{ "cells": [ { "cell_type": "markdown", "id": "b54a4353", "metadata": {}, "source": [ "```{include} ../math-definitions.md\n", "```" ] }, { "cell_type": "code", "execution_count": 1, "id": "776c32cb", "metadata": { "tags": [ "hide-input" ] }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "plt.style.use('seaborn-talk')\n", "\n", "\n", "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf\n", "from statsmodels.tsa.statespace.sarimax import SARIMAX" ] }, { "cell_type": "markdown", "id": "0343bafe", "metadata": {}, "source": [ "# Modelo ARIMA estacional\n", "\n", "En un modelo ARIMA estacional, términos AR y MA predicen $ y_{t} $ usando valores de datos y errores con rezagos que son múltiplos de $s$\n", "\n", "Por ejemplo, con datos trimestrales (s=4),\n", "\n", "- un modelo autorregresivo estacional de primer orden usa $y_{t-4}$ para predecir $y_{t}$, mientras que uno de segundo orden usa $y_{t-4}, y_{t-8}$ para ello.\n", "- un modelo de media móvil estacional de primer orden usa $\\epsilon_{t-4}$ para predecir $y_{t}$, mientras que uno de segundo orden utiliza $\\epsilon_{t-4}, \\epsilon_{t-8}$.\n", "\n", "\n", "Por ejemplo, si quisiéramos pronosticar el número de pasajeros extranjeros que viajarán por el SJO en agosto 2020, tiene mucho sentido modelar ese valor en función del número de pasajeros extranjeros que viajaron por SJO en agosto de años anteriores." ] }, { "cell_type": "code", "execution_count": 2, "id": "607660f6", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/html": [ "
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123456789101112
2011116.3105.4128.9103.182.788.0103.3102.964.662.677.590.3
2012115.8108.1130.9106.082.289.1105.9105.767.860.479.392.4
2013122.9109.6133.0108.585.395.0110.3112.870.067.383.5107.7
2014132.3120.9146.3111.993.196.4111.4116.871.767.385.3104.9
2015137.2122.7143.8122.896.5105.1121.5129.979.676.4100.5122.6
2016149.2141.8161.3132.0108.1113.3134.6138.784.583.2102.4124.2
2017153.6145.1179.0148.7119.4126.8141.0142.897.990.2117.1135.0
2018165.7161.1189.4161.3127.4134.1148.9156.0100.393.9120.4140.7
2019185.3170.4206.7157.0128.2137.0151.4156.4101.2102.0122.1153.3
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" ], "text/plain": [ " 1 2 3 4 5 6 7 8 9 10 \\\n", "2011 116.3 105.4 128.9 103.1 82.7 88.0 103.3 102.9 64.6 62.6 \n", "2012 115.8 108.1 130.9 106.0 82.2 89.1 105.9 105.7 67.8 60.4 \n", "2013 122.9 109.6 133.0 108.5 85.3 95.0 110.3 112.8 70.0 67.3 \n", "2014 132.3 120.9 146.3 111.9 93.1 96.4 111.4 116.8 71.7 67.3 \n", "2015 137.2 122.7 143.8 122.8 96.5 105.1 121.5 129.9 79.6 76.4 \n", "2016 149.2 141.8 161.3 132.0 108.1 113.3 134.6 138.7 84.5 83.2 \n", "2017 153.6 145.1 179.0 148.7 119.4 126.8 141.0 142.8 97.9 90.2 \n", "2018 165.7 161.1 189.4 161.3 127.4 134.1 148.9 156.0 100.3 93.9 \n", "2019 185.3 170.4 206.7 157.0 128.2 137.0 151.4 156.4 101.2 102.0 \n", "\n", " 11 12 \n", "2011 77.5 90.3 \n", "2012 79.3 92.4 \n", "2013 83.5 107.7 \n", "2014 85.3 104.9 \n", "2015 100.5 122.6 \n", "2016 102.4 124.2 \n", "2017 117.1 135.0 \n", "2018 120.4 140.7 \n", "2019 122.1 153.3 " ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# read data from previous example\n", "\n", "sjodatos =pd.read_pickle(\"https://github.com/randall-romero/econometria/raw/master/data/SJO-pasajeros.pickle\")\n", "sjodatoscuadro = sjodatos.unstack()\n", "sjodatoscuadro['extranjeros'].round(1)" ] }, { "cell_type": "markdown", "id": "8f565c07", "metadata": {}, "source": [ "## Un modelo estacional puro\n", "\n", "| Año | May | Jun | Jul | Ago |\n", "| ---: | --------------: | --------------: | --------------: | ---------------: |\n", "| 2016 | | | | $y_{t-36}=138.7$ |\n", "| 2017 | | | | $y_{t-24}=142.8$ |\n", "| 2018 | | | | $y_{t-12}=156.0$ |\n", "| 2019 | $y_{t-3}=128.2$ | $y_{t-2}=137.0$ | $y_{t-1}=151.4$ | $y_{t}=156.4$ |\n", "\n", "En general, un modelo puramente estacional puede representarse por\n", "\\begin{multline*}\n", "y_t = \\varphi_1y_{t-s} + \\varphi_2y_{t-2s} + \\dots+ \\varphi_Py_{t-Ps} +\\\\\n", "+ \\varepsilon_t + \\vartheta_{1}\\varepsilon_{t-s} + \\vartheta_{2}\\varepsilon_{t-2s} + \\dots + \\vartheta_{Q}\\varepsilon_{t-Qs}\n", "\\end{multline*}\n", "\n", "o bien, en términos de polinomios de rezagos\n", "\\begin{equation*}\n", "\\notationbrace{\\left(1 - \\varphi_1\\Lag^{s} - \\dots - \\varphi_P\\Lag^{Ps} \\right)}{$\\varPhi(\\Lag^s)$}y_{t} = \\notationbrace{\\left(1 + \\vartheta_{1}\\Lag^{s}+\\dots+\\vartheta_{Q}\\Lag^{Qs}\\right)}{$\\varTheta(\\Lag^s)$}\\varepsilon_{t}\n", "\\end{equation*}\n", "\n", "\n", "## Diferenciación estacional\n", "\n", "La diferenciación estacional se define como la diferencia entre un valor $ y_{t} $ y un valor rezagado un múltiplo de $s$ períodos.\n", "\\begin{equation*}\n", "\\Delta_{s} y_{t} = \\left(1-\\Lag^{s}\\right)y_t = y_t - y_{t-s}\n", "\\end{equation*}\n", "\n", "Por ejemplo:\n", "trimestral\n", ": $\\Delta_{4} y_{t} = \\left(1-\\Lag^{4}\\right)y_t = y_t - y_{t-4}$\n", "\n", "mensual\n", ": $\\Delta_{12} y_{t} = \\left(1-\\Lag^{12}\\right)y_t = y_t - y_{t-12}$\n", "\n", "\n", "Nótese que siguiendo esta notación $ \\Delta y_t = \\Delta_1 y_t $. Pero\n", "```{warning}\n", "\\begin{align*}\n", " \\Delta_2 y_t &\\neq \\Delta^2 y_t \\\\\n", "\\left(1 - \\Lag^2\\right)y_t &\\neq \\left(1-\\Lag\\right)^2y_t \\\\\n", "\\left(1 - \\Lag^2\\right)y_t &\\neq \\left(1-2\\Lag + \\Lag^2\\right)y_t \\\\\n", " y_t- y_{t-2} &\\neq y_t - 2y_{t-1} + y_{t-2}\n", "\\end{align*}\n", "```\n", "\n", "## Un modelo ARIMA para observaciones de la misma estación\n", "\n", "En general, podríamos plantear un modelo ARIMA para observaciones de una sola estación (mes, trimestre)\n", "\\begin{equation*}\n", "\\varPhi(\\Lag^s)\\Delta_s^D y_t = \\varTheta(\\Lag^s)\\varepsilon_{t}\n", "\\end{equation*}\n", "\n", "Es usualmente razonable asumir que esta misma relación la cumplen las observaciones de la estación anterior\n", "\\begin{equation*}\n", "\\varPhi(\\Lag^s)\\Delta_s^D y_{t-1} = \\varTheta(\\Lag^s)\\varepsilon_{t-1}\n", "\\end{equation*}\n", "\n", "En general, los errores de estas relaciones $\\varepsilon_{t}, \\varepsilon_{t-1}$ podrían estar correlacionadas, por lo que en principio podemos plantear el modelo ARIMA:\n", "\\begin{equation*}\n", "\\Phi(\\Lag)\\Delta^d \\varepsilon_{t} = \\Theta(\\Lag)\\epsilon_{t}\n", "\\end{equation*}\n", "donde $\\epsilon_{t}$ es ruido blanco.