Granger_causality.ipynb

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   "source": [
    "import pandas\n",
    "import numpy as np\n",
    "from statsmodels.tsa.vector_ar.var_model import VAR\n",
    "import data as dta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. test Granger-causality between 2 variables in a system of 3 variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "iidata = dta.load_pandas();\n",
    "mdata = iidata.data\n",
    "dates = mdata[['year', 'quarter']].astype(int).astype(str)\n",
    "quarterly = dates[\"year\"] + \"Q\" + dates[\"quarter\"]\n",
    "from statsmodels.tsa.base.datetools import dates_from_str\n",
    "quarterly = dates_from_str(quarterly)\n",
    "mdata = mdata[['realgdp','realcons','realinv']]\n",
    "mdata.index = pandas.DatetimeIndex(quarterly)\n",
    "data = mdata"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model = VAR(data)\n",
    "var_res = model.fit(maxlags=4, trend=\"c\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
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   "outputs": [
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     "text": [
      "Granger causality f-test\n",
      "=============================================================\n",
      "   Test statistic   Critical Value          p-value        df\n",
      "-------------------------------------------------------------\n",
      "        19.785068         2.387906            0.000  (4, 558)\n",
      "=============================================================\n",
      "H_0: ['realcons'] do not Granger-cause realgdp\n",
      "Conclusion: reject H_0 at 5.00% significance level\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'conclusion': 'reject',\n",
       " 'crit_value': 2.3879062135285474,\n",
       " 'df': (4, 558),\n",
       " 'pvalue': 3.0302722513051643e-15,\n",
       " 'signif': 0.05,\n",
       " 'statistic': 19.785068360428099}"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var_res.test_causality(variables='realcons', equation='realgdp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Granger causality f-test\n",
      "=============================================================\n",
      "   Test statistic   Critical Value          p-value        df\n",
      "-------------------------------------------------------------\n",
      "         5.953535         2.387906            0.000  (4, 558)\n",
      "=============================================================\n",
      "H_0: ['realgdp'] do not Granger-cause realcons\n",
      "Conclusion: reject H_0 at 5.00% significance level\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'conclusion': 'reject',\n",
       " 'crit_value': 2.3879062135285474,\n",
       " 'df': (4, 558),\n",
       " 'pvalue': 0.00010721139549973668,\n",
       " 'signif': 0.05,\n",
       " 'statistic': 5.9535349329950709}"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var_res.test_causality(variables='realgdp', equation='realcons')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## results: test statistics are 19.79 and 5.95"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. test Granger-causality between 2 variables without further variables in the system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mdata2 = iidata.data\n",
    "mdata2 = mdata2[['realgdp','realcons']]\n",
    "mdata2.index = pandas.DatetimeIndex(quarterly)\n",
    "data2 = mdata2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model2 = VAR(data2)\n",
    "var_res2 = model2.fit(maxlags=4, trend=\"c\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Granger causality f-test\n",
      "=============================================================\n",
      "   Test statistic   Critical Value          p-value        df\n",
      "-------------------------------------------------------------\n",
      "        16.888324         2.395430            0.000  (4, 380)\n",
      "=============================================================\n",
      "H_0: ['realcons'] do not Granger-cause realgdp\n",
      "Conclusion: reject H_0 at 5.00% significance level\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'conclusion': 'reject',\n",
       " 'crit_value': 2.3954299347613008,\n",
       " 'df': (4, 380),\n",
       " 'pvalue': 9.3501742398327963e-13,\n",
       " 'signif': 0.05,\n",
       " 'statistic': 16.888324307247704}"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var_res2.test_causality(variables='realcons', equation='realgdp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Granger causality f-test\n",
      "=============================================================\n",
      "   Test statistic   Critical Value          p-value        df\n",
      "-------------------------------------------------------------\n",
      "         2.956067         2.395430            0.020  (4, 380)\n",
      "=============================================================\n",
      "H_0: ['realgdp'] do not Granger-cause realcons\n",
      "Conclusion: reject H_0 at 5.00% significance level\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'conclusion': 'reject',\n",
       " 'crit_value': 2.3954299347613008,\n",
       " 'df': (4, 380),\n",
       " 'pvalue': 0.019942769805285872,\n",
       " 'signif': 0.05,\n",
       " 'statistic': 2.9560671453411649}"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var_res2.test_causality(variables='realgdp', equation='realcons')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## results: test statistics are 16.88 and 2.96"
   ]
  }
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