Recursive least squares.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Recursive least squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "from pandas_datareader.data import DataReader\n",
    "\n",
    "np.set_printoptions(suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 1: Copper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This data describes the world copper market from 1951 through 1975.  In an\n",
      "example, in Gill, the outcome variable (of a 2 stage estimation) is the world\n",
      "consumption of copper for the 25 years.  The explanatory variables are the\n",
      "world consumption of copper in 1000 metric tons, the constant dollar adjusted\n",
      "price of copper, the price of a substitute, aluminum, an index of real per\n",
      "capita income base 1970, an annual measure of manufacturer inventory change,\n",
      "and a time trend.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(sm.datasets.copper.DESCRLONG)\n",
    "\n",
    "dta = sm.datasets.copper.load_pandas().data\n",
    "dta.index = pd.date_range('1951-01-01', '1975-01-01', freq='AS')\n",
    "endog = dta['WORLDCONSUMPTION']\n",
    "\n",
    "# To the regressors in the dataset, we add a column of ones for an intercept\n",
    "exog = sm.add_constant(dta[['COPPERPRICE', 'INCOMEINDEX', 'ALUMPRICE', 'INVENTORYINDEX']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>WORLDCONSUMPTION</th>\n",
       "      <th>COPPERPRICE</th>\n",
       "      <th>INCOMEINDEX</th>\n",
       "      <th>ALUMPRICE</th>\n",
       "      <th>INVENTORYINDEX</th>\n",
       "      <th>TIME</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1951-01-01</th>\n",
       "      <td>3173.0</td>\n",
       "      <td>26.56</td>\n",
       "      <td>0.70</td>\n",
       "      <td>19.76</td>\n",
       "      <td>0.98</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1952-01-01</th>\n",
       "      <td>3281.1</td>\n",
       "      <td>27.31</td>\n",
       "      <td>0.71</td>\n",
       "      <td>20.78</td>\n",
       "      <td>1.04</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1953-01-01</th>\n",
       "      <td>3135.7</td>\n",
       "      <td>32.95</td>\n",
       "      <td>0.72</td>\n",
       "      <td>22.55</td>\n",
       "      <td>1.05</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1954-01-01</th>\n",
       "      <td>3359.1</td>\n",
       "      <td>33.90</td>\n",
       "      <td>0.70</td>\n",
       "      <td>23.06</td>\n",
       "      <td>0.97</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1955-01-01</th>\n",
       "      <td>3755.1</td>\n",
       "      <td>42.70</td>\n",
       "      <td>0.74</td>\n",
       "      <td>24.93</td>\n",
       "      <td>1.02</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-01-01</th>\n",
       "      <td>3875.9</td>\n",
       "      <td>46.11</td>\n",
       "      <td>0.74</td>\n",
       "      <td>26.50</td>\n",
       "      <td>1.04</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-01-01</th>\n",
       "      <td>3905.7</td>\n",
       "      <td>31.70</td>\n",
       "      <td>0.74</td>\n",
       "      <td>27.24</td>\n",
       "      <td>0.98</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-01-01</th>\n",
       "      <td>3957.6</td>\n",
       "      <td>27.23</td>\n",
       "      <td>0.72</td>\n",
       "      <td>26.21</td>\n",
       "      <td>0.98</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-01-01</th>\n",
       "      <td>4279.1</td>\n",
       "      <td>32.89</td>\n",
       "      <td>0.75</td>\n",
       "      <td>26.09</td>\n",
       "      <td>1.03</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-01-01</th>\n",
       "      <td>4627.9</td>\n",
       "      <td>33.78</td>\n",
       "      <td>0.77</td>\n",
       "      <td>27.40</td>\n",
       "      <td>1.03</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1961-01-01</th>\n",
       "      <td>4910.2</td>\n",
       "      <td>31.66</td>\n",
       "      <td>0.76</td>\n",
       "      <td>26.94</td>\n",
       "      <td>0.98</td>\n",
       "      <td>11.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1962-01-01</th>\n",
       "      <td>4908.4</td>\n",
       "      <td>32.28</td>\n",
       "      <td>0.79</td>\n",
       "      <td>25.18</td>\n",
       "      <td>1.00</td>\n",
       "      <td>12.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1963-01-01</th>\n",
       "      <td>5327.9</td>\n",
       "      <td>32.38</td>\n",
       "      <td>0.83</td>\n",
       "      <td>23.94</td>\n",
       "      <td>0.97</td>\n",
       "      <td>13.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1964-01-01</th>\n",
       "      <td>5878.4</td>\n",
       "      <td>33.75</td>\n",
       "      <td>0.85</td>\n",
       "      <td>25.07</td>\n",
       "      <td>1.03</td>\n",
       "      <td>14.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1965-01-01</th>\n",
       "      <td>6075.2</td>\n",
       "      <td>36.25</td>\n",
       "      <td>0.89</td>\n",
       "      <td>25.37</td>\n",
       "      <td>1.08</td>\n",
       "      <td>15.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1966-01-01</th>\n",
       "      <td>6312.7</td>\n",