\n", "\n", "\n", "## El modelo SARIMA\n", "\n", "Asumiendo que el proceso ARIMA de cada estación es invertible obtenemos\n", "\\begin{align*}\n", " \\varPhi(\\Lag^s)\\Delta_s^D y_t &= \\varTheta(\\Lag^s)\\varepsilon_{t}\\\\\n", "\\varTheta^{-1}(\\Lag^s)\\varPhi(\\Lag^s)\\Delta_s^D y_t &= \\varepsilon_{t}\\\\\n", "\\Phi(\\Lag)\\Delta^d\\varTheta^{-1}(\\Lag^s)\\varPhi(\\Lag^s)\\Delta_s^D y_t &= \\Phi(\\Lag)\\Delta^d\\varepsilon_{t}\\\\\n", " &= \\Theta(\\Lag)\\epsilon_{t} \\\\\n", "\\notation{\\Phi(\\Lag)}{$p$}\\notation{\\varPhi(\\Lag^s)}{$P$}\\notation{\\Delta^d_{\\phantom{D}}}{$d$}\\notation{\\Delta_s^D}{$D$} y_t &= \\notation{\\Theta(\\Lag)}{$q$}\\notation{\\varTheta(\\Lag^s)}{$Q$}\\epsilon_{t}\n", "\\end{align*}\n", "\n", "Este modelo se denomina $\\alert{\\text{SARIMA}(p,d,q)\\times(P,D,Q)_s}$.\n", "\n", "\n", "\n", "{{ empieza_ejemplo }} Algunos modelos SARIMA {{ fin_titulo_ejemplo }}\n", "\n", "- $\\text{SARIMA}(0,0,0)\\times(0,1,0)_4 = \\text{SARIMA}(0,1,0)_4$\n", "\\begin{align*}\n", "\\Delta_4 y_t &= \\epsilon_{t} \\\\\n", "(1-\\Lag^4) y_t &= \\epsilon_{t} \\\\\n", "y_{t} - y_{t-4} &= \\epsilon_{t}\n", "\\end{align*}\n", "\n", "- $\\text{SARIMA}(2,0,0)_4 = \\text{SAR}(2)_4$\n", "\\begin{align*}\n", "\\left(1-\\varphi_1\\Lag^4-\\varphi_2\\Lag^8\\right) y_t &= \\epsilon_{t} \\\\\n", "y_{t} - \\varphi_1y_{t-4} - \\varphi_2y_{t-8} &= \\epsilon_{t}\n", "\\end{align*}\n", "\n", "- $\\text{SARIMA}(0,0,3)_4 = \\text{SMA}(3)_4$\n", "\\begin{align*}\n", "y_t &= (1+\\vartheta_1\\Lag^4 +\\vartheta_2\\Lag^8 + \\vartheta_3\\Lag^{12})\\epsilon_{t} \\\\\n", " &= \\epsilon_{t} + \\vartheta_1\\epsilon_{t-4} +\\vartheta_2\\epsilon_{t-8} + \\vartheta_3\\epsilon_{t-12}\n", "\\end{align*}\n", "\n", "- $\\text{SARIMA}(0,1,1)\\times(0,1,1)_4$\n", "\\begin{align*}\n", "\\Delta \\Delta_4 y_t &= (1+\\theta\\Lag)(1+\\vartheta\\Lag^4 )\\epsilon_{t} \\\\\n", "(1-\\Lag)(1-\\Lag^4) y_t &= (1+\\theta\\Lag)(1+\\vartheta\\Lag^4 )\\epsilon_{t} \\\\\n", "(1-\\Lag -\\Lag^4 + \\Lag^5) y_t &= (1+\\theta\\Lag +\\vartheta\\Lag^4 +\\theta\\vartheta\\Lag^5)\\epsilon_{t} \\\\\n", "y_{t} - y_{t-1} - y_{t-4} + y_{t-5} &= \\epsilon_{t} + \\theta\\epsilon_{t-1} + \\vartheta\\epsilon_{t-4} + \\theta\\vartheta\\epsilon_{t-5}\n", "\\end{align*}\n", "\n", "- $\\text{SARIMA}(1,0,0)\\times(0,1,1)_4$\n", "\\begin{align*}\n", "(1-\\phi\\Lag) \\Delta_4 y_t &= (1+\\vartheta\\Lag^4 )\\epsilon_{t} \\\\\n", "(1-\\phi\\Lag)(1-\\Lag^4) y_t &= (1+\\vartheta\\Lag^4 )\\epsilon_{t} \\\\\n", "(1-\\phi\\Lag -\\Lag^4 + \\phi\\Lag^5) y_t &= (1+\\vartheta\\Lag^4 )\\epsilon_{t} \\\\\n", "y_{t} - \\phi y_{t-1} - y_{t-4} + \\phi y_{t-5} &= \\epsilon_{t} + \\vartheta\\epsilon_{t-4}\n", "\\end{align*}\n", "\n", "{{ termina_ejemplo }}\n", "\n", "\n", "## Identificación de un modelo SARIMA\n", "\n", "La identificación de modelos estacionales es más difícil que la identificación de modelos no estacionales por dos razones:\n", "\n", "1. Muchas series estacionales exhiben también patrones no estacionales y por lo tanto las FAC y las FACP estimadas contienen ambos patrones.