{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# El operador de rezagos\n",
    "\n",
    "Ejemplo numérico para ilustrar el uso de los operadores de rezago, diferencia, y diferencia estacional."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Cargar paquetes necesarios"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Importar los datos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "* Leer una serie de tiempo ficticia de data\\LandD.csv y mostrarlos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['y'], dtype='object')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "datos = pd.read_csv('https://github.com/randall-romero/econometria/raw/master/data/LandD.csv', index_col=0, parse_dates=True)\n",
    "datos.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Obtener las series transformadas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "* Operador de rezagos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "datos['Lag_y'] = datos['y'].shift(1)\n",
    "datos['Lag2_y'] = datos['y'].shift(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "* Operador de diferencias\n",
    "\\begin{align*}\n",
    "\\Delta y_t &= (1-L)y_t = y_t - y_{t-1} \\\\\n",
    "\\Delta^2 y_t &= (1-L)^2y_t = y_t - 2y_{t-1} + y_{t-2}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "datos['D_y'] = datos.y.diff()\n",
    "datos['D2_y'] = datos.y.diff(1).diff(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "* Operador de diferencia estacional\n",
    "\n",
    "\\begin{equation*}\n",
    "\\Delta_4 y_t = (1-L^4)y_t = y_t - y_{t-4}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "datos['S_y'] = datos.y.diff(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "* Mostrar los resultados"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>Lag_y</th>\n",
       "      <th>Lag2_y</th>\n",
       "      <th>D_y</th>\n",
       "      <th>D2_y</th>\n",
       "      <th>S_y</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>trimestre</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2018-01-01</th>\n",
       "      <td>10</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-04-01</th>\n",
       "      <td>13</td>\n",
       "      <td>10.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>2018-07-01</th>\n",
       "      <td>10</td>\n",
       "      <td>13.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-3.0</td>\n",
       "      <td>-6.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-10-01</th>\n",
       "      <td>8</td>\n",
       "      <td>10.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>-2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-01-01</th>\n",
       "      <td>15</td>\n",
       "      <td>8.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-04-01</th>\n",
       "      <td>16</td>\n",
       "      <td>15.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-6.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-07-01</th>\n",
       "      <td>14</td>\n",
       "      <td>16.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>-2.0</td>\n",
       "      <td>-3.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-10-01</th>\n",
       "      <td>11</td>\n",
       "      <td>14.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>-3.0</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             y  Lag_y  Lag2_y  D_y  D2_y  S_y\n",
       "trimestre                                    \n",
       "2018-01-01  10    NaN     NaN  NaN   NaN  NaN\n",
       "2018-04-01  13   10.0     NaN  3.0   NaN  NaN\n",
       "2018-07-01  10   13.0    10.0 -3.0  -6.0  NaN\n",
       "2018-10-01   8   10.0    13.0 -2.0   1.0  NaN\n",
       "2019-01-01  15    8.0    10.0  7.0   9.0  5.0\n",
       "2019-04-01  16   15.0     8.0  1.0  -6.0  3.0\n",
       "2019-07-01  14   16.0    15.0 -2.0  -3.0  4.0\n",
       "2019-10-01  11   14.0    16.0 -3.0  -1.0  3.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "datos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Nótese que a pesar de que la serie original está en números enteros, las demás están en floats (dependiendo de su versión de pandas). Esto se debe a que versiones de Pandas anteriores a la 1.0 no tienen un valor para datos faltantes (NaN) para números enteros."
   ]
  }
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