       "      <td>36.24</td>\n",
       "      <td>0.93</td>\n",
       "      <td>24.55</td>\n",
       "      <td>1.05</td>\n",
       "      <td>16.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1967-01-01</th>\n",
       "      <td>6056.8</td>\n",
       "      <td>38.23</td>\n",
       "      <td>0.95</td>\n",
       "      <td>24.98</td>\n",
       "      <td>1.03</td>\n",
       "      <td>17.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1968-01-01</th>\n",
       "      <td>6375.9</td>\n",
       "      <td>40.83</td>\n",
       "      <td>0.99</td>\n",
       "      <td>24.96</td>\n",
       "      <td>1.03</td>\n",
       "      <td>18.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1969-01-01</th>\n",
       "      <td>6974.3</td>\n",
       "      <td>44.62</td>\n",
       "      <td>1.00</td>\n",
       "      <td>25.52</td>\n",
       "      <td>0.99</td>\n",
       "      <td>19.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1970-01-01</th>\n",
       "      <td>7101.6</td>\n",
       "      <td>52.27</td>\n",
       "      <td>1.00</td>\n",
       "      <td>26.01</td>\n",
       "      <td>1.00</td>\n",
       "      <td>20.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1971-01-01</th>\n",
       "      <td>7071.7</td>\n",
       "      <td>45.16</td>\n",
       "      <td>1.02</td>\n",
       "      <td>25.46</td>\n",
       "      <td>0.96</td>\n",
       "      <td>21.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1972-01-01</th>\n",
       "      <td>7754.8</td>\n",
       "      <td>42.50</td>\n",
       "      <td>1.07</td>\n",
       "      <td>22.17</td>\n",
       "      <td>0.97</td>\n",
       "      <td>22.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-01-01</th>\n",
       "      <td>8480.3</td>\n",
       "      <td>43.70</td>\n",
       "      <td>1.12</td>\n",
       "      <td>18.56</td>\n",
       "      <td>0.98</td>\n",
       "      <td>23.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1974-01-01</th>\n",
       "      <td>8105.2</td>\n",
       "      <td>47.88</td>\n",
       "      <td>1.10</td>\n",
       "      <td>21.32</td>\n",
       "      <td>1.01</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975-01-01</th>\n",
       "      <td>7157.2</td>\n",
       "      <td>36.33</td>\n",
       "      <td>1.07</td>\n",
       "      <td>22.75</td>\n",
       "      <td>0.94</td>\n",
       "      <td>25.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            WORLDCONSUMPTION  COPPERPRICE  INCOMEINDEX  ALUMPRICE  \\\n",
       "1951-01-01            3173.0        26.56         0.70      19.76   \n",
       "1952-01-01            3281.1        27.31         0.71      20.78   \n",
       "1953-01-01            3135.7        32.95         0.72      22.55   \n",
       "1954-01-01            3359.1        33.90         0.70      23.06   \n",
       "1955-01-01            3755.1        42.70         0.74      24.93   \n",
       "1956-01-01            3875.9        46.11         0.74      26.50   \n",
       "1957-01-01            3905.7        31.70         0.74      27.24   \n",
       "1958-01-01            3957.6        27.23         0.72      26.21   \n",
       "1959-01-01            4279.1        32.89         0.75      26.09   \n",
       "1960-01-01            4627.9        33.78         0.77      27.40   \n",
       "1961-01-01            4910.2        31.66         0.76      26.94   \n",
       "1962-01-01            4908.4        32.28         0.79      25.18   \n",
       "1963-01-01            5327.9        32.38         0.83      23.94   \n",
       "1964-01-01            5878.4        33.75         0.85      25.07   \n",
       "1965-01-01            6075.2        36.25         0.89      25.37   \n",
       "1966-01-01            6312.7        36.24         0.93      24.55   \n",
       "1967-01-01            6056.8        38.23         0.95      24.98   \n",
       "1968-01-01            6375.9        40.83         0.99      24.96   \n",
       "1969-01-01            6974.3        44.62         1.00      25.52   \n",
       "1970-01-01            7101.6        52.27         1.00      26.01   \n",
       "1971-01-01            7071.7        45.16         1.02      25.46   \n",
       "1972-01-01            7754.8        42.50         1.07      22.17   \n",
       "1973-01-01            8480.3        43.70         1.12      18.56   \n",
       "1974-01-01            8105.2        47.88         1.10      21.32   \n",
       "1975-01-01            7157.2        36.33         1.07      22.75   \n",
       "\n",
       "            INVENTORYINDEX  TIME  \n",
       "1951-01-01            0.98   1.0  \n",
       "1952-01-01            1.04   2.0  \n",
       "1953-01-01            1.05   3.0  \n",
       "1954-01-01            0.97   4.0  \n",
       "1955-01-01            1.02   5.0  \n",
       "1956-01-01            1.04   6.0  \n",
       "1957-01-01            0.98   7.0  \n",
       "1958-01-01            0.98   8.0  \n",
       "1959-01-01            1.03   9.0  \n",
       "1960-01-01            1.03  10.0  \n",
       "1961-01-01            0.98  11.0  \n",
       "1962-01-01            1.00  12.0  \n",
       "1963-01-01            0.97  13.0  \n",
