python-pour-finance/08-Analyse-Time-Series/.ipynb_checkpoints/1-Introduction-à-Statsmodels-checkpoint.ipynb

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   "source": [
    "___\n",
    "\n",
    "<a href='http://www.pieriandata.com'> <img src='../Pierian_Data_Logo.png' /></a>\n",
    "___\n",
    "<center>*Copyright Pierian Data 2017*</center>\n",
    "<center>*For more information, visit us at www.pieriandata.com*</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Statsmodels\n",
    "\n",
    "Statsmodels is a Python module that provides classes and functions for the estimation of many different statistical models, as well as for conducting statistical tests, and statistical data exploration. An extensive list of result statistics are available for each estimator. The results are tested against existing statistical packages to ensure that they are correct. The package is released under the open source Modified BSD (3-clause) license. The online documentation is hosted at statsmodels.org.\n",
    "\n",
    "The reason we will cover it for use in this course, is that you may find it very useful later on when discussing time series data (typical of quantitative financial analysis).\n",
    "\n",
    "Let's walk through a very simple example of using statsmodels!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# You can safely ignore the warning:\n",
    "#  Please use the pandas.tseries module instead. from pandas.core import datetools\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = sm.datasets.macrodata.load_pandas().data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "::\n",
      "    Number of Observations - 203\n",
      "\n",
      "    Number of Variables - 14\n",
      "\n",
      "    Variable name definitions::\n",
      "\n",
      "        year      - 1959q1 - 2009q3\n",
      "        quarter   - 1-4\n",
      "        realgdp   - Real gross domestic product (Bil. of chained 2005 US$,\n",
      "                    seasonally adjusted annual rate)\n",
      "        realcons  - Real personal consumption expenditures (Bil. of chained\n",
      "                    2005 US$, seasonally adjusted annual rate)\n",
      "        realinv   - Real gross private domestic investment (Bil. of chained\n",
      "                    2005 US$, seasonally adjusted annual rate)\n",
      "        realgovt  - Real federal consumption expenditures & gross investment\n",
      "                    (Bil. of chained 2005 US$, seasonally adjusted annual rate)\n",
      "        realdpi   - Real private disposable income (Bil. of chained 2005\n",
      "                    US$, seasonally adjusted annual rate)\n",
      "        cpi       - End of the quarter consumer price index for all urban\n",
      "                    consumers: all items (1982-84 = 100, seasonally adjusted).\n",
      "        m1        - End of the quarter M1 nominal money stock (Seasonally\n",
      "                    adjusted)\n",
      "        tbilrate  - Quarterly monthly average of the monthly 3-month\n",
      "                    treasury bill: secondary market rate\n",
      "        unemp     - Seasonally adjusted unemployment rate (%)\n",
      "        pop       - End of the quarter total population: all ages incl. armed\n",
      "                    forces over seas\n",
      "        infl      - Inflation rate (ln(cpi_{t}/cpi_{t-1}) * 400)\n",
      "        realint   - Real interest rate (tbilrate - infl)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(sm.datasets.macrodata.NOTE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>quarter</th>\n",
       "      <th>realgdp</th>\n",
       "      <th>realcons</th>\n",
       "      <th>realinv</th>\n",
       "      <th>realgovt</th>\n",
       "      <th>realdpi</th>\n",
       "      <th>cpi</th>\n",
       "      <th>m1</th>\n",
       "      <th>tbilrate</th>\n",
       "      <th>unemp</th>\n",
       "      <th>pop</th>\n",
       "      <th>infl</th>\n",
       "      <th>realint</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1959.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2710.349</td>\n",