\n", "2. No hay muchas correlaciones en valores $k$ múltiplos de $s$. Por ejemplo, en una serie mensual podríamos contar únicamente con $k = 12$, $k = 24$ y $k = 36$\n", "\n", "En la práctica, cuando se tienen dudas, se utilizan herramientas que automatizan esta selección de parámetros a partir de criterios de selección.\n", "\n", "\n", "\n", "{{ empieza_ejemplo }} Estimación de un modelo SARIMA {{ fin_titulo_ejemplo }}\n", "\n", "El correlograma de la serie de movimientos de pasajeros extranjeros en SJO sugiere que la serie tiene un componente estacional." ] }, { "cell_type": "code", "execution_count": 3, "id": "4ae84c90", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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WZth9hKY7D7t7uRrpepSbfzEfxeOz7u0YVRhcBlwWXba/GfiAmf171IzhDEJg/UIv7YIsuS3Gc1/0vnkS+zGUlqVJZcvSCR67dZenZnY2obb5IsLN3Vea2TPcPf7Hot7joCjLY7OctPbZus997n4H4Q8dZvYUwpW4jxGa5FTKL0B+kvvXpHm4gfEPhJr6/Qk325dzG+GGz5PNbLG7b04miI7F0wnH3vezyXFnUhvt1vdlQjvRc8zs5HIJzOxZFu62hnAndT9wtpntEUuzB6Emt4+xXh8mxN23EG54e42Z/XWZ/FgNbca+TWiqkCy43xoNjxd0NxJucFqVSHtOHdkuyrN7rdwc4L0TmFety6PMMl9Koq2phfbiJcdk1GznQUL7yLraEkZ+RKgNe6eZzY4t6wBCzVR8WQVCu+1jzexUyqjUtjaax1ZCIX2imSXvBSjWlsH46+XplLbPn4hiP8BV+5aNfCd6L+mJwsKT0p6aSFtzvqOg8TeEk9vyWNrp1Li/RbVg3wWOMbMXxuZhlH9A1dej90+YWXdyZLXtl3BatJ8k813ME9SxPsxsvoU+f0d56AO7GFwVm4TkCUFiV2xaA86rMd/XEbqqu8DCcwhKRPmYUcN8VhO62nuzme0Tm34aYV9xon1nMsduveWpma0gtBH/KaGnjtcTLvl/PZGHeo+DoiyPzXLS2mdrPvdZaE+d9CihsqHa+vo94c/UWWaWbIaJmfVYuFclNWb28ljZGR++F6FHkRxjfwB2E9Xg/19CM7RvJI+LaL1/nnDT+yXl2u3LxKlGu8W5+4CFp0J9j9BF0Q8JhcUWQkD6QsKlr09G6beb2QcIXRzdbmZXRrM6k9B+9u1eodu9OryDcOPHzy20Tfw94cR4MKGm5Srg/ArTf5Jw1/XnzGxlNP3RhDaKaym90etiQlD4X9GlvnsJl2b/hnDjZD01N9cDbzez/yE0kVhCuHt7Sx3zqMcviboGs9Dt3aPAMwm1dn8EjoqlfSOhveC3CLVcI4R+ul8GXFe8QaweUXvyjxBuHL0t2lazgbMIBXOy5vlfCOv1OjO7jhAoDhMK4L8F7iTsS5W8i1CD8v3o0uadhMvbzyZcnfggIbi6m1CTWezNYDnhJp8/Uf0SZyV/JjTP+UczGyDU0m9y92SNPgDufrOZ3Qi8KTpB/oDQvV8xL0+PJa833+8j9N7zKzP7HGPd+9VT9p5HuKz+XTO7jLAPnUQ4/pO/5bdm9lFC29E/mNn/Evpj3pdwc9/fEnqtqMU6QhlyOWF9voHQzd6/unuxG7h61scLgSvM7IYoXV+Up38Abnf34o2n1xN6P7gl2l+nEW5YnU0N3P1RM3sHoZLiHgtPu9tAWF9HRfN6GmFfrDSfvJm9i/Cn/7dmdkW0Hv4PoavKT7h7MbiZ7LFbU3kaVQr8d5SP06M/x783sw8Sbrb7IOHhJlDncRCT5bG5m7T22TrPfedFlR3fJfwZMsIxdTjlbzKOL8fN7AzCFcK7LDSFupuwfx5KuMLwIUJvI2m5Hthk4bHqfyYE1gcTziNLCFcftlbJ9xUW7hf6APDnaD97iNDt3yrCsfENxm93LhPlLdD1iV7VX4SD+L2EwngboSDfSAjAz2D3h62cQgh2+qPXbcCry8z3IRLd48XG/Qx4qEKeFhNqVooPtNhOCB4/Azwtlu5MEt3IRcP3IvyLfjT6PY8SCsnFZZa1jNCvcS/hxo7vRMNKusiL0jrjdEMXrcdLCCfeQUKweS6hiUeyW6ay+a60DMo/4OQZhOBtW5T/nxHap5akJQTgXyOcqPuj37mG0NZzxiT3n7cTTpjFB9a8h/EfWDOb0JftHwm14b2Ek++XqP0BC/sTuqAqPnxjI6Hd54tiaQ4k9Fv8JKHN5R3Rfnt+lK+DKq3XStuCcHJeHW1jp/oDa2YR2lw+Ef3m3xKCpHLbs+Z8R+lfQDj+BglNQT5H/Q+sOSpaf8UH1lxN5QfWvILQJGNrtM0fIVxpeEcNyzo+mu+ZhG7Q7ovmcR/wT2XS17Q+CMdrsR/8ndFvuYfQNnZ+Yp5vJQQUg4R21lcQahrLbevx1sHfEILkTYw9AOanhONpZizdQ4xTBkbjjyNUbuyM8vN7du8K8JlM8tilhvKU0Ld9AfjbMtN/l1COxh/gNN5xMLqNx8lLJscmlR9YU9M+O972jo2veu6Lfv//RNt+V7TM2wl/+nbr/rXCOro8mscwobLmTsIfnadMtOwaJ91rGXuuQfz8/33CE