       "1964-01-01            1.03  14.0  \n",
       "1965-01-01            1.08  15.0  \n",
       "1966-01-01            1.05  16.0  \n",
       "1967-01-01            1.03  17.0  \n",
       "1968-01-01            1.03  18.0  \n",
       "1969-01-01            0.99  19.0  \n",
       "1970-01-01            1.00  20.0  \n",
       "1971-01-01            0.96  21.0  \n",
       "1972-01-01            0.97  22.0  \n",
       "1973-01-01            0.98  23.0  \n",
       "1974-01-01            1.01  24.0  \n",
       "1975-01-01            0.94  25.0  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>const</th>\n",
       "      <th>COPPERPRICE</th>\n",
       "      <th>INCOMEINDEX</th>\n",
       "      <th>ALUMPRICE</th>\n",
       "      <th>INVENTORYINDEX</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1951-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>26.56</td>\n",
       "      <td>0.70</td>\n",
       "      <td>19.76</td>\n",
       "      <td>0.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1952-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>27.31</td>\n",
       "      <td>0.71</td>\n",
       "      <td>20.78</td>\n",
       "      <td>1.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1953-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>32.95</td>\n",
       "      <td>0.72</td>\n",
       "      <td>22.55</td>\n",
       "      <td>1.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1954-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>33.90</td>\n",
       "      <td>0.70</td>\n",
       "      <td>23.06</td>\n",
       "      <td>0.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1955-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>42.70</td>\n",
       "      <td>0.74</td>\n",
       "      <td>24.93</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>46.11</td>\n",
       "      <td>0.74</td>\n",
       "      <td>26.50</td>\n",
       "      <td>1.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>31.70</td>\n",
       "      <td>0.74</td>\n",
       "      <td>27.24</td>\n",
       "      <td>0.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>27.23</td>\n",
       "      <td>0.72</td>\n",
       "      <td>26.21</td>\n",
       "      <td>0.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>32.89</td>\n",
       "      <td>0.75</td>\n",
       "      <td>26.09</td>\n",
       "      <td>1.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>33.78</td>\n",
       "      <td>0.77</td>\n",
       "      <td>27.40</td>\n",
       "      <td>1.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1961-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>31.66</td>\n",
       "      <td>0.76</td>\n",
       "      <td>26.94</td>\n",
       "      <td>0.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1962-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>32.28</td>\n",
       "      <td>0.79</td>\n",
       "      <td>25.18</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1963-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>32.38</td>\n",
       "      <td>0.83</td>\n",
       "      <td>23.94</td>\n",
       "      <td>0.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1964-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>33.75</td>\n",
       "      <td>0.85</td>\n",
       "      <td>25.07</td>\n",
       "      <td>1.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1965-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>36.25</td>\n",
       "      <td>0.89</td>\n",
       "      <td>25.37</td>\n",
       "      <td>1.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1966-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>36.24</td>\n",
       "      <td>0.93</td>\n",
       "      <td>24.55</td>\n",
       "      <td>1.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1967-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>38.23</td>\n",
       "      <td>0.95</td>\n",
       "      <td>24.98</td>\n",
       "      <td>1.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1968-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>40.83</td>\n",
       "      <td>0.99</td>\n",
       "      <td>24.96</td>\n",
       "      <td>1.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1969-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>44.62</td>\n",
       "      <td>1.00</td>\n",
       "      <td>25.52</td>\n",
       "      <td>0.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1970-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>52.27</td>\n",
       "      <td>1.00</td>\n",
       "      <td>26.01</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1971-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>45.16</td>\n",
       "      <td>1.02</td>\n",
       "      <td>25.46</td>\n",
       "      <td>0.96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1972-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>42.50</td>\n",
       "      <td>1.07</td>\n",
       "      <td>22.17</td>\n",
       "      <td>0.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>43.70</td>\n",
       "      <td>1.12</td>\n",
       "      <td>18.56</td>\n",
       "      <td>0.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1974-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>47.88</td>\n",