       "      <td>1707.4</td>\n",
       "      <td>286.898</td>\n",
       "      <td>470.045</td>\n",
       "      <td>1886.9</td>\n",
       "      <td>28.98</td>\n",
       "      <td>139.7</td>\n",
       "      <td>2.82</td>\n",
       "      <td>5.8</td>\n",
       "      <td>177.146</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1959.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2778.801</td>\n",
       "      <td>1733.7</td>\n",
       "      <td>310.859</td>\n",
       "      <td>481.301</td>\n",
       "      <td>1919.7</td>\n",
       "      <td>29.15</td>\n",
       "      <td>141.7</td>\n",
       "      <td>3.08</td>\n",
       "      <td>5.1</td>\n",
       "      <td>177.830</td>\n",
       "      <td>2.34</td>\n",
       "      <td>0.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1959.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2775.488</td>\n",
       "      <td>1751.8</td>\n",
       "      <td>289.226</td>\n",
       "      <td>491.260</td>\n",
       "      <td>1916.4</td>\n",
       "      <td>29.35</td>\n",
       "      <td>140.5</td>\n",
       "      <td>3.82</td>\n",
       "      <td>5.3</td>\n",
       "      <td>178.657</td>\n",
       "      <td>2.74</td>\n",
       "      <td>1.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1959.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2785.204</td>\n",
       "      <td>1753.7</td>\n",
       "      <td>299.356</td>\n",
       "      <td>484.052</td>\n",
       "      <td>1931.3</td>\n",
       "      <td>29.37</td>\n",
       "      <td>140.0</td>\n",
       "      <td>4.33</td>\n",
       "      <td>5.6</td>\n",
       "      <td>179.386</td>\n",
       "      <td>0.27</td>\n",
       "      <td>4.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1960.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2847.699</td>\n",
       "      <td>1770.5</td>\n",
       "      <td>331.722</td>\n",
       "      <td>462.199</td>\n",
       "      <td>1955.5</td>\n",
       "      <td>29.54</td>\n",
       "      <td>139.6</td>\n",
       "      <td>3.50</td>\n",
       "      <td>5.2</td>\n",
       "      <td>180.007</td>\n",
       "      <td>2.31</td>\n",
       "      <td>1.19</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     year  quarter   realgdp  realcons  realinv  realgovt  realdpi    cpi  \\\n",
       "0  1959.0      1.0  2710.349    1707.4  286.898   470.045   1886.9  28.98   \n",
       "1  1959.0      2.0  2778.801    1733.7  310.859   481.301   1919.7  29.15   \n",
       "2  1959.0      3.0  2775.488    1751.8  289.226   491.260   1916.4  29.35   \n",
       "3  1959.0      4.0  2785.204    1753.7  299.356   484.052   1931.3  29.37   \n",
       "4  1960.0      1.0  2847.699    1770.5  331.722   462.199   1955.5  29.54   \n",
       "\n",
       "      m1  tbilrate  unemp      pop  infl  realint  \n",
       "0  139.7      2.82    5.8  177.146  0.00     0.00  \n",
       "1  141.7      3.08    5.1  177.830  2.34     0.74  \n",
       "2  140.5      3.82    5.3  178.657  2.74     1.09  \n",
       "3  140.0      4.33    5.6  179.386  0.27     4.06  \n",
       "4  139.6      3.50    5.2  180.007  2.31     1.19  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "index = pd.Index(sm.tsa.datetools.dates_from_range('1959Q1', '2009Q3'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df.index = index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>quarter</th>\n",
       "      <th>realgdp</th>\n",
       "      <th>realcons</th>\n",
       "      <th>realinv</th>\n",
       "      <th>realgovt</th>\n",
       "      <th>realdpi</th>\n",
       "      <th>cpi</th>\n",
       "      <th>m1</th>\n",
       "      <th>tbilrate</th>\n",
       "      <th>unemp</th>\n",
       "      <th>pop</th>\n",
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       "      <th>realint</th>\n",
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       "    <tr>\n",
       "      <th>1959-03-31</th>\n",
       "      <td>1959.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2710.349</td>\n",
       "      <td>1707.4</td>\n",
       "      <td>286.898</td>\n",
       "      <td>470.045</td>\n",
       "      <td>1886.9</td>\n",
       "      <td>28.98</td>\n",
       "      <td>139.7</td>\n",
       "      <td>2.82</td>\n",
       "      <td>5.8</td>\n",
       "      <td>177.146</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-06-30</th>\n",
       "      <td>1959.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2778.801</td>\n",
       "      <td>1733.7</td>\n",
       "      <td>310.859</td>\n",
       "      <td>481.301</td>\n",
       "      <td>1919.7</td>\n",
       "      <td>29.15</td>\n",
       "      <td>141.7</td>\n",
       "      <td>3.08</td>\n",
       "      <td>5.1</td>\n",
       "      <td>177.830</td>\n",
       "      <td>2.34</td>\n",
       "      <td>0.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-09-30</th>\n",
       "      <td>1959.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2775.488</td>\n",
       "      <td>1751.8</td>\n",
       "      <td>289.226</td>\n",
       "      <td>491.260</td>\n",
       "      <td>1916.4</td>\n",
       "      <td>29.35</td>\n",
       "      <td>140.5</td>\n",
       "      <td>3.82</td>\n",
       "      <td>5.3</td>\n",
       "      <td>178.657</td>\n",
       "      <td>2.74</td>\n",
       "      <td>1.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-12-31</th>\n",
       "      <td>1959.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2785.204</td>\n",
       "      <td>1753.7</td>\n",
       "      <td>299.356</td>\n",
       "      <td>484.052</td>\n",
       "      <td>1931.3</td>\n",
       "      <td>29.37</td>\n",
       "      <td>140.0</td>\n",
       "      <td>4.33</td>\n",
       "      <td>5.6</td>\n",
       "      <td>179.386</td>\n",
       "      <td>0.27</td>\n",
       "      <td>4.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-03-31</th>\n",
       "      <td>1960.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2847.699</td>\n",
       "      <td>1770.5</td>\n",
       "      <td>331.722</td>\n",
       "      <td>462.199</td>\n",
       "      <td>1955.5</td>\n",
       "      <td>29.54</td>\n",
       "      <td>139.6</td>\n",
       "      <td>3.50</td>\n",
       "      <td>5.2</td>\n",
       "      <td>180.007</td>\n",
       "      <td>2.31</td>\n",
       "      <td>1.19</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              year  quarter   realgdp  realcons  realinv  realgovt  realdpi  \\\n",
       "1959-03-31  1959.0      1.0  2710.349    1707.4  286.898   470.045   1886.9   \n",
       "1959-06-30  1959.0      2.0  2778.801    1733.7  310.859   481.301   1919.7   \n",
       "1959-09-30  1959.0      3.0  2775.488    1751.8  289.226   491.260   1916.4   \n",
       "1959-12-31  1959.0      4.0  2785.204    1753.7  299.356   484.052   1931.3   \n",
       "1960-03-31  1960.0      1.0  2847.699    1770.5  331.722   462.199   1955.5   \n",
       "\n",
       "              cpi     m1  tbilrate  unemp      pop  infl  realint  \n",
       "1959-03-31  28.98  139.7      2.82    5.8  177.146  0.00     0.00  \n",
       "1959-06-30  29.15  141.7      3.08    5.1  177.830  2.34     0.74  \n",
       "1959-09-30  29.35  140.5      3.82    5.3  178.657  2.74     1.09  \n",
       "1959-12-31  29.37  140.0      4.33    5.6  179.386  0.27     4.06  \n",
       "1960-03-31  29.54  139.6      3.50    5.2  180.007  2.31     1.19  "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x21b98304860>"
      ]
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     "metadata": {},
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PbS/OYdqywG2vmjaK5/QuGfzfpd212ywMHTZszKwt8BFQCMwjsDvtEuDPZnaWc25z/ZQo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\nBJ3CRkREgk5hIyIiQff/N5q1+nuHm0EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21b9829e320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df['realgdp'].plot()\n",
    "plt.ylabel(\"REAL GDP\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using Statsmodels to get the trend\n",
    "The Hodrick-Prescott filter separates a time-series  y_t  into a trend  τ_t and a cyclical component  ζt\n",