6PjaYtt3r9T4fi+gbEH7TwZzafsA7f0mvzLohUvMuVY6HJqM/BFdz+r2fkRaQdmdjwhIH2zu1/Z1MxUEV3yzhGelJhF+2FJUVSjej/hCbpl71GRybHQXeR2QteNb2pydgS10ZYpolxbS8JlUphkm3MRmbL2i97VpnRq0PbKXrGdv3oOaRFqoy1TxffNbAPhwQzdhKYeryRcFvx2E/MlIk1gZm8mXFKH0ORAWlTUtnwV4R6cPLv3CiKTZGbHAc8lNAvsZ/cHvEmTKNCWqeJGwg1Hrya0p32U0Kb2Ah+/f1IRaV9fJtzI9i53v7XZmZGKivfj3A+83t3XV0kv9XsvoZvS3wHnuvtjTc6PRNRGW0RERKYcM/s+oQ/u3Z5TINIq1EZbREREphQzWwK8mNALyxlNzo7IuBRoi4iIyFSzihDDfAo4Lv5wJZFWokBbJMHMfmlmN5UZfrqZDVl2j2sXEZHanEF4JsGnou8lT7pVOS6tQoG2yO5uA46NDzCzuYQnVH7K3e9vSq5ERAQzO4LwhMpr3P0vhH7fk81HVI5LS1CgLbK724BF0cMVij5CeOLWx5uTJRERiZxBeHrkDdH3a4Cnm9mKWBqV49ISFGiL7O626P1YADNbTuib9IPu3hcNm2FmH2hO9kREOpOZGXAacJO7b48G30B4zPzpsaQqx6UlKNAWSXD3TcB6xi47/gewGvhGLNnRwEmNzZmISMd7AbCUUIsNgLvvAG4C3mBmXdEwlePSEhRoi5T3a+BYM3sVoZ/Wd3vU6byZHQV8CzjUzP5gZv/UxHyKiHSSM4CdwHcTw68mPOL9hNgwlePSdHpgjUgZZvYOwpMn/wLc6u5/nxj/JeBX7n5lE7InItJxzGwm8ATwLXd/c2LcDGAj8G13PzMapnJcmk6PYBcp7zbCo973Aj5UZvyzgMsamiMRkc52EjAf2GRmry4z/m7g78zsH919AJXj0gIUaIuU92T0fqG7b4yPMLPpwCHAnxueKxGRzlXswq/aDYwnA9eiclxagJqOiJRhZl8Gngc8w92HE+MOBX7o7gc3JXMiIlKVynFpBarRFomY2SzgKMJNM2cCJyQL58gG4EEzuwe4yt3/rXG5FBGR8agcl1aTeo22mb0eeCewApjt7hWDeTN7OeFmhYMJXfG8z91/mGqmRGpgZq8AbgQeAT7i7lc1OUsiIlIHlePSarIItF8G7Em4AeGKSoG2mR0M/Al4G3Ad8FrgCuBId38o1YyJiIiIiDRQZm20zex44MdVAu0LCJd1nh8b9otougtqXM4iYFH0dYu7b5lwpkVEJHMqt0WkUzS7jfYK4M7EsNXR8FqdDXwUYNasWRxzzDGjI/742I6ShAY8ff/5E8mniEjm7rzzzs3uvlez89EAKrdFZMqrpcxudqC9B7AjMWw7cGQd87iM6FGsy5cvX/u73/1udMTJ//lL1jw6Nvtjl+3JdW9/zkTzKiKSKTPb0Ow8NIjKbRGZ8mops5v9CPZeQufzcQsIj1etibtvcfd17r6up6f0f8O5Jx4++nnFAfO59NR6KspFRCQLKrdFpFM0O9BeA6xMDDs6Gj5p+y2YNfr5s6uOZumi2WnMVkREMqJyW0TaSeqBtpl1m9lMYHr0fWb0sjLJrwKOMbNVZjbNzFYRHon6tbTzJSIiIiLSSFnUaJ8B7AJuBrqjz7uAA83sNDPrKyZ09/XAa4DzCM1FzgNOUdd+IiIiIjLVpX4zpLtfCVw5zuiHgKsT6X8A/CDtfIiIiIiINFOzex0RERERSdXDWwY45/o1rN6wjZUHLuTSU1eovb80RbNvhhQRERFJ1TnXr+GOB7eSKzh3PLiVc65PpY8Fkbop0BYREZG2cueGbSXfVye+izSKAm2RKh7eMsDrvvhrDv3wTbzui7/m4S0Dzc6SiIhU8PT95pV8X3ngwiblRDqdAm2RKnQJUkRkatGDj6RVKNAWqUKXIEVEphY9+EhahQJtkSp0CVJERKTzpNF0VIG2SBW6BCkiItJ50mg6qkBbpApdghQREek8aTQdVaAtIiIiIpKQRtNRBdoiIiIiIglpNB3VI9gT9NhWEREREUmj6ahqtBPUZ7KIiIiIpEGBdoL6TBYRERGRNCjQTlCfySIiIiKSBgXaCeozWUSyksbDD0REZOpQoJ2gPpNFJCu6B0REpLMo0BYRaRDdAyIi0lkUaIuINIjuARER6SwKtKXjqJ2sNIvuARER6SwKtKXjNKKdrIJ5KUf3gIiIdJbUA20z6zazS8zsSTPrNbMbzGzxOGmPNzM3s77Y67a08yQS14h2srrpTURERLKo0T4XOBl4NnBANOzrFdLn3X1u7PXcDPIkMqoR7WR105uIiIhkEWi/DbjY3R9w9x3AB4CXm9lBGSwLM1tkZsvNbHkul8tiEdJmGtFOVje9iYxP5baIdIpUA20zmw8sBe4sDnP39cBO4BnjTNZtZo+Y2RNm9j0zqzfqORtYC6zdtGnTRLItHaYR7WR105tIRSq3RaQjpF2jXazG25EYvj02Lu5e4JnAMuBw4C7gFjPbr45lXgY8FXjq3nvvXU9eRTKjm95EKlK5LSIdIe1Auzd6n58YvoBQq13C3Z9w9zXunnP37e7+IWArcGKtC3T3Le6+zt3X9fT0TDTfIiLSICq3RaRTpBpou/t24GFgZXGYmR1MqM2+q8bZFABLM18iIq3I3ckXnOFcgZF8odnZERGRlGVRlXAF8EEz+ymwBbgYuNndH0omNLMTCIH5A8Bs4BxgCXBzBvkSmTLcHXfw4meIvofhRN8hDKt//onvZZY/3vjktBNYfGLySc6gOJ90ZlM6z9F5+27D4sssRAFzwZ1CAfLRd3cf/VwowGPbx/pT/8Mj23l8++Do90Vzp6f/A0REpKmyCLQvAhYCvwVmAD8CTgcws9OAL7r73CjtCuC/gMVAP7AaeIm7P5JBvkSabiRfYChXYDhXYCiXZ2gkfB/K5RnKFaLgrNm5lFps3DnI5beu576NfRy2ZC5nHXcIS+bNrDjN4MhYrbW2s4hI+0s90Hb3PKFm+pwy464Gro59/zTw6bTzINJsw7mxgGr9k31sHxgZDaSlPVx+63rufSLclnLvE71cfut6PnrSkU3OlYhI+yhe3S24U4jeofS7e0hXGE2XmKYQ/z52hbjM0nYb8vj2XaOfH9rcX3Ju7+6qrZWz7kIRScngSJ6t/cNs7R/m/k19o8N37soxa5oOtXazbmNvyff7NvaNk1JEpDIfbX42FhAWv++euMq8GGt6WJx3vPkho80Sx9LmE8FooULwmpx3PEtjAawnvtcnHkQ309b+kdHP2wZGmN7TPfp9eo8CbZHM7RrOs6V/iK39w/QP5ZudHWmgZYvnsP7J/tHvhy2ZWyG1iLS6QsEZHuem5HjAF7+vpBAFqYVCuB+j+J7Le8m9G/kCY/dxxO/piAW50p4UaIvUqX8ox9b+Ybb0D7NrWMF1p1p17FI+9r17ADhkrzmcddwhTc6RiEzEUC7Ppp1DbNw5yEheEa+kS4H2JD28ZYBzrl/D6g3bWHngQi49dYUeTtJGCgVnIBZM3/34ThbOVu8QAovnzhj9fPYJh1W9EVJEWsvOwRE27hhkS/+wapQlMwq0J+mc69dwx4NbAbjjwa2cc/0arnv7c5qcK5mIoVyegaE8AyN5dg3n6B/Ks2skzxM7xrpgi98IISIiU0uh4GzuH2LjjiH6hnLNzo50AAXak3Tnhm0l31cnvkvjFWJt3+I3dhTc8QLsGBi7ueGRbbvoG8qxazivS4YiIm2q2DxkU+8gwzmV9dI4CrQn6en7zWPNoztGv688cGHmyywUwq0Y8buASXx3wAvhpo343cPFu493u4N4nBs9YPyHm8TvZGa3u5xjdz4nHrQSHx+ff/HhLGOfd19qaT5L81f8jdVs3DlWQ725d4hu04NIRUTa1UOb+/nLjkE1D5GmUKA9SeeeeDirvnQ7AEftP59/PflIdg6OkM87uUK4s3gkH/pPLn7PFQq7BaDxJwDC7sFrPCgWERGZyord2RXPi3n3kvNmrlCgUIBcofT8mXwi7ngVNfEmf9sGRlgyrxuRZlCgPQHuTv9wnt7BkZInvb3lecvY2j9S0u+iZG8iT+gTEekU8QqeeD/Io1cBY5U+8Qd6JK9uVuWMBc7F4Dn2vWRcxg/v0v000ioUaNegGFjv3DXCzsERegdz5KL2vDt2KahuNj2hT0TaTfJek2IQnI/uNSl4ae1vLqoNjn/OR5/1QFqR5lGgXcETOwcZGM7TNzQWWDdavbW1nVi72w5P6OvE7SYyFeXyBXLRg01y+dA0MLycXL4wOjxXrCqu4omdg3zulvtZu7GP5Uvm8o7jDmGvPXTsi7QLBdqEGuveoRy9g7mSR2f/ZfsghXlNzBj119Z2Yu1uOzyhrxO3m0ircHdG8iF4HsmFwHkoNxZAD+cKjBTCuLRrhy/7yf2jx/49f+nl8z/TsS/STjo60N4+MMzj2wfpG8qNthfrHWytfjXrra1th9rderXDE/o6cbuJ1GvXcJ5NvWM3ucVvhAvfx6LgZK9E8aHukPcogI6C6WbdaN6IY19XzDqDtnNr6uhAe+euXMPbWNd7INRbW9uI2t1WO5jb4Ql97VArL5K1wZE8j28frJ5wCmnEsa8rZp1B27k1dTU7A52meCDk3UcPhEpWHbt09HMttbX1pp+Ien/Dxp2DXHDj3Zz+5du54Ma7S/qxlqAR201EWk8jjn1dMesMWW9nncsnRoF2g9V7INRbW9uI2t16f0O9gXknaoda+alOJxFphkYc+8sWzyn5PhWvmOn4rC7r7axz+cR0dNORZmiHJgL1/oZ6A/NWa5rSDtR7TXW67Do1deK+Wq92uI8l6+OzHfajrLdzO1wZacZ2Vo12g7VaE4GJ1BLU+xvq/Zetf83pq3edduI2aIeTSCfqxH21Xu1wxSzr47Md9qOst3M7XBlpxnZWoN1grVbgTWSnq/c31BuYK+BJn3qvqa4dTiKdqBP31U6U9fGp/ai6VqsonIhmbGcF2h2uETtdvYG5Ap7q6r0SUe86bcQ2aLU2l+1wEulEKi86Q9bHp/aj6lqtonAimrGdFWh3uFYsXBTwVKfea9IPzNvhJNKJWq28aLU/kO0i6+NT+1FnaMZ2Tj3QNrNuM7vEzJ40s14zu8HMFldI/3Izu9vMdpnZn8zspWnnScbXaoULKOCphXqvmZptKCV9rVZeaD+dmrQfdYZmbOcseh05FzgZeDawBfgq8HXgxGRCMzsY+CbwNuA64LXAt8zsSHd/qN4FD+cKbNgy1hvGY9t2lf1c9Pi2QTb2lv5L3Nw3VPbzeKZ6+rhi0F3tn3Or/YZWS9+IZRywcDYPbx0Y/X7Q4tkVt1sj96Na1fsbkoH5uo29VX/ztXc8zIOb+1m2eA6rjl1aUsiWS1/uc1rpq00zlMvXNI92U0+5vWNgZLdt3oh9tR4T2U/LfU7TRPbteo6dRmjFcj5L9e5HkP1v0H5Umn5at9W0TPOUnztrZhuAC939K9H3Q4D7gWXJ4NnMLgBOcPfnx4b9Avixu19Q4/IWAYsApu9z6Np93/QfafwMEZGG23DxK+9092OanY+sqdwWkXZQS5mdatMRM5sPLAXuLA5z9/XATuAZZSZZEU8bWR0Nr9XZwNroJSIirU/ltoh0hLSbjsyL3nckhm+PjYvbY5y09fRCfxlwDcAhi2ev/f77j695wnJNR0RkYt533R8oxC6QdRl86nXPbFp+LrvlvpIHKx2y1xzOPuGwpuWnmgWzp/HCi5udi4aZULm9Y2CEBzb3V09Ywea+odGHepz3iiOqXsquN30jZJ2neo+ddlin9WqH36z9aHKmdRuvrKHMTjvQLjYqmp8YvoBQq10ufa1py3L3LYS24BxzzDEcuGhOlSnGGAa1NbERkSqWL9lj9Mltxe/NvKHo7BMOm1JPels0d3qzs9AwEy23t80cpn84vbbsi+fOqGufqDd9I2SRp8kcO+2wTuvVDr9Z+1H9pvfUFkCmGmi7+3YzexhYCfwBRm94nAfcVWaSNcALE8OOBn6SZr5EJHtnHXfIboVqMy2ZN1OPUBeZAB07kgbtR0EWvY5cAXzQzH5KqLG4GLh5nF5ErgLeb2argOuBU4FnAW/MIF8ikiEVqiIiIqWyeGDNRcCNwG+Bx4Bu4HQAMzvNzEY7y41ulHwNcB6huch5wCkT6dpPRERERKSVpF6j7e554JzolRx3NXB1YtgPgB+knQ8RERERkWbSI9hFRERERDKgQFtEREREJAMKtEVEREREMqBAW0REREQkA1l07zdldHfraTUiIlNFV5cxvSdePxQeReqeHJIYFn1x0EPKRKShOjrQ3n/BLPbeYwY7d42wczBH7+AI/UPpPXVMRETSM3/WNJ514MJJzWPDlrFHQj9tv3ksmTeTkXyBkXyB4Vzx3RmOhomITEZHB9oA07q7WDR3BovmzgBgJF+gdzAXBd8jDAznS2pGRESkPczo6WL+rGkV0yyeM/roB5YtnsM+84uBuZOL3kfyBXKF8FnnC5GJ2dw3NPr5slvu4+wTDmu5R9VPRMcH2knTurvYc8509pwzHYBcMfAeHGHnrhz9wzkVpCIiHaKra6ytyYLZ0yqe+N2dXKEYeI9/ohjvHOLuFBwK7hQ8BO2F4rDC2PdcYaymfc6MbmZP7yZXKJDLh7QitWi1wPbaOx4e/bz+yX4uv3V9xacNt1r+x6NAu4qe7i4WzpnOwjKBd+9gjr4hBd4iIgJmxrRuY1p3tv0MWKyd+fIle3Dgojmj3/MFHw26cwUP36PAvxi8u4MzFrg7xeA/BOrx8bUYGM6Nfp4zo5tZ07vJFwrkCyE/0prqDWyz9tDmgZLv923sGydl0Gr5H48C7TolA+98wekdHGE4Vxgr1ApOvhC+jxV2qm0QEZFsdXcZ3V3dzGjg2X37wPDo5/+85X4uW7WSpYtmA6GWvnheLEQ1/r27RkbTf/Hn6zn/pCPZe97MkvNmMW0+ek31Cq1WrH2tN7DN2mFL5nLvE70l3ytptfyPR4H2JHV3GQtmT685fSFW4EBpzcHY3fKxGoYyNQ+FKHHx8+i4WE1EqJUYex8vbck8Y0q/lh9XzGNJfkVEJFOPb981+vnd1/6+JLBthou+f+/o5zWP7uCc69dw3dufA4Ra/p5uo6d7LP3nfnb/6Od7/tLLv/9o3Wj68eTyBfJeGnAXz3fFz1B6Hi04bOsf5sm+IXL5dE9Q9QbOrVj7Wm9gm7WzjjuEy29dz30b+zhsyVzOOu6QiulbLf/jUaDdYF1dxvSu9u1fykv+QJQG4clLkWMFY+k0xKZLpo0mKJkuPu14bRtHP7uPFsAj+QK7hvOMpFwAi0j7aLWgFioHts1w9+M7S76v3rAt1fQQriZPJGCZP2saT9lzNk/2DvHEzkF2DafTs1i9gXMr1r7WG9hmbcm8mXX9+Wi1/I9HgbakyqLGg2NtCFv/T8VwLgTc/cM5BobzDAzn2DWcVzMfkTZUb+DcakEtTCxQzdLKAxdyx4NbS76nmX6yuruMfebPZJ/5M9k+MMxfdgyyfWCk+oQV1Bs4t2Lta72BbauZKvnXkyGl403v6WL+7Gnst2AWh+49l2ccsIBjl+3JiqfM57Alc9l/wSwWzpnG9J7W/9MgIpWVC5wrabWgFnYPTLMOVKu59NQVHLtsT3q6jGOX7cmlp65INX2aFsyezhH7zuPopQvYZ/5Muid4hTkZKFcLnM867hAO32cPus04fJ89Wrb2VdKnGm2RMsyM2dN7mD29B2LlZ99Qjq19w2zpH2JwRA+zEJlq6g2cG137WotLT13BOdevYfWGbaw8cGFDA9Vyli6aXVctf73pszBzWjfLFs9h6QSbldTbbGGq1L5K+hRoi9Rh7owe5s7oYemi2QwM59jSN8zW/mEGUmr3JyLZqjdwbrWgFlojUG0XyWYlA8P5xP1BpfcCFR2wcBZfeuMxFKJeVcI7sc9O3n20AwR1FtC5FGiLTNDs6T3M3rOHp+w5m13DebYODLO1b5i+oVz1iUWkKeoNnBXUdo4Fs6ezIKP7XAtR4F3sqjAf3bgfbtYfC9AL8TSxHsrKGW/M2CQe65gg1sNZonOCsc4DxnoqyxfUm1haFGiLpGDW9G72nz6L/RfMYnAkz7aBUNOtXk1EWosCZ2mGri6jC2Nad/W0rWT3XrsSQXqUbrTHsdHvlCaoQ7xL44KX+Z7oqjg+fLwnq3qZ9/LLHidPkziNK9AWSdnMad3sO38W+86fBYRaiaFcnqGRAkO5AkO5PMO5+GcF4iIi0nqKfxBk4hRoi2Ssu6t4Y2X58YWCjwbd8ct1ztiDiZIPNir+o5+o5LSe+B+/+/jk9F5xfFr5Ss/EZlzS73uZ4cX1li84hUKoPSm2y8wX9CRYEZFOp0BbpMm6uoxZ07uZNX2KXVOUqoqXKZPtL3cLyt2Z0aPtLyLSblINtM1sNvCfwCmEJ5XcALzL3XeNk/5M4KtAvOf3G919VZr5EhFpBjOj25hwX70iIjK1pf3Ams8Ah0ev5cARwKeqTPOAu8+NvRRki4iIiMiUl1qgbWazgNOBj7j7RnffBHwEeJOZzUxrOWWWu8jMlpvZ8lxO3aqJiLQ6ldsi0inSrNF+KjATuDM2bDUwi1C7PZ6nmNkTZvaImf23mS2rc7lnA2uBtZs2bapzUhERaQKV2yLSEWoKtM3sSjPzCq+PAXtEyXfEJi1+njfOrH8OHAXsB/wVMAj8yMzm1PEbLiME+U/de++965hMRESaROW2iHSEWmu03wXsVeH1CaA3Sjs/Nl3x885yM3X3B9x9nbsX3P0J4K2EoPuva/0B7r4lmse6nh51oiIi0upUbotIp6iphHP3PqCvUhozW0uokV4J3BINPhrYBayrMT8evXSLvoiIiIhMaam10Y668PsGcKGZ7W1mewMXAle5+2C5aczsFWZ2gAV7Ap8DNgO/SStfIiIiIiLNkHb3fv9EqL0uvtYC7y2ONLMPm9ndsfTHA3cQasvvBhYBL4lq0EVEREREpqxUG8e5+wDw99Gr3PhPENpzF7+/H3h/mnkQEREREWkFaddoi4iIiIgICrRFRERERDKhQFtEREREJAMKtEVEREREMqBAW0REREQkAwq0RUREREQyoEBbRERERCQDCrRFRERERDKgQFtEREREJAMKtEVEREREMqBAW0REREQkAwq0RUREREQyoEBbRERERCQDCrRFRERERDKgQFtEREREJAMKtEVEREREMqBAW0REREQkAwq0RUREREQyoEBbRERERCQDCrRFRERERDKgQFtEREREJAOpBtpm9m4zu93MBszs/hqneaOZrY+mud3MnpVmnkREREREmiHtGu3HgU8CH68lsZk9D/gC8A5gIXADcJOZzUs5XyIiIiIiDZVqoO3u17v7DcBjNU7yVuCb7v5Ddx8CLgGGgFNqXaaZLTKz5Wa2PJfL1Z9pERFpKJXbItIpepq8/BXAlcUv7u5m9vtoeK3OBj4KsGbNmgEzuycxvhtYAmwE8pPKbfvSOqpO66g2Wk/VVVpHBzY+O02hcnvytI6q0zqqTuuoukmV2TUF2mZ2JfCmCkk+7u7n1TKvhD2AHYlh24F6mo5cBlwTfd7i7lviI81sObAWON7d100gj21P66g6raPaaD1Vp3UEqNyeNK2j6rSOqtM6qm6y66jWGu13AedUGD9Q74IjvcD8xLAFwPpaZxAV0FuqJhQRkZagcltEOkVNgba79wF9GSx/DbCy+MXMDHgm8M0MliUiIiIi0jBpd+/XY2YzgWnhq82Mvo/nS8BrzOxFZjYd+GdgJvCtFLO1BbgA1Z5UonVUndZRbbSeqtM6qk7rqDqto+q0jqrTOqpuUuvI3D21nJjZ+UQ3uMS5u0XjPwyc5u5HxqZ5I3A+sC/wR+Ad7n5napkSEREREWmCVANtEREREREJ9Ah26Shm9n0zczN7c7PzIiIiY2otn1WOy1SiQFs6hpktAV4MFIAzmpwdERGJ1Fo+qxyXqUaBtnSSVYR9/lPAcWZ2QJPzIyIiQa3ls8pxmVIUaEsnOQP4GaGABnhDWjM2s1+a2U1lhp9uZkNmdmhayxIRaUO1ls8qx2VKUaAtHcHMjiD02X6Nu/8F+CnpXna8DTg2scy5wMXAp9z9/hSXJSLSNmotn1WOy1SkQFs6xRnAEHBD9P0a4OlmtiKl+d8GLDKzQ2LDPgIY8PGUliEi0o5qLZ9VjsuUo0Bb2l70xNHTgJvcfXs0+AZgEDg9lu5iM3swupv98NjwRWZ2k5ndY2Z3mdn/mtmeicXcFr0fG02zHHgP8MHoyaqY2Qwz+0AGP1FEZEqqo3yuKV2UdqJledVyPBquslxqpkBbOsELgKWE2g8A3H0HcBPwBjMrHgf/L0q7ITG9Axe5+xHu/gzgIRK1G+6+CVjP2GXH/wBWA9+IJTsaOGnyP0dEpG3UWj7Xmg4mWJbXWI6DynKpgwJt6QRnADuB7yaGXw3sB5wA4O6/cvdHkhO7+1Z3/3ls0G+AZWWW82vgWDN7FfBy4N0ePRHKzI4CvgUcamZ/MLN/muRvEhFpBzWVz3Wkm2xZPm45DirLpX4KtKWtmdlM4FTgm+4+mBj9PWAHicuOVeZnwFnAjWVG30ao6fg0cKW7/7Y4wt3/SDhBfMjdn+nun6nrh4iItJlay+e0y/Fo2eOV5eOW46CyXOrX0+wMiGTsJGA+sMnMXl1m/N3A35nZP7r7QA3z+yzQC3yhzLjbgFnAXsCHyox/FnBZLZkWEekANZXPhN5F0izHYfyyvFo5DirLpQ4KtKXdFbt+qnbjysnAtZUSmNklwGHAq9y9UCbJk9H7he6+MTHtdOAQ4M9Vcywi0hlqLZ+/XGO6quU4VC3Lxy3Ho2lVlktdFGhLW3P3V6UxHzP7OKH/1le6+/A4yS4E1hJqSpKWAlvcPZdGfkREprq0yud61FCWVyrHQWW51MlibfxFOpqZfQp4HbAPsBnY5O7PMLMjgT8B64BdUfL73f1UM5sFHEW4aeb/AickbrYpznsa8APCTTtXufu/Zf6DREQ6UL1lOaFmvWo5Hs1bZbnUJfVA28xeD7wTWAHMdveKteZm9nLg34GDCd3qvM/df5hqpkQyYmavINxM8wjwEXe/qslZEhGROqgclyxlEWi/DNiTcDPBFZUCbTM7mPDv8m3AdcBrgSuAI939oVQzJiIiIiLSQJk1HTGz44EfVwm0LyBconl+bNgvoukuyCRjIiIiIiIN0OybIVcAdyaGrY6G18TMFgGLoq9b3H1LSnkTEZEMqNwWkU7R7EB7D0JH83HbgSPrmMfZwEcBZs2axTHHHDM64o+Plc7agKfvP38C2RQRyd6dd9652d33anY+GkDltohMebWU2c0OtHsJndDHLSA8ZrVWlwHXACxfvnzt7373u9ERJ//nL1nz6FihfeyyPbnu7c+ZaF5FRDJlZhuanYcGUbktIlNeLWV2sx/BvobQn2Xc0dHwmrj7Fndf5+7renpK/zece+Lho59XHDCfS0+tuUWKiIhkROW2iHSK1ANtM+s2s5nA9Oj7zOhlZZJfBRxjZqvMbJqZrSI82vRraeRlvwWzRj9/dtXRLF00O43ZiohIRlRui0g7yaJG+wxCR/A3A93R513AgWZ2mpn1FRO6+3rgNcB5hOYi5wGnqGs/EREREZnqUm+j7e5XAleOM/oh4OpE+h8QnrIkIiIiItI2mt1GW0RERESkLSnQFhERERHJgAJtEREREZEMKNAWEREREcmAAm0RERERkQwo0BYRERERyYACbRERERGRDCjQFhERERHJgAJtEREREZEMKNAWEREREcmAAm0RERERkQwo0BYRERERyYACbRERERGRDCjQFhERERHJgAJtEREREZEMKNAWEREREcmAAm0RERERkQwo0BYRERERyYACbRERERGRDPQ0OwNT3cNbBjjn+jWs3rCNlQcu5NJTV7B00exmZ0tEREREmkw12pN0zvVruOPBreQKzh0PbuWc69c0O0siIiIi0gJSD7TNrNvMLjGzJ82s18xuMLPF46Q93szczPpir9vSzlOW7tywreT76sR3EREREelMWdRonwucDDwbOCAa9vUK6fPuPjf2em4GecrM0/ebV/J95YELm5QTEREREWklWQTabwMudvcH3H0H8AHg5WZ2UAbLarpzTzx89POKA+Zz6akrmpgbEREREWkVqQbaZjYfWArcWRzm7uuBncAzxpms28weMbMnzOx7ZlZXpGpmi8xsuZktz+VyE8570cNbBnjdF3/NoR++idd98dc8vGWgYvr9Fswa/fzZVUfrRkgRkSrSLrdFRFpV2jXaxXYUOxLDt8fGxd0LPBNYBhwO3AXcYmb71bHMs4G1