       "      <td>1.10</td>\n",
       "      <td>21.32</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975-01-01</th>\n",
       "      <td>1.0</td>\n",
       "      <td>36.33</td>\n",
       "      <td>1.07</td>\n",
       "      <td>22.75</td>\n",
       "      <td>0.94</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            const  COPPERPRICE  INCOMEINDEX  ALUMPRICE  INVENTORYINDEX\n",
       "1951-01-01    1.0        26.56         0.70      19.76            0.98\n",
       "1952-01-01    1.0        27.31         0.71      20.78            1.04\n",
       "1953-01-01    1.0        32.95         0.72      22.55            1.05\n",
       "1954-01-01    1.0        33.90         0.70      23.06            0.97\n",
       "1955-01-01    1.0        42.70         0.74      24.93            1.02\n",
       "1956-01-01    1.0        46.11         0.74      26.50            1.04\n",
       "1957-01-01    1.0        31.70         0.74      27.24            0.98\n",
       "1958-01-01    1.0        27.23         0.72      26.21            0.98\n",
       "1959-01-01    1.0        32.89         0.75      26.09            1.03\n",
       "1960-01-01    1.0        33.78         0.77      27.40            1.03\n",
       "1961-01-01    1.0        31.66         0.76      26.94            0.98\n",
       "1962-01-01    1.0        32.28         0.79      25.18            1.00\n",
       "1963-01-01    1.0        32.38         0.83      23.94            0.97\n",
       "1964-01-01    1.0        33.75         0.85      25.07            1.03\n",
       "1965-01-01    1.0        36.25         0.89      25.37            1.08\n",
       "1966-01-01    1.0        36.24         0.93      24.55            1.05\n",
       "1967-01-01    1.0        38.23         0.95      24.98            1.03\n",
       "1968-01-01    1.0        40.83         0.99      24.96            1.03\n",
       "1969-01-01    1.0        44.62         1.00      25.52            0.99\n",
       "1970-01-01    1.0        52.27         1.00      26.01            1.00\n",
       "1971-01-01    1.0        45.16         1.02      25.46            0.96\n",
       "1972-01-01    1.0        42.50         1.07      22.17            0.97\n",
       "1973-01-01    1.0        43.70         1.12      18.56            0.98\n",
       "1974-01-01    1.0        47.88         1.10      21.32            1.01\n",
       "1975-01-01    1.0        36.33         1.07      22.75            0.94"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exog"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1951-01-01    3173.0\n",
       "1952-01-01    3281.1\n",
       "1953-01-01    3135.7\n",
       "1954-01-01    3359.1\n",
       "1955-01-01    3755.1\n",
       "1956-01-01    3875.9\n",
       "1957-01-01    3905.7\n",
       "1958-01-01    3957.6\n",
       "1959-01-01    4279.1\n",
       "1960-01-01    4627.9\n",
       "1961-01-01    4910.2\n",
       "1962-01-01    4908.4\n",
       "1963-01-01    5327.9\n",
       "1964-01-01    5878.4\n",
       "1965-01-01    6075.2\n",
       "1966-01-01    6312.7\n",
       "1967-01-01    6056.8\n",
       "1968-01-01    6375.9\n",
       "1969-01-01    6974.3\n",
       "1970-01-01    7101.6\n",
       "1971-01-01    7071.7\n",
       "1972-01-01    7754.8\n",
       "1973-01-01    8480.3\n",
       "1974-01-01    8105.2\n",
       "1975-01-01    7157.2\n",
       "Freq: AS-JAN, Name: WORLDCONSUMPTION, dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "endog"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           Statespace Model Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:       WORLDCONSUMPTION   No. Observations:                   25\n",
      "Model:                    RecursiveLS   Log Likelihood                -153.737\n",
      "Date:                Wed, 29 Aug 2018   AIC                            317.474\n",
      "Time:                        08:58:23   BIC                            323.568\n",
      "Sample:                    01-01-1951   HQIC                           319.164\n",
      "                         - 01-01-1975                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==================================================================================\n",
      "                     coef    std err          z      P>|z|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------\n",
      "const          -6513.9926   2367.656     -2.751      0.006   -1.12e+04   -1873.472\n",
      "COPPERPRICE      -13.6553     15.035     -0.908      0.364     -43.123      15.812\n",
      "INCOMEINDEX     1.209e+04    762.592     15.853      0.000    1.06e+04    1.36e+04\n",
      "ALUMPRICE         70.1441     32.667      2.147      0.032       6.117     134.171\n",
      "INVENTORYINDEX   275.2808   2120.277      0.130      0.897   -3880.385    4430.947\n",
      "===================================================================================\n",
      "Ljung-Box (Q):                       14.53   Jarque-Bera (JB):                 1.91\n",
      "Prob(Q):                              0.75   Prob(JB):                         0.39\n",
      "Heteroskedasticity (H):               3.48   Skew:                            -0.74\n",