    "\n",
    "$y_t = \\tau_t + \\zeta_t$\n",
    "\n",
    "The components are determined by minimizing the following quadratic loss function\n",
    "\n",
    "$\\min_{\\\\{ \\tau_{t}\\\\} }\\sum_{t}^{T}\\zeta_{t}^{2}+\\lambda\\sum_{t=1}^{T}\\left[\\left(\\tau_{t}-\\tau_{t-1}\\right)-\\left(\\tau_{t-1}-\\tau_{t-2}\\right)\\right]^{2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Tuple unpacking\n",
    "gdp_cycle, gdp_trend = sm.tsa.filters.hpfilter(df.realgdp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1959-03-31     39.511915\n",
       "1959-06-30     80.088532\n",
       "1959-09-30     48.875455\n",
       "1959-12-31     30.591933\n",
       "1960-03-31     64.882667\n",
       "1960-06-30     23.040242\n",
       "1960-09-30     -1.355312\n",
       "1960-12-31    -67.462365\n",
       "1961-03-31    -81.367438\n",
       "1961-06-30    -60.167890\n",
       "1961-09-30    -46.369224\n",
       "1961-12-31    -20.695339\n",
       "1962-03-31     -2.162153\n",
       "1962-06-30     -4.718648\n",
       "1962-09-30    -13.556457\n",
       "1962-12-31    -44.369262\n",
       "1963-03-31    -43.320274\n",
       "1963-06-30    -44.546971\n",
       "1963-09-30    -26.298758\n",
       "1963-12-31    -44.261196\n",
       "1964-03-31    -14.434412\n",
       "1964-06-30    -20.266867\n",
       "1964-09-30    -19.137001\n",
       "1964-12-31    -54.824590\n",
       "1965-03-31    -15.962445\n",
       "1965-06-30    -13.740115\n",
       "1965-09-30     13.254828\n",
       "1965-12-31     56.030402\n",
       "1966-03-31    103.074337\n",
       "1966-06-30     72.175348\n",
       "                 ...    \n",
       "2002-06-30    -95.260035\n",
       "2002-09-30   -114.798768\n",
       "2002-12-31   -190.025905\n",
       "2003-03-31   -221.225647\n",
       "2003-06-30   -207.139428\n",
       "2003-09-30    -89.685415\n",
       "2003-12-31    -61.895316\n",
       "2004-03-31    -56.628782\n",
       "2004-06-30    -49.616781\n",
       "2004-09-30    -38.362890\n",
       "2004-12-31     -8.956672\n",
       "2005-03-31     39.070285\n",
       "2005-06-30     18.652990\n",
       "2005-09-30     42.798035\n",
       "2005-12-31     39.627354\n",
       "2006-03-31    141.269129\n",
       "2006-06-30    125.653779\n",
       "2006-09-30     70.676428\n",
       "2006-12-31    110.887665\n",
       "2007-03-31     99.564908\n",
       "2007-06-30    157.161271\n",
       "2007-09-30    231.874638\n",
       "2007-12-31    263.554667\n",
       "2008-03-31    204.422097\n",
       "2008-06-30    221.373942\n",
       "2008-09-30    102.018455\n",
       "2008-12-31   -107.269472\n",
       "2009-03-31   -349.047706\n",
       "2009-06-30   -397.557073\n",
       "2009-09-30   -333.115243\n",
       "Name: realgdp, Length: 203, dtype: float64"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gdp_cycle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pandas.core.series.Series"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(gdp_cycle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df[\"trend\"] = gdp_trend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x21b98541080>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9RNUazoIHGlM2wMfRZSlVqDQ0lCogYwwrVvxA+7UvsIYmBN71MpNuqqGPAlFu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\nUkrlmYaGUkqpPNPQUEoplWf/D7y3/9YQMLN0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21b9856ac18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[['trend','realgdp']].plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x21b98785390>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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k8KQdhak3wv7V0PM56PJwka7MkJdnWBR1mK+W72b17kTcXJzo17waozvUomVN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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21b98971d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[['trend','realgdp']][\"2000-03-31\":].plot(figsize=(12,8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Great job!"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}