Trends Generations with Stats Models .ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import statsmodels.api as sm\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    " df = sm.datasets.macrodata.load_pandas().data\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>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": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.index = pd.Index(sm.tsa.datetools.dates_from_range('1959Q1', '2009Q3'))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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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>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": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#plot the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "ax = df['realgdp'].plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#using statsmodel to get the trend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Hodrick–Prescott filter\n",
    "# it sepates a time series yt, into trend component and cyclic component"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.tsa.filters.hp_filter import hpfilter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#When analyzing quarterly data, \n",
    "#the default lambda value of 1600 is recommended. \n",
    "#Use 6.25 for annual data, and \n",
    "#use 129,600 for monthly data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#tuple unpacking\n",
    "\n",
    "gdp_cycle, gdp_trend = hpfilter(df['realgdp'], lamb=1600)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['trend']=gdp_trend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "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().autoscale(axis='x',tight=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "airline.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}