      "Prob(H) (two-sided):                  0.12   Kurtosis:                         2.65\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Parameters and covariance matrix estimates are RLS estimates conditional on the entire sample.\n"
     ]
    }
   ],
   "source": [
    "mod = sm.RecursiveLS(endog, exog)\n",
    "res = mod.fit()\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[    2.88890056     4.94425555  1505.2705786   1856.55228281\n",
      "  1597.9741118   2171.97840966  -889.39020347   122.17036038\n",
      " -4184.27521999 -6242.73120711 -7111.45819909 -6400.38438413\n",
      " -6090.45569382 -7154.96712847 -6290.92468563 -5805.25759066\n",
      " -6219.31805425 -6684.49666283 -6430.13849572 -5957.57771077\n",
      " -6407.06003687 -5983.49315596 -5224.7172207  -5286.62180288\n",
      " -6513.99259408]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x231b064bbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(res.recursive_coefficients.filtered[0])\n",
    "res.plot_recursive_coefficient(range(mod.k_exog), alpha=None, figsize=(10, 6));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.2781906   0.51898719  1.0539959   1.94931158  2.44814403  3.37264225\n",
      "  3.04779699  2.47333119  2.96188541  2.58228688  1.49433914 -0.50008446\n",
      " -2.01112588 -1.75503207 -0.90603879 -1.41035932 -0.80383113  0.71254056\n",
      "  1.19151854 -0.93369946]\n"
     ]
    },
    {
     "data": {
      "image/png": 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DbgKeaf4pY/XaYP78+WRmZlJdXc1NN91EXFycrUMSdkQ3L6Dd0qmanJzM5s2b+eSTT7jiiivo06cPCQkJ3HnnnZjNZuLi4vDw8DD2P/G+6H7aa1jmCpo6aP2VUvnAX2hK9B8qpW4F9gPXtkdZXZ10iokTlZSUkJqair+/P7GxsezcudOYX8bDw4PExET+8Ic/GCOnkpKS+Oijj2wZsrBj7TVKZ9YpnmqXBkF9itEhovPQdrSymj3TWrNo0SKjBt+yXvK8efNYtGgRQ4cOZdGiRSQlJREZGYmTk8274UQnYvdLHO7duxdvb2/8/Pwk6XdSWmuKioooKytrtU5od3fgwAGjWcbV1ZWnnnoKgPDwcMrKyjCZTMY0wImJie3SgS+6pi6zxGFISAj5+fnY45BN0XZubm7G3OXdUW1tLS4uLgD86U9/YtmyZRw4cAAAFxeXViO/LBaLVHBEh7D7hO/s7Cy1QtGptCygfWLH6p49eyguLjaG5I4fP95YXzUmJqbVhW7+/v42jF50ZXaf8IWwd4WFhVgsFsaOHUuPHj149tlnefTRRwHo0aMHJpOJqVOnGpPstTwnhLVJwhfiLB05coQPP/zQqMFnZ2cDTVexTpkyhSuvvJLevXtjNpsZOnSozDEj7Ibdd9oKYStaa3Jzc41mmSlTpjBlyhS2bNlCTEwMQUFBmM3mVh2rMs5d2EKX6bQVwloaGxtxcHCgurqaGTNmYLFYOHr0KADu7u7069ePKVOmMGLECPbv309ISIh0rIpORRK+6JYaGhrIzMxs1bEaFRXFihUrcHNzo7y8nEsvvdToWI2KijIWtnF0dKRfv342/gRCnD1J+KJbOHToEHv27GHs2LFA00I669atA5rm9TebzYwZM8Z4/Q8//GCTOIXoSJLwRZeUkZHBd999Z9Tg9+/fj5eXl7Ei0913382CBQswm82Eh4dL04zoFiThi05Na01WVpbRLPP000/To0cPPvroIxYuXEhoaCijRo3ivvvuw2w2G/vNmDHDhlELYRsySkd0Ki3zKqWkpPCXv/yFlJQUYyEWLy8vfvrpJ+Li4jhy5Ahaa/r06WPjiIXoeDJKR3R6dXV1bN261WiWsVgsLFy4kJkzZ+Lo6Eh+fj7Tp0835pyJiIgwFtDu3bu3jaMXwv5Iwhd2QWtNXl4etbW1DBo0iCNHjhAWFkZ1dTWAcSGTn58f0LSQ+7Zt22wZshCdjiR8YTNr165lw4YNRvv74cOHmT17Nu+99x6BgYE88MADREVFYTab6d+/v3SsCnGepA1fdLjGxkZ27NiBxWKhtLSUP/zhDwBERUWRkZHB4MGDjfHu48aNY+TIkTaOWIjORdrwhc29/fbbvP/++6SkpFBWVgbAgAEDuO+++1BKsWLFCoKCgoxmGiFEx5KEL85LdXU1mzZtMjpV09LS2Lx5M56enuzdu5djx45xww03GPPNDB482GiaGTFihI2jF6J7kYQv2kxrTXZ2Nr1798bb25v333+fm2++mbq6OgD69euHyWSitLQUT09PFi5cyMKFC20ctRCihSR8cUpVVVWsW7eO5ORkY2hkUVERn3zyCdOnT2fkyJH84Q9/MGrvwcHBtg5ZCHEa0mkrAKivrycjI4Pk5GSGDRvGhAkTyMrKYsiQISiliIiIMDpWL7vsMpk8TAg7Ip224oy01jz66KP88ssvpKWlUVlZCcAdd9zBhAkTGDRoEKtXryYhIUEW0BaiC5CE3w1UVFSQnp5udKz27NmTxYsXo5Ti66+/xt3dnXnz5hlXrIaFhQGglGLSpEm2DV4I0W4k4XcxjY2N7N+/30jat956K8uWLaOhoQGAgQMHcumllxqv37RpkyzBJ0Q3IQm/kysuLuaXX34xrlZNSUmhqqqK48eP4+rqitlsNpbiM5lMBAQEtNpfkr0Q3Yck/E6ktraWzZs3Y7FYuP766/Hz82Px4sU88sgjODg4EBUVxcyZMzGbzTQ2NgIwb948G0cthLAXkvDtXE5ODv/85z+xWCxs3LiR2tpaAAYNGsSll17KzJkzMZlMxMfH4+XlZeNohRD2TBK+nTh+/DipqanGePcbbriBGTNmUF1dzaJFi4iPj+eee+4xOlZDQkIACA0NJTQ01MbRCyE6A0n4NtDQ0EBJSQl+fn5UVlaSlJREZmYmLddEDB061BgiGRERQWlpqbGAthBCnCtJ+FZw6NAhY0hkcnIyaWlpXHTRRXz66ad4eHiQlJTEjBkzMJvNJCYm0qtXL2NfpZQkeyFEu+jwhK+UygXKgAagvi1Xg3VmVVVVbNy4kf379zNr1iwApk2bRkpKCs7OzsTExDBnzpxW49uXLFliq3CFEN2ItWr4E7XWhVYqy+p+/PFHPv74YywWC1u2bKG+vh43NzeuueYanJ2d+fvf/46rqyuxsbG4ubnZOlwhRDclTTpnobi4mJSUFKNjdfny5fTq1Yv169fzzjvvkJSUxEMPPWSMeW9pipkwYYJtAxdCCKwweZpSai9wDNDAG1rrRb96fj4wH6B///7x+/bt69B42qquro7GxkZcXV358ccfue2229i9ezfQ1K4eGRnJBx98QGRkJJWVlbi6uhoLaAshhDXZ0+RpF2itDyqlAoHvlVI7tdZrW55s/gJYBE2zZVohnt9oWUC7pVPVYrGQnp7Om2++yQ033EBgYCARERHMmTMHs9lMQkIC3t7exv4eHh62CFsIIc5Khyd8rfXB5p9HlVKfAknA2tPv1bHKy8tJS0vD09OTxMREDh8+bIxld3V1JT4+nttvv52IiAgAIiMj+fe//23LkIUQ4rx1aMJXSnkCDlrrsub7lwA2WQLpnXfeYd26dVgsFjIyMmhsbGTGjBmsXLmSoKAg3nzzTWJiYhg5ciQuLi62CFEIITpUh7bhK6UGAp82P3QClmut/3qq17fHAihHjhwxxrzX1tbyj3/8A4C4uDhyc3NJSkoyOlWTkpJkAW0hRKdnF234WuscILojy2jxzDPP8MYbb5CbmwuAk5MTF1xwgfH8d999h5+fn7GAthBCdDddZlimh4cHCQkJ3HXXXZjNZuLi4nB3dzee9/f3t2F0Qghhe7KmrRBCdHJtbdKR1S+EEKKbkIQvhBDdhCR8IYToJiThCyFEN9FlRumIc1NcUcv7yfv4YushfD1dGBToRXiAJ4MCvQkP9KRPDzcZyipEFyEJv5vKLihnybq9fLIxn+q6RpIG+FJV18C/Nx2grKbeeJ2niyPhgV6EB3id8GXgRX9fT1yc5ARRiM5EEn43orXGsreYxT/nsHrHUVycHLgqpi+3jh3AkN7exmsKymrYU1BOdkEF2UfLyS4oJzmniE83HTDey9FBEerrYXwZDA70ImmAL/18ZSI5IeyVJPxuoK6hka+2HeLNn3PIOHAcX08X7pk0mBvNoQR4u7Z6rVKKwB5uBPZwY3R464vVymvq2VtQwZ6CMrKPVpBd0PRlsGbXUeoamq7nGBjgybjBAYwfGoB5gB/uLh03ZXRtfSPbDpSSmltM5sHjBPd0JyLIm+FBPRjg74mTo5yBCHEiufCqCyutquODlP0s3ZDLodJqBgZ4MnfMQKbH9cXNuf0ScX1DIzmFFfycVcja3QUk5xRRU9+Ii5MDpgG+xhfA4ECv8+oPKK+pZ+O+Y6TmFpOaW8zmvBKq6xoBCPJxo7C8xvjicXVyYEhvbyKCvIkI6mHcfNxlfWDR9bT1witJ+F1QXnElS9bv5cPUPCpqGxg10I954wYwYUggDg4d3wFbXddAyt5iftpdwNrdBWQdLQegTw83xg3xZ/yQQMYM8sfH4/TJt6CshrTcYlJyi0nLPcb2g6U0anBQEBnsQ2KYL0kDehEf6kuAtyu19Y1kF5Sz49Dx5lsZOw4dp6ii1njPvj3diQjqwfATvgj6+3pY5fciREeRhN8Nbdx/jMU/5/BNxmEclOKK6GBuHTOAEX19bBrXwZIq1u4uYG1WAT9nFVJWXY+Dgph+PRk3JIDxQwIYGdKT/GOVpOxtqr2n5R4jp7ACaKqtx/bvSVKYL4kDfInt3wsv17a1RmqtOVpWQ+avvgRyCsppbD70PV0ciQjqwXVJ/bkqti+OkvxFJyMJvxuoqW9ga34pKXuLWb3jCJv2l9DDzYnrTaHMGR1GHx/7WzC9vqGRLfkl/LS7kJ92F7A1vwStwcXRgdqGpuYZH3dnEsN6kdic4EcE+7T7iKDqugZ2HykzvgSSc4rYebiMwYFePHDJUCZH9pbhqKLTkITfBVXW1rNxXwkpe4uw7C1mU14JtfVNSXJYH2+uS+zHtQn98Gxj7dceHKuo5ec9hWzeX8LAAE+SBvgyKMDL6k0sWmu+zjjMc9/tIqegguh+PXlk8lBGD5JZVoX9k4TfBZRW1pG2r5iUvcVY9haTcaCU+kaNg4IRfX1ICvMlaYAviWG+9PKUVbraQ31DI//aeID/W72bQ6XVjBnkz0OThxLdr6etQxPilCThd0IFZTWk5v43we88fNxo7oju50PSAF+SBvgRH9r2NmxxbqrrGngveR//b002xRW1XDqiDw9cMoRBgd5n3lkIK5OE30mUVNbyQWoeH6XlkV3Q1Enp4eJIfGgvowYf3a9nuw6jFG1XVl3HW+v28ubaHKrqGrg6LoT7Lh5C357uZ95ZCCuRhG/n9hwt4+31ufxr4wGq6howDfBlUkQgSQP8iAzugbNcNGRXispr+H9rsnk3eR9omG3uz50TB+Hv5XrmnYXoYJLw7VBjo+anrAKWrNvLz1mFxtQGcy4IIyKoh63DE21wsKSKl1Zn8VF6Hu7Ojtw6diDzxg7A200u6BK2IwnfjlTU1PPJxnyWrs8lp7CC3j1cudEcyqyk/vhJDbFT2nO0nBe+38VX2w7Ty8OZOyYM4qbRYTKhnLAJSfh2IK+4knd+yeWD1DzKquuJ7teTWy4I49IRQZIYuoht+aU8++1Ofs4qZOLQAF67IV76W4TVScK3kZYZKd9ev5fvM4/goBSXRgVx8wVhxPXvZevwRAd537KPP/87gwvC/Vn0+3g8XGQUlbCetiZ8OSrbSXVdA59vOcjb63PJPHScnh7O3DY+nBtHhRLkIyM6urrZplBcnRx5+OMtzHk7lSVzEmXobBfW0KjZceg46c2T+WUePM7V8SHcOXGQrUM7LTkiz8PBkirW7ynkl+wi1uwuoLiiliG9vXh6ehTTYvp26NTAwv5cEx+Ci5MDf1i5mRvfsrD05iSZnbOLqKipZ3NeCWm5x0jbV8ym/SWUNy8UFOTjRqC3K//4dhdaa+66cLCNoz01Sfhnoai8hl9yitiQXcSGPYXkFlUC4OvpwuhwP2Yl9Wd0uJ/MwdKNXRkdjIujA3ev2Mjsxcm8e4tJroLuhI4crzaSe1ruMTIPHaehUaMUDO3tzVWxfUkI60VCmC99e7rT0Kh58KMtPPfdblydHJk3bqCtP8JJSRv+aZRV15Gyt5gN2UWs31PIzsNlAHi5OmEe6MuocH8uGOTHkEBvmV5XtPLDziPc9t5GBvp78t5ck4zXt3P7iypZt6eQtNxiUvcVk1dcBYCbswMx/XqSGOZLfGgvYvv3OuVZW31DI/d+sJkvtx1i4e8i+f2oMKvFL52256C6roGN+46xPruQDdlFbM0vpaFR4+rkQEJYL0aH+zM63I+ovj6ympI4o3VZhcx9J5W+Pd1ZPs9M7x72N3tpd9fYqFn0cw7PfbuL+kaNv5crCaG9jNr72V4EWdfQyB3vb+T7zCM8PT2KWUn9OzD6/5KEfwq19Y0cOV7NgZIqDjbfDpRUs7ewnI37m2afdHRQRIf4NCX4QX7E9e8lQ+3EObHkFHHL0lQCvF1ZPs9MsEzJYDcKymq4/8PN/JxVyGVRfXho8jDC/DzOu0m2pr6B+e+kszargOeuiebq+JB2ivjU7CbhK6WmAC8BjsBirfUzp3rt+SZ8rTXFFbUcKm2d0A+W/PdxQXkNv/7Ifp4uhPRyJyHMlwsG+ZEY5itXTop2k77vGHOWpODj4cyKeWZZ6N0OrMsq5L6VmymrruMvV0QyK6lfu/a9Vdc1cOuyVH7JLuKl62K5Ijq43d77ZOwi4SulHIHdwMVAPpAKzNJaZ57s9eea8H/cdZSnPs/kQEm2PEJgAAAa9ElEQVQVNc3zw7dwc3Yg2Med4J7uBPd0a/7p3ryt6bHU3kVH25Zfyg1vWfBwceT9uSYGBnjZOqRuqa6hkf/7fjev/ZTNoAAvXrk+jqF9OmYG1MraeuYsSSV9/zFevT6OKSP6dEg5YD8JfxTwhNZ6cvPjRwG01k+f7PXnmvA355Xw5tqcVgm9b/PPXh7OMmpG2IUdh45zw2ILDg6K5XNNDO4tUy1bU15xJfd+sImN+0uYldSPx6dGdvjQ6fKaem58y0LGgVIW3ZjAxGGBHVKOvST8a4ApWuu5zY9vBExa67tO9vrzadLZsGHDOccphLUcKGvgrxvKaNDwx1FehPrIyGhrSDlYy6ItlWitmRvtyai+1hsqW1HXyF83lHOgrIEHTV5EBZy8uXj06NHnXEZbE35HDzU5WdW61TeMUmq+UipNKZVWUFDQweEIYVt9vR157AJvXBzhfzeUk1NSb+uQurTaBs2SrZW8mFZBkKcDfxvfw6rJHsDT2YFHR3nRx9OR51PK2VFUZ9XyT9QlmnSE6Gzyiiu5fnEyJRV1LL0lkfhQX1uH1OXsOVrGXcs3sfNwGQvGDeSBS4badNLCwvIarluUzKGSKt651UR8aPvNrWUvNfxUYLBSaoBSygW4Dvisg8sUwu718/XgwwWj8Pd25ca3UkjOKbJ1SF2G1poPU/OY+vI6CspqWHpzIo9eFmHzGWr9vVxZPtdEgLcrc5aksDW/xOoxdOhvQGtdD9wFfAvsAD7UWm/vyDKF6CyCfNxZOd9M357uzHk7hS+3HrJ1SJ1eWXUd936wmYc/2Up8aC++vncsE4Z2TEfpuQjs4cbyeWZ8PJy58a0UMg8et2r53e7CKyHsTVF5DXPfSWPT/hKuN/Xn8anDZajwOdiSV8LdKzZxoKSK+y8ewm3jw3G00ylP8oormfHGL9TUN7Jyvvm8R2zZS5OOEOIM/Lxc+XDBKG4bH85yy36ufGUdu4+U2TqsTuNwaTWv/JDF1a9toKFR8+ECM3dOHGS3yR6amvSWzzPj6KC4frGFnIJyq5QrNXwh7Mja3QXc/+Fmymvq+csVkVyX2L5XgHaEbfmlrNp8AH9vV0wDfBnR1+es5p85Ww2Nmi35Jfy48yg/7DzK9uZmkcmRvfn71SPp6dF5ZifNOlLGdYuScXZ04MMFo+jvd25XYdvFOPyzJQlfCDhaVs0DH27h56xCLh8ZxNPTo+hhZ1N9tCz4817yPrbkl+LsqKhraMolHi6OxIf2wjTAF9NAP0aG+ODqdH5NVMer61i7u4Afdh7lp10FFFXU4qAgIdSXicMCuXBYIEN6e9n9l+PJ7Dh0nFlvJjMtpi9PXBl5Tu8hCV+ITqyxUfPG2hye+24XQT5uvDwrllg7WCIzp6Cc9y37+Tg9n9KqOgYFenGjOZSr4vpSXddA6t5jWPYWYckpZldzs5SrkwOx/XtiGuCHaYAvsf17nfEKV6012QUV/LDzCD/sPEpa7jHqGzU9PZyZMCSAicMCGT8koFPV5k9nb2EF/Xq5n/MsvJLwhegC0vcd454VmzhyvJoHJw9l/tiBVl97ob6hkdU7jvJe8j7W7SnEyUExeUQfbjSHYhrge8pa9bGKWlJyi7HkFGPZW0TmoeNoDc6OiuiQniQ1nwHEh/bCy9WJmvoGLDnF/NDcVLO/uGmBoWF9vLmwuRYf27+XXbfN24okfCG6iNKqOh7911a+2naYsYP9eWFGDAHeHb+gypHj1XyQkseKlP0cPl5NsI8bs5L6MzOpH4HeZz+3f2lVHen7Wr4Aitl2oGm9CUcHxZDe3uwrqqCytgFXJwcuGORvNNX0lSmlz0gSvhBdiNaaFSl5PPn5drzdnPm/mdGMHRzQIeX8klPEe8n7+G77EeobNeOGBHCDqT8XDgts14V/KmrqSd93jJS9xWzOKyHM34MLhwUyaqC/rAd9liThC9EF7Tpcxl3LN7KnoJzbxodz/8VD2mVETGlVHf/amM97yfvILqigp4czMxL6cX1Sf8L8PdshctGR2prwZao+ITqRoX28+eyuMSz8YjuvrckmOaeIf14Xe8ZFVarrGjhYUkX+sZZbJQdK/nv/aFnTwkAx/Xry/LXRXD4ySC7+6oKkhi9EJ/XF1oM8+sk2UPC3q6KICOpB/rFKI6k3JfSmxwVlNa32dXJQBPV0I6SnByG93Anp5cGkiEBG9PWx0acR50Nq+EJ0cVNHBhMd0pO7Vmzi7hWbWj3n7KgI7ulOSC93Jg4NIKTXfxN7317u9PZ2bdf2eNE5SMIXohPr5+vBx7eNYtXmgzg5KEJ6udO3lzuB3m4yfFH8hiR8ITo5Z0cHrokPsXUYohOQczohhOgmJOELIUQ3IQlfCCG6CUn4QgjRTUjCF0KIbkISvhBCdBOS8IUQopuQhC+EEN2EJHwhhOgmJOELIUQ3IQlfCCG6CUn4QgjRTUjCF0KIbkISvhBCdBNdZnrkDz/8kG3btmE2mzGZTPj7+9s6JCGEsCtdJuFv2LCBl19+mcbGRgAGDhzIhAkTeOuttwDQWqOULAghhOi+utSathUVFaSnp5OcnIzFYqGxsZFPP/0UgEmTJlFRUWGcAZjNZsLCwuRLQAjR6bV1TdsOS/hKqSeAeUBB86Y/aq2/Ot0+HbmI+eOPP86aNWtIS0ujqqoKgNmzZ/Pee+8BsG7dOqKiovDxkUWchRCdi70sYv5/WuvnOriMNlm4cCEAdXV1ZGRkYLFYCAlpWhauqKiIsWPHopQiIiLCOAuYPHkyoaGhtgxbCCHaTZdpw28rZ2dnYmNjiY2NNbZ5eXnx7bffYrFYSE5OZtWqVSxZsoRFixYxb948cnNzef31142moKCgIBt+AiGEODcdnfDvUkr9HkgDHtBaH+vg8s6Jq6srl1xyCZdccgnQ1MGbnZ2Nr68vABkZGbzwwgvU1dUB0K9fP0wmE08//TSDBg2yWdxCCHE2zqsNXym1Guhzkqf+BCQDhYAGngKCtNa3nOQ95gPzAfr37x+/b9++c46nI1VXV7Np0ybjLCA5OZlffvmFoKAg/vnPf7Js2bJWHcKDBw+WDmEhhFXYvNP2V8GEAV9orUec7nUd2WnbkVasWMHixYtJTU2lrKwMgMDAQPLz83F2dmb37t34+/sbZwxCCNGebN5pq5QK0lofan54FZDRUWXZ2qxZs5g1axYNDQ3s2LEDi8XCwYMHcXZ2BmD+/Pn89NNPDB482DgLGDNmDNHR0TaOXAjRnXTksMx3gRiamnRygQUnfAGcVGet4Z/JunXrWLdundEcdPjwYSZPnsw333wDwDPPPMPAgQMxm83069dPmoKEEGfFrpp02qqrJvwTaa3Zv38/5eXlREZGUllZSUBAAJWVlQD06dMHk8nE3LlzmTp1qo2jFUJ0BjZv0hEnp5RqNbbfw8ODY8eOsXXrVuMMwGKxsH//fgD27t3L7373O6Mz2GQyERERgaOjo60+ghCik5Iavp1qmfsnIyODBx98EIvFQklJCQDe3t6sWrWKiRMncuzYMWpra+ndu7eNIxZC2IrU8Du5lnb8ESNG8M0339DY2EhWVhYWiwWLxcLgwYMBeO+997jnnnsICwvDZDIZZwKJiYk4OcmfVwjxX1LD7+R27NjBV199ZTQH5eXl4eDgQGlpKV5eXnz55ZccO3YMs9lMeHi4dAgL0QVJDb+biIiIICIiwnh88OBBtm/fjpeXFwCvv/46X3zxBQB+fn6YTCYmTZrE/fffb5N4hRC2IzX8Lq6+vp7MzEyjM9hisRAcHMx3330HwDXXXIOXl5fRIRwVFSVNQUJ0MjIsU5xSfX09Tk5OaK25+uqrWb9+PUePHgWaRg099NBDPPHEE0DTGUNwcLANoxVCnIk06YhTaqnBK6X417/+hdaa3Nxcox9g+PDhAOTn59OvXz/69u1rdAibTCYSEhLw9PS05UcQQpwDqeGLUyoqKmL58uXGZHE5OTlA08ig2bNnk5uby48//ojZbGbo0KE4ODjYOGIhuidp0hHtrqCgAIvFQlJSEoGBgSxatIgFCxYA4OPjQ1JSEiaTiXvvvVcWkRfCiiThiw7X2NjIrl27WnUIZ2RkUFBQQM+ePXnttddYt26dcW1ATEwMLi4utg5biC5H2vBFh3NwcDCGhd58880AVFVV4e7uDkBJSQk//fQTy5cvB8DFxYUxY8awevVqlFKUlJTg4+Mj1wYIYSVSwxcdLj8/3zgDqKqq4uWXXwYgKSmJffv2teoQTkxMlIXkhThL0qQj7N5bb73Fzz//jMViYefOnQBMnz6dTz75BGjqHI6KiiIyMlKuDRDiNCThi06lpKSElJQUvLy8GD16NEeOHKFPn6bVMz09PUlISMBsNjNz5sxWC9ALIaQNX3QyPXv2NBaRh6YlIvfs2WN0CCcnJ/PCCy8wdOhQYmNj2bVrF3/+85+NK4Tj4uLw8PCw4ScQwv5Jwhd2SSlFeHg44eHhzJ49G2haSL6xsRFougI4LS2Njz/+GABHR0eio6N55513iIyMpLq6GhcXF7k2QIgTSMIXnYabm5txf+LEiezdu5cjR44YHcLJyckEBgYC8OKLL/Lss8+SlJRknAUkJSXh5+dnq/CFsDlpwxdd0n/+8x9WrlxJcnIy27dvp7GxEVdXV8rKynB2dmb9+vW4uroycuRIuTZAdHrShi+6tUmTJjFp0iQAysrKSE9PJzc3F2dnZwAeeeQR1q9fj5ubG3FxcZjNZi688EIuv/xyW4YtRIeSGr7olvLy8ow5giwWC+np6Vx88cV89tlnANx+++2EhoYak8V5e3vbOGIhTk1q+EKcRr9+/ejXrx/XXnstAHV1dRQXFwNNncM//PADu3fvBpquKI6MjOSBBx7gpptuQmtNY2OjLCQvOh1J+EIAzs7OxkLwbm5u7Nq1i6KiIlJSUowO4ZaLv7KyskhISCAxMdGYJ8hkMslC8sLuSZOOEGcpJyeH559/nuTkZLZu3Up9fT0AX3zxBZdffjn5+fnk5eURGxvbamSREB1FmnSE6CADBw7k1VdfBZomi9u4cSPJyckkJiYCsHLlSh588EGcnZ2JiYkxzgCmT59uTCwnhC1IDV+IdlZQUMD69euNDuHU1FSqq6s5fvw4Hh4eLFu2jP379xvXBvTs2dPWIYtOTmr4QthIQEAA06ZNY9q0aUDTGsI5OTnG1A9r1qxh2bJltFS2hg0bxuTJk3nxxRcB0FrLlNGiQ0gNXwgbKC0tJS0tzegQ9vHx4d133wWapo12c3Nr1SEcEhJi44iFPZPZMoXohLTWPPjgg2zYsIGNGzdSW1sLwJ133skrr7yC1pr169cTGxsrC8kLgzTpCNEJKaV4/vnnAaipqWHLli1YLBaGDRsGwL59+xg7diyOjo6MGDHCOAOYPHkywcHBtgxddALnVcNXSl0LPAFEAEla67QTnnsUuBVoAO7RWn97pveTGr4Qp1dRUcGaNWuMpqCUlBRKS0tZuXIlM2bMYMeOHSxfvtxYQSwgIMDWIQsrsFYNPwOYDrzxq8KHA9cBkUAwsFopNURr3XCe5QnRrXl6enL55Zcbc/60LCTfUrvfuHEjf/vb34xppAcOHIjZbObZZ5+lb9++Notb2IfzSvha6x3AyUYU/A74QGtdA+xVSu0BkoBfzqc8IURrLQvJt5g9ezbTpk0jPT3dOAv4+eef6dGjBwB//etf+fzzz42mILPZTFhYmIwK6iY6qg2/L5B8wuP85m1CiA7m6enJuHHjGDdu3G+eCwoKwtXVlUWLFvHSSy8BMGjQIHbv3o1Sil27dhEUFGR8QYiu5YwJXym1Guhzkqf+pLVedardTrLtpJ0FSqn5wHyA/v37nykcIcR5uOWWW7jllluor69n27ZtWCwWSktLjRr+rFmz2Lx5MxEREcYZwNixY1udRYjOq12GZSql1gAPtnTaNnfYorV+uvnxt8ATWuvTNulIp60QtvWf//yHDRs2GFcJFxUVMXPmTD744AMAnnrqKUaMGIHJZJJRQXbE1sMyPwOWK6VeoKnTdjCQ0kFlCSHayYkLx2ityc7ONiaHKygo4KmnnqKurg5ommLaZDJx2223GfsI+3ZeCV8pdRXwMhAAfKmU2qy1nqy13q6U+hDIBOqBO2WEjhCdi1KKQYMGGY8DAgI4fvw4mzZtMjqELRYLhw8fBmDLli3ccsstra4QHjx4sCwkb0fkSlshxHlpmfsnJSWFP/7xj6SkpFBWVgZAz549+f7770lISKCwsBCllCwk3wFs3aQjhOgmWjp8k5KSWL16NQ0NDezcudM4AwgPDwfgtdde4/HHH2fw4MHGhWFms5m4uDg5C7ASqeELIaxiy5YtfP3110Zz0OHDh3F3d6e0tBRnZ2c+/fRT6urqMJlM9O/fX64NOAtSwxdC2JXo6Giio6OBpmagvLw8srKycHZ2BuD5559n/fr1APTp0weTycSUKVO47bbbbBZzVyMJXwhhdUop+vfv3+ramx9//JGtW7e26hB2dHQ0Ev7ll19OcHCw0RQUEREhC8mfJWnSEULYrfr6epycnKipqWHatGlYLBaOHTsGgJeXF08++ST3338/jY2NHD16lD59TnaNaNcnTTpCiE7PyakpRbm6uvL111+jtSYrK8s4Axg8eDAAO3bsYMSIEYSGhraaJ0gWkm9NavhCiE7v8OHDvP/++0ZzUF5eHgCff/45U6dOZffu3aSmpmIymQgPD+9yHcJSwxdCdBt9+vThgQceMB4fOnQIi8XCmDFjAFi1ahUPP/wwAH5+fsYZwL333tutJoqTGr4QostraGhg+/btrTqEs7OzKSkpwdXVleeff55t27YZXwRRUVFGc1JnIDV8IYRo5ujoyMiRIxk5ciTz5s0DoLKyEldXVwAKCwv5+uuvWbZsGQDu7u5MnjyZTz/9FGhadN7Hx8c2wbcjqeELIQRN1wbk5uZisViwWCw4Ozvz7LPPAjB06FDKy8uNDmGTyURCQoLdLCTf1hq+JHwhhDgNrTWvvvoqycnJJCcnk52dDcDNN9/MkiVL0Frz7rvvkpiYyNChQ20yTYQkfCGE6AAFBQWkpKQQGBhIYmIiWVlZDBkyBAAfHx8SExMxmUxcf/31DB8+3CoxSRu+EEJ0gICAAGMReYDw8HAyMzONpqDk5GSeeeYZ4uLiGD58OBs3buS5554zmoNiYmKMvgNrk4QvhBDnoWUh+YiICObMmQNARUWFMe1Dfn4+a9euZcWKFQC4uLgQGxvLihUrGDBgADU1Nbi4uFjl2gCZk1QIIdqZp6encYXvlVdeSX5+Pnl5eXz88cfce++9uLm50bt3bwCeeOIJkpKSrBKX1PCFEMIKQkJCCAkJ4eqrr261/YILLmg1iVxHkoQvhBA2NHXqVKuVJU06QgjRTUjCF0KIbkISvhBCdBOS8IUQopuQhC+EEN2EJHwhhOgmJOELIUQ3IQlfCCG6CbuaLVMpVQDsO8fd/YHCdgxHyu98MUj5Un53LT9Uax1wphfZVcI/H0qptLZMDyrld90YpHwpvzuX3xbSpCOEEN2EJHwhhOgmulLCXyTl25ytY5DypfzuXP4ZdZk2fCGEEKfXlWr4QgghTsOuE75SaolS6qhSKuOEbdFKqV+UUtuUUp8rpXo0bw9TSlUppTY3314/YR8XpdQipdRupdROpdTVJyuvA8uf1fz6rUqpb5RS/u1dfvNzI5uf2978vFvz9vjmx3uUUv9UbVxLrT3KV0p5KKW+bP69b1dKPdOWstvz85/w/Gcnvpe1yrfG8XeG8jv8+FNKzT7h2N+slGpUSsU0P9fhx9+pyrfW8Xe6z3/Cvmd1/HUIrbXd3oBxQByQccK2VGB88/1bgKea74ed+Lpfvc+TwP8233cA/K1VPk2LzBxtKRN4FniiA8p3ArYC0c2P/QDH5vspwChAAV8Dl1qrfMADmNi8zQX42Zrln7DfdGD5qY6RDv79W+P4O9Xv3yrH36/2iwJyTnjc4cffqcq31vF3us9/rsdfR9xsVnCbA/xVIgWO89++h35A5sle96v3yAM8bVE+4AwUAKHNB/zrwPwOKP8y4L2T7B8E7Dzh8SzgDWuVf5L3ewmYZ83yAS9gHTD8bP/h2ql8axx/p/r7W+X4+9U+fwP+as3j71TlW+v4O13553P8tffNrpt0TiEDuLL5/rU0/dJbDFBKbVJK/aSUGguglOrZ/NxTSqmNSqmPlFK9rVW+1roOuB3YBhyk6Y/+VgeUPwTQSqlvmz/nw83b+wL5J+yf37zNWuUbmv8WVwD/sXL5TwHPA5XnUe45lW/F4++k5Vvx+DvRTGBF831rHX+nKt/Qwcff6cpvz+PvvHTGhH8LcKdSKh3wBmqbtx8C+mutY4H7geXN7WtOQAiwXmsdB/wCPGet8pVSzjT9w8UCwTSddj/aAeU7AWOA2c0/r1JKTaKpVvdr5zM062zLB0Ap5UTTP8E/tdY51iq/uR11kNb60/Mo85zLx3rH36k+v7WOPwCUUiagUmvd0lZtrePvVOW3bO/o4++k5XfA8XdeOt0i5lrrncAlAEqpIcDlzdtrgJrm++lKqWyaaj3pNH2ztvzCPwJutWL5qnlbdvM+HwL/097l01Rz+klrXdj83Fc0tT++R1PCaRFCU03PWuW31KYWAVla6xfPtexzLL8ciFdK5dJ0vAcqpdZorSdYqfwfsMLxd5ryjzfv19HHX4vraF27zcc6x9+pym/R0cffqcofRTsef+er09XwlVKBzT8dgD/T1CaJUipAKeXYfH8gMJimjhMNfA5MaH6LSUCmtcoHDgDDlVItExtdDOxo7/KBb4GRzaMSnIDxNLUvHgLKlFJmpZQCfg+sslb5za/9X8AHuO9cyz3X8rXWr2mtg7XWYTTVfHefzz/bOZRvlePvVOVjveOvZdu1wAct26x4/J20/Obt1jj+TvX52/X4O2+27EA4042mb8pDQB1NNYVbgXuB3c23Z/hvB8rVwHZgC7ARuOKE9wkF1tJ0OvsfmpperFn+bTT9k22l6Z/fr73Lb379Dc0xZADPnrA9oXlbNvDKift0dPk01eh08+ff3Hyba83Pf8LzYZzdKJ32+v13+PF3hvKtdfxNAJJP8j7WOv5+U76Vj7+Tfv5zPf464iZX2gohRDfR6Zp0hBBCnBtJ+EII0U1IwhdCiG5CEr4QQnQTkvCFEKKbkIQvhBDdhCR8IYToJiThCyFEN/H/AbiYwadsyT1vAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x231b064b6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(res.cusum)\n",
    "fig = res.plot_cusum();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x231b0895cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res.plot_cusum_squares();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantity theory of money"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "start = '1959-12-01'\n",
    "end = '2015-01-01'\n",
    "m2 = DataReader('M2SL', 'fred', start=start, end=end)\n",
    "cpi = DataReader('CPIAUCSL', 'fred', start=start, end=end)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ewma(series, beta, n_window):\n",
    "    nobs = len(series)\n",
    "    scalar = (1 - beta) / (1 + beta)\n",
    "    ma = []\n",
    "    k = np.arange(n_window, 0, -1)\n",
    "    weights = np.r_[beta**k, 1, beta**k[::-1]]\n",
    "    for t in range(n_window, nobs - n_window):\n",
    "        window = series.iloc[t - n_window: t + n_window + 1].values\n",
    "        ma.append(scalar * np.sum(weights * window))\n",
    "    return pd.Series(ma, name=series.name, index=series.iloc[n_window:-n_window].index)\n",
    "\n",
    "m2_ewma = ewma(np.log(m2['M2SL'].resample('QS').mean()).diff().iloc[1:], 0.95, 10*4)\n",
    "cpi_ewma = ewma(np.log(cpi['CPIAUCSL'].resample('QS').mean()).diff().iloc[1:], 0.95, 10*4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x231b0ddac88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13,3))\n",
    "\n",
    "ax.plot(m2_ewma, label='M2 Growth (EWMA)')\n",
    "ax.plot(cpi_ewma, label='CPI Inflation (EWMA)')\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           Statespace Model Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:               CPIAUCSL   No. Observations:                  141\n",
      "Model:                    RecursiveLS   Log Likelihood                 686.268\n",
      "Date:                Wed, 29 Aug 2018   AIC                          -1368.536\n",
      "Time:                        17:25:08   BIC                          -1362.639\n",
      "Sample:                    01-01-1970   HQIC                         -1366.140\n",
      "                         - 01-01-2005                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         -0.0033      0.001     -5.935      0.000      -0.004      -0.002\n",
      "M2             0.9098      0.037     24.597      0.000       0.837       0.982\n",
      "===================================================================================\n",
      "Ljung-Box (Q):                     1857.32   Jarque-Bera (JB):                18.30\n",
      "Prob(Q):                              0.00   Prob(JB):                         0.00\n",
      "Heteroskedasticity (H):               5.30   Skew:                            -0.81\n",
      "Prob(H) (two-sided):                  0.00   Kurtosis:                         2.29\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Parameters and covariance matrix estimates are RLS estimates conditional on the entire sample.\n"
     ]
    }
   ],
   "source": [
    "endog = cpi_ewma\n",
    "exog = sm.add_constant(m2_ewma)\n",
    "exog.columns = ['const', 'M2']\n",
    "\n",
    "mod = sm.RecursiveLS(endog, exog)\n",
    "res = mod.fit()\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x231b0e7e710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res.plot_recursive_coefficient(1, alpha=None);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x231b0997860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res.plot_cusum();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The CUSUM plot now shows subtantial deviation at the 5% level, suggesting a rejection of the null hypothesis of parameter stability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x231b0f2b198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res.plot_cusum_squares();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, the CUSUM of squares shows subtantial deviation at the 5% level, also suggesting a rejection of the null hypothesis of parameter stability."
   ]
  }
 ],
 "metadata": {
  "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}