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

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction à Statsmodels\n",
    "\n",
    "Statsmodels est un module Python qui fournit des classes et des fonctions pour l'estimation de nombreux modèles statistiques différents, ainsi que pour la réalisation de tests statistiques et l'exploration de données statistiques. Une liste exhaustive de statistiques sur les résultats est disponible pour chaque estimateur. Les résultats sont testés par rapport aux progiciels statistiques existants pour s'assurer qu'ils sont corrects. Le paquet est publié sous la licence Open Source Modified BSD (3-clause). La documentation en ligne est hébergée sur statsmodels.org.\n",
    "\n",
    "La raison pour laquelle nous l'aborderons dans ce cours est qu'il pourrait vous être très utile plus tard lorsque vous discuterez des données de séries temporelles (typiques de l'analyse financière quantitative).\n",
    "\n",
    "Prenons un exemple très simple d'utilisation de statsmodels !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "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": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = sm.datasets.macrodata.load_pandas().data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": 5,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <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": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "index = pd.Index(sm.tsa.datetools.dates_from_range('1959Q1', '2009Q3'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.index = index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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",
       "      <th>infl</th>\n",
       "      <th>realint</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <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": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'REAL GDP')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AAZONmbUGPge2APMInU47B3jYzIY45zQzpohUKucc783bxN0fLCUQdLz1++Pp0uoov8OSSlBRz+Y+4Bnn3KNlC83sJuDf/DjjpohIpXjmy9U8+MkK+iU14oHf9CalpRJNpKgo2Qxyzl2xf6Fz7nEzWxG+kEQkGs1em8N/p6zgnN6JPD6ir67LRJiKburcU8G2gsoORESiV3rWbka/Npd2TRP493maWTMSVTj02czOK6fcAD26RkQqxeJNO7l83GxiDJ67rD9H1Yn3OyQJg4qSzZfALw+w7aswxCIiUSZzVyFXvvQ9deJimPC7QbRvluB3SBImFd1nc2VVBiIi0WVPcYDrJ8wlv6iUd68/XokmwlU09PloINk59423fguhB3ICvOacS6+C+EQkwhSXBhk/Yx3PfrmabbuLeeqSfnRtpTPzka6i02j/ASaUWb8WGAPUA/4FXBrGuEQkgjjnmJ+Ry+LNu3jp27Wszs5ncKdm/OHUFFKTm/gdnlSBipJNF+fcB2XWC5xzDwGY2dfhDUtEIkUw6Pi/SYt5deYGANo1rce4K1I5pWtLnyOTqlRRsqmz3/rQMstNwxCLiESYQNBxx7sLeTNtI9cMbs+Vg9vTumEdzagZhSpKNnlm1tk5txJ+nFLAzLoCu6siOBGpuUoDQW57awH/m7+Zm4am8MdTU5RkolhFyeZO4AMzu5cfpxboD/wVuDncgYlIzVUSCHLzxHl8tGgrfzq9C6OHdPI7JPFZRUOfP/Fu6vwzcJNXvBg4zzm3uCqCE5Gap6g0wOgJ85i2LJO/n92Na07Q1FdS8eNqcM4tds5d7pzr7/2MrIxEY2Z/NLMlZrbYzF43szpm1t7MZpnZKjN7w8xqefvW9tbTve3JZV7nDq98hZmdfqRxiciRKSwJMGr8HKYty+Su4T2UaOQHVT7VnZm1IdRT6u6c22NmbwIjgLOAR5xzE83sWeBq4Bnv9w7nXCczGwE8AFxkZt29ej2A1sA07xpToKqPSSSSrczM44MFm8ncVUSd+BiuOaEDbZvU22efguJSPl2SyYvfrmXhpp3cf14vRgxI8iliqY78mlc1DqhrZiWE7tvZApwCXOJtfxn4J6FkM9xbBngbeNJCVxmHAxOdc0XAWjNLBwYAM6roGEQiWmkgyB3vLuKtORuJjTGa16/NjoJi/jd/Mw9d0Ieh3VqwIaeAx6en8/HiLRQUB2jTqC6Pj+jLL/u09jt8qWYOK9mY2R/2n+fmYDnnNpnZf4ENhJ4s/SkwB8gtMwPoRqCNt9wGyPDqlprZTkJDr9sAM8u8dNk6+8c7ChgFkJSkb1siFdmRX8yc9TuYMGs9n6/I5tqTOvC7EzrQrH5t1m/P59pX5nDN+DRSWtRnfU4BcTHGr/q05td923BschM9sVnKdbg9m1uAw0o2ZtaYUK+kPZALvEVo6un9ub1VDrDtQOU/LXRuDKGnH5CamlruPiLRzjnHW2kbufuDpeQVlRIXY9w1vAeXH5f8wz7tmibwv9G/4H/zNvFGWgbn9ErkL2d2pWWD/W/LE9nX4SabI/nqciqw1jmXDWBm7wLHA43MLM7r3RwN7J12eiPQFthoZnFAQyCnTPleZeuIyCHYurOQO95dyOcrshnQvgm3ntaZnm0aklD7p38i6sTHMmJAkq7JyCE53GRzJL2DDcAgM6tH6DTaUCAN+Bw4H5hIaMrp9739J3nrM7ztnznnnJlNAl4zs4cJDRBIAWYfQVwiUenzFVnc/Po8igNB7vxld0Yel6xTYVLpKnrqcx7lJxUjdFH/sDjnZpnZ24RuFC0F5hE6xfUhMNHM7vHKxnpVxgKveAMAcgiNQMM5t8QbybbUe53RGokmcmjGfrOWez5cStdWDXj60n56zL+EjTkXXZcwUlNTXVpamt9hiPjuzbQM/vz2Qs7s2YqHLzyGurVi/Q5JqjEzm+OcSz3c+hXe1FnOmyWY2aVm9uHhvqGI+GvnnhKe+3I1f313ESekNOPxi/sq0UjY/ew1G+9O/rMI3QNzBvAO8GyY4xKRMJi7YQcjx80mr7CUE1Ka8fSl/YiPPaTvnCKHpaJrNqcBFwOnE7p4/wowQNNFi9RMy7bs4soXv6dJQi1e/90gerZp6HdIEkUq6tlMAb4GBjvn1gKY2WNVEpWIVJotO/dw74fL+GTxVprWr8WrVw/8yeNmRMKtomTTn9DIr2lmtobQkGSd2BWpQUoCQX7/6lxWbs3jiuOTufqE9iQ2rOt3WBKFKppiYB6hIch/MbNfEDqlVsvMPgbe8+7KF5Fq7NFpK1mQkctTl/Tj7N6JfocjUeygrgw65751zt1A6NljjwKDwhqViByRwpIA93ywlKc+X80F/Y9WohHfHTDZmNlvyyz/AsA5F3TOTeHHmTtFpJrZurOQ85/9jhe+WctvByVx97k9/Q5JpMKezS1llp/Yb9tVYYhFRI5ASSDIhwu3cO5T37I2O58xl/XnnnN7USdel1rFfxUNELADLJe3LiI+ycor5NWZG5g4ewNZeUUkN63HuCuOp3vrBn6HJvKDipKNO8Byeesi4oPPlmfyxzcWsKuwhJM7N+f+49pxUucWxOpBmlLNVJRsuprZQkK9mI7eMt66JhYX8Ukg