      "\n",
      "        # State covariance\n",
      "        self[self._state_cov_idx] = params[1:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Using this simple model, we can estimate the parameters from a local linear trend model. The following example is from Commandeur and Koopman (2007), section 3.4., modeling motor vehicle fatalities in Finland."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Load Dataset\n",
      "df = pd.read_table('data/NorwayFinland.txt', skiprows=1, header=None)\n",
      "df.columns = ['date', 'nf', 'ff']\n",
      "df.index = pd.date_range(start='%d-01-01' % df.date[0], end='%d-01-01' % df.iloc[-1, 0], freq='AS')\n",
      "\n",
      "# Log transform\n",
      "df['lff'] = np.log(df['ff'])\n",
      "\n",
      "# Setup the model\n",
      "mod = LocalLinearTrend(df['lff'])\n",
      "\n",
      "# Fit it using MLE (recall that we are fitting the three variance parameters)\n",
      "res = mod.fit()\n",
      "print(res.summary())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                           Statespace Model Results                           \n",
        "==============================================================================\n",
        "Dep. Variable:                ['lff']   No. Observations:                   34\n",
        "Model:               LocalLinearTrend   Log Likelihood                  26.740\n",
        "Date:                Thu, 20 Nov 2014   AIC                            -47.480\n",
        "Time:                        17:50:26   BIC                            -42.901\n",
        "Sample:                    01-01-1970   HQIC                           -45.919\n",
        "                         - 01-01-2003                                         \n",
        "======================================================================================\n",
        "                         coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
        "--------------------------------------------------------------------------------------\n",
        "sigma2.measurement     0.0032      0.001      3.070      0.002         0.001     0.005\n",
        "sigma2.level        2.741e-10   4.95e-06   5.53e-05      1.000     -9.71e-06  9.71e-06\n",
        "sigma2.trend           0.0015      0.001      1.764      0.078        -0.000     0.003\n",
        "======================================================================================\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(figsize=(10,4))\n",
      "\n",
      "# Perform prediction and forecasting\n",
      "predict, cov, ci, idx = res.predict(alpha=0.05, end='2014')\n",
      "\n",
      "# Plot the results\n",
      "dates = df.index._mpl_repr()\n",
      "ax.plot(dates, df['lff'], 'k.', label='Observations');\n",
      "ax.plot(idx[:-10], predict[0][:-10], label='One-step-ahead Prediction');\n",
      "ax.plot(idx[:-10], ci[0, :-10], 'k--', alpha=0.5);\n",
      "\n",
      "ax.plot(idx[-10:], predict[0][-10:], 'r', label='Forecast');\n",
      "ax.plot(idx[-10:], ci[0, -10:], 'k--', alpha=0.5);\n",
      "\n",
      "# Cleanup the image\n",
      "ax.set_ylim((4, 8));\n",
      "legend = ax.legend(loc='lower left');\n",
      "legend.get_frame().set_facecolor('w')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
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       "output_type": "display_data",
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WhIQEdDodHh4ewz5fTk4Ozz//fH+yc+/99dcv8nSYTL1XNBkfXmSBdw+rglSs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\n8bZCNn2Z7/iN3kLe/9o69F9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mfKc5sWZO7whU+Ah1X0M9x0h9La7vILusEVdHe1bOno7P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\nhBBCeEA6U0IIIYQQHpDOlBBCCCGEB/4/a2x/vh9ZsfQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1098358d0>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### References\n",
      "\n",
      "    Commandeur, Jacques J. F., and Siem Jan Koopman. 2007.\n",
      "    An Introduction to State Space Time Series Analysis.\n",
      "    Oxford\u202f; New York: Oxford University Press.\n",
      "\n",
      "    Durbin, James, and Siem Jan Koopman. 2012.\n",
      "    Time Series Analysis by State Space Methods: Second Edition.\n",
      "    Oxford University Press."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}

python_state_space.ipynb

sarimax_stata.ipynb