6Hht9gYmz9/M7HU5dE9swDsXH0+nFvX9Dk3kgCpKNt2qLAoROSiZuwq5eeI8Zq7JoWuro7j1tM787sQOui4j1V5F99msL6/czGIJ3exZ7nYRqXylgSAvfruOx6avIhB0PHRBH37T/2i/wxI5aBU9G60BMJrQvTWTgKnADcBtwHxgQlUEKBLtnHP87b3FvJGWwSldW/CPc7pr3hmpcSo6jfYKsIPQDJnXAH8CagHDnXPzqyA2EQHGfLWGN9IyuGFIJ247vYvf4YgcloqSTQfnXC8AM3sB2AYkOefyqiQykSiXW1DMvyYv5b15mzi7VyK3nNbZ75BEDltFyaZk74JzLmBma5VoRKrGtKWZ/PW9ReTkF3PT0BRuGNKJGA1nlhqsomTTx8x2ecsG1PXWDXDOOd0xJlLJtuzcwz0fLOPDRVvo2uooxl1xrOadkYhQ0Wg0jaUUqSLOOd6Zu4k7319MadBxy2md+f1JHakVp1k0JTL87LTQIhJ+/5q8lJe+W8eA9k146II+mtxMIo6SjYjPJsxaz0vfreOK45P5xznd9agZiUjqo4v4aO6GHfxz0hJO6txciUYimpKNiE927inhxtfm0bJBHR4f0VeJRiKaTqOJ+MA5x1/fXUTmrkLe/P1xNKwX73dIImGlno2ID974PoMPF23h1mFd6JfU2O9wRMJOyUakiqVn7eZfk5cyuFMzrj1Rs3VIdFCyEalChSUBbnx9HnVrxfLwhX30VACJGr4kGzNrZGZvm9lyM1tmZseZWRMzm2pmq7zfjb19zcweN7N0M1toZv3KvM5Ib/9VZjbSj2MRORQPfLKcZVt28Z/ze9OiQR2/wxGpMn71bB4DPnHOdQX6AMuA24HpzrkUYLq3DnAmkOL9jAKeATCzJsCdwEBgAHDn3gQlUlUKiksJBA9ulvQvV2bz4reh+2mGdmsZ5shEqpcqTzbePDknAmMBnHPFzrlcYDjwsrfby8C53vJwYLwLmQk0MrNE4HRgqnMuxzm3g9B8O2dU4aFIFNqRX8xf31vEFyuy+GbVNo6//zPOfepbtu4srLDezj0l/OXthaS0qM/tZ3atomhFqg8/hj53ALKBF82sDzAHuBlo6ZzbAuCc22JmLbz92wAZZepv9MoOVP4TZjaKUK+IpKSkyjsSiSrOOW57awHTl2fx2qwNAHRonsCa7N386slvmHDNQFJaHvWTesGg45+TlpC9u4jnLuuvKZwlKvmRbOKAfsCNzrlZZvYYP54yK095V1BdBeU/LXRuDDAGIDU19eDOeUhUcc4xPyOX+Rm5LN60iyWbd3Jylxb79EJe/HYd05dn8bezulE7PoY12fncdnoXNu4o4LKxs7l83GyeurQf8zfkUq9WLP3aNcY5+M+UFUxblskfT+1Mn7aNfDxKEf/4kWw2Ahudc7O89bcJJZtMM0v0ejWJQFaZ/duWqX80sNkrP3m/8i/CGLdEkIycAtZvL2B7fhHZeUX8b/4mFm8KzajR/KjaNKtfm2e/XE2vNg05u3ci36Vv476PlnFa95Zcc0J7zH78rtO1VQPGXzWAC5+bwXlPf/eT94qNMf71qx5cfly7Kjs+keqmypONc26rmWWYWRfn3ApgKLDU+xkJ3O/9ft+rMgm4wcwmEhoMsNNLSFOA+8oMChgG3FGVxyI1j3OO575awwOfLMeV6eN2aJbA/ef14pSuLWjRoA4lgSAXPjeD299ZyNwNO3h7zkbaN0vg4Qv77JNo9uqW2IAJ1wzku9XbOaNHK0qDQRZt2kl8bAydWx5F53JOr4lEE3Ou6s8qmdkxwAtALWANcCWhwQpvAknABuAC51yOhf5nP0no4n8BcKVzLs17nauAv3ove69z7sWfe+/U1FSXlpZWyUckNUFOfjH/mryE9+dv5uzeiVw+qB1N69eiaUJtGtWL/0kS2bijgNET5rIiM4+mCbWZOGqQHv0vUcvM5jjnUg+7vh/Jxk9KNtFpQUYuV7w4m7zCUm48JYUbTzn4aZadcziHbsCUqHakyUYP4pSo8Nj0VcTGGB/edAJdWh3aKS0zo5wzZyJyCPS4Gol4GTkFfL4ii0sGJB1yohGRyqFkIxHv1ZnriTHjkoEaDSbiF51Gk4izI7+Y/83fRCDo2JxbyFtpGQzr3pJWDfUsMhG/KNlIRNldVMpl42b9cM9MnfgYerdpxK3DOvscmUh0U7KRiFFcGuS6V+ewbEsez1+eysAOTagXH0tcrM4Wi/hNyUYiQjDo+PPbC/h61TYePL83p3XXU5VFqhMlG6nx9hQHuOuDJfxv/mZuG9aZC1Pb/nwlEalSSjZSYxWXBvl48RYenbaKtdvyue7kjowe0snvsESkHEo2UqOUBoJMW5bJR4u28tWqbHILSujQLIHXrhnI8Z2a+R2eiByAko3UGAsycrl+wlw25e6hWf1anNKlBcP7tuGETs30KBmRak7JRmqE7LwiRr2SRlxMDGMu68/Qbi2JVYIRqTGUbKRKBYOONdvy6dAs4aB7I9t3F/H7V+ewc08J7173C7q3bhDmKEWksinZSFjtKizhoSkrWLhpJwOSm/DFimxWZObRqUV9TuveksxdhaS2a8IFqUcTX879MN+t3sbNE+ezs6CERy46RolGpIbSFAMSNquzd3PJ8zPJziuiR+uGLN2yi3ZN6nF+6tFMmr+ZlZl5NK5Xi+35xbRrWo+TOzdnSNcWnNylBQDvz9/EbW8toF3TBJ64uC/dEpVoRPyiKQakWiosCTB6wlyKS4O8d/0v6NO2EXuKA9SOiyEmxrjupI4Ego7YGGPasizGfbOWt+Zs5OUZ672ZLh3TlmUyoH0Tnr88lYZ14/0+JBE5Ako2UumCQcc/Jy1h+dY8XrziWPq0bQRA3VqxP+xjZsTFhq7ZnNa9Jad1b0lJIMiYr9bw2LRVNKgbx42ndGL0kE7UiY8t931EpOZQspFKVVgS4E9vL2Tygs1cf3JHhnRtcdB142NjGD2kEyOPT6ZWbAy14vRMM5FIoWQjlSIYdLz+/Qae/nw1m3L3cPuZXbn2xA6H9Vr1a+tjKRJp9L9aKsUj01byxGfp9E1qxIPn9+YXuptfRMpQspEj9v78TTzxWToXph7NA7/pjZluthSRfemkuByRN77fwC1vLmBg+ybcc24vJRoRKZd6NnJISgNBvliRzQcLN5OevZvFm3ZxYufmPH1pP13QF5EDUrKRg5KetZvHpq/im1XZ7CgooWlCLXq0acgfTk1h9JBO5d79LyKyl5KNHFBWXiG1Y2PB4MqXZpNbUMJp3VsyrHsrhnZroQQjIgdNySYK5ReVsnTLLlZn7ebLldmszt5Nj9YN6dSiPg3qxrO7sJS5G3YwfVkmteNiade0HltyC3nj2uPo366x3+GLSA2kZBNlvlu9jT9MnE9WXhEALRvUpltiA75J38Z78zb9sF+z+rW59qSObM7dw+QFm/nHOd2VaETksCnZRLiSQJDvVm/ns2WZzM/IZeGmnbRvmsA95/YkpcFPrQUAAAu1SURBVOVRJDet98MIssKSALv2lFC/Thz1av340fj3eb32WRcROVS+/QUxs1ggDdjknDvHzNoDE4EmwFzgMudcsZnVBsYD/YHtwEXOuXXea9wBXA0EgJucc1Oq/kiqr/SsPH7/6lzSs3ZTNz6WPm0bcuOQTlx7UkcSyrlLv058bLnPIVOiEZEj5edfkZuBZcDe58Y/ADzinJtoZs8SSiLPeL93OOc6mdkIb7+LzKw7MALoAbQGpplZZ+dcoKoPpDqatjSTmybOo258LE9d0o+h3VrogZYi4htfhhOZ2dHA2cAL3roBpwBve7u8DJzrLQ/31vG2D/X2Hw5MdM4VOefWAunAgKo5guqrNBBkwqz1XPvqHDq1qM+HN53A2b0TlWhExFd+9WweBf4MHOWtNwVynXOl3vpGoI233AbIAHDOlZrZTm//NsDMMq9Zts4+zGwUMAogKSmp8o6iGti2u4jcghKy8gr5aNEWPl60le35xZyQ0oxnf9u/3NNlIiJVrcr/EpnZOUCWc26OmZ28t7icXd3PbKuozr6Fzo0BxkBops5DCrga2pFfzPTlWfxv3ia+Xb2NvZOt1omPYWi3lvyydyKndmtJnO6DEZFqwo+vvb8AfmVmZwF1CF2zeRRoZGZxXu/maGCzt/9GoC2w0czigIZATpnyvcrWiSh5hSXMXJPD6uzdfLkim9nrcggEHW0a1eWmU1Lo2KI+CbViGdShqXoyIlItVflfJufcHcAdAF7P5jbn3KVm9hZwPqERaSOB970qk7z1Gd72z5xzzswmAa+Z2cOEBgikALOr8liqQuauQi4eM5M12/IBSGlRn+tO6siwHi3p1aahHnwpIjVCdfoa/BdgopndA8wDxnrlY4FXzCydUI9mBIBzbomZvQksBUqB0ZE2Em1vosncVcjzl6eS2q4xjRNq+R2WiMghM+dq/CWMQ5KamurS0tL8DuNnZe4qZMSYmWTtKuTlqwaQmtzE75BEJIqZ2RznXOrh1q9OPRvxrMrM45rxaWzLK2L81QPo306JRkRqNiWbaiQQdLw7dyP/nLSEurXieOWagfRL0vPIRKTmU7KpJtKz8rjhtXks35pH36RGPH1pPxIb1vU7LBGRSqFk47PCkgALMnL5/atziI2J4YmL+3J2r0RiYjTKTEQih5KNT9LW5fDw1JV8t3o7AG0a1WXCNQNJbpbgc2QiIpVPyaaKTV2ayTNfpDN3Qy7N6tfmhiGdSGpaj6FdW9C0fm2/wxMRCQslmypSGghy/8fLeeGbtSQ3rcedv+zORce21eP7RSQq6C9dmGXkFPDItJV8tTKbbbuLGXlcO/5+Tnfi9dwyEYkiSjZhkl9UyuuzN/Dw1JXEmHFqtxac1SuRYT1a+R2aiEiVU7KpZJtz9zB+xnpem7WeXYWlnNS5Of8+rxetG2kYs4hELyWbI5SRU8CHi7bw4cItpGftZk9JgBiDM3q24urBHejfTjdliogo2RymmWu2898pK0hbvwOAY9o24pKBSbRsUJszeybStkk9nyMUEak+lGwO0Zade7jvo+VMXrCZNo3q8uczuvDL3q2VXEREKqBkc5CKSgO88PVanvwsnYBz3DQ0hetO6kjdWrF+hyYiUu0p2QA7C0qYsWYbiQ3rklA7jqLSACktjqJWXGh48mfLM7lr8lLWbS9gWPeW/OOc7urJiIgcgqhMNrkFxcTEGIXFAeZn5PJ/7y9h667CffZpVr82J6Y0Y1XWbhZt2kmH5gmMv2oAJ3Zu7lPUIiI1V9Qlm4wdBRxz19R9yjq1qM/48wewpyRAYUloss/JCzbz1apsOjSvz9/P7sblxyX/0NMREZFDE3XJJreghBsHt6dlgzrUjo+hdcO6DE5pRp34fa+9DD+mjU8RiohEnqhLNu2bJfD3c7r7HYaISFSJuvNC9WtHXX4VEfFd1CUbERGpeko2IiISdko2IiISdko2IiISdko2IiISdko2IiISdko2IiISdko2IiISduac8zuGKmVmecAKn8NoCOz0OYZmwDafY1A7hFSHdgC1xV5qh5D926Gdc+6wn0QcjbfTr3DOpfoZgJmNcc6N8jmGNLWD2mG/ONQWqB3KxFCp7aDTaP6Y7HcA1YTaIUTt8CO1RUjEtYOSjQ+ccxH3QTocaocQtcOP1BYhkdgO0ZhsxvgdQDWhdghRO/xIbRGidgip1HaIugECIiJS9aKxZyMiIlVMyUZERMKuxicbMxtnZllmtrhMWR8zm2Fmi8xsspk18MqTzWyPmc33fp4tU+ciM1toZkvM7EE/juVIHEo7eNt6e9uWeNvreOU1uh3gkD8Tl5b5PMw3s6CZHeNtq9FtcYjtEG9mL3vly8zsjjJ1bjazxV47/MGPYzkSh9gOtczsRa98gZmdXKZOTf88tDWzz71/3yVmdrNX3sTMpprZKu93Y6/czOxxM0v3jrtfmdd6wPtMLDaziw4qAOdcjf4BTgT6AYvLlH0PnOQtXwXc7S0nl92vzP5NgQ1Ac2/9ZWCo38cWxnaIAxYCfcocf2wktMOhtsV+9XoBa6L0M3EJMNFbrges8/6/9AQWe2VxwDQgxe9jC2M7jAZe9JZbAHMIfSmPhM9DItDPWz4KWAl0Bx4EbvfKbwce8JbPAj4GDBgEzPLKzwamep+HBCANaPBz71/jezbOua+AnP2KuwBfectTgd/8zMt0AFY657K99WkHUadaOcR2GAYsdM4t8Opud84FiIB2gCP6TFwMvO4t1/i2OMR2cECCmcUBdYFiYBfQDZjpnCtwzpUCXwK/DnfslekQ26E7MN2rlwXkAqlExudhi3NurrecBywD2gDDCSVPvN/nesvDgfEuZCbQyMwSCbXRl865UudcPrAAOOPn3r/GJ5sDWAz8ylu+AGhbZlt7M5tnZl+a2QleWTrQ1TvNFkeoscvWqakO1A6dAWdmU8xsrpn92SuP1HaAij8Te13Ej8kmUtviQO3wNpAPbCH0Df6/zrkcb/8TzaypmdUj9G03ktthATDczOLMrD3Q39sWUZ8HM0sG+gKzgJbOuS0QSkiEenQQSkQZZapt9MoWAGeaWT0zawYM4SDaIlKTzVXAaDObQ6i7WOyVbwGSnHN9gVuA18ysgXNuB3Ad8AbwNaFTCKVVHnXlO1A7xAGDgUu93782s6ER3A5w4LYAwMwGAgXOucUAEdwWB2qHAUAAaA20B241sw7OuWXAA4S+/X9C6A9NJLfDOEJ/VNOAR4HvgNJI+jyYWX3gHeAPzrldFe1aTplzzn0KfESobV4HZnAQbRGRz0Zzzi0ndKoIM+tM6BwjzrkioMhbnmNmqwl9y09zoTt2J3t1RhH6j1ejHagdCP1n+tI5t83b9hGhc9rTI7EdoMK22GsEP/Zq9taJuLaooB0uAT5xzpUAWWb2LaHTR2ucc2OBsV6d+wh9fmq0Cv5GlAJ/3LufmX0HrPK21fjPg5nFE0o0E5xz73rFmWaW6Jzb4p0my/LKN7Jvj+VoYDOAc+5e4F7vNV/Da6OKRGTPxsxaeL9jgL8Dz3rrzc0s1lvuAKQAa/ar0xi4Hnih6iOvXAdqB2AK0NvrBscBJwFL96sTMe0AFbbF3rILgIkHqBMxbVFBO2wATvFGICUQuiC8fL86ScB57JeUa6IK/kbU844fMzuNUK8mIv5vmJkR+tKwzDn3cJlNk4CR3vJI4P0y5Zd7n4lBwE4vIcWaWVPvNXsDvYFPfzYAv0dIVMIIi9cJnR4rIZSJrwZuJjTSYiVwPz8+KeE3wBJCpwLmAr/c73WWej8j/D6ucLaDt/9vvbZYDDwYKe1wmG1xMqGL4OW9To1ti0P8v1EfeMv7TCwF/lTmdb72yhZQw0ZgHUY7JBOagmQZoUEA7SLo8zCY0ECQhcB87+csQiPtphPqnUwHmnj7G/AUsBpYBKR65XXKtMNM4JiDeX89rkZERMIuIk+jiYhI9aJkIyIiYadkIyIiYadkIyIiYadkIyIiYadkIyIiYadkIyIiYff/RNUeSHcrw08AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df['realgdp'].plot()\n",
    "plt.ylabel(\"REAL GDP\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Utiliser Statsmodels pour obtenir la tendance\n",
    "Le filtre Hodrick-Prescott sépare une série temporelle  y_t  en une composante de tendance  τ_t et en une composante de cycle  ζt\n",
    "\n",
    "$y_t = \\tau_t + \\zeta_t$\n",
    "\n",
    "Les composantes sont déterminées en minimisant la fonction de perte quadratique suivante:\n",
    "\n",
    "$\\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": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Décomposition du tuple\n",
    "gdp_cycle, gdp_trend = sm.tsa.filters.hpfilter(df.realgdp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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",
       "                 ...    \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": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gdp_cycle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pandas.core.series.Series"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(gdp_cycle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"trend\"] = gdp_trend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1c1a790c90>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[['trend','realgdp']].plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1c1a8de890>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[['trend','realgdp']][\"2000-03-31\":].plot(figsize=(12,8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bon Travail!"
   ]
  }
 ],
 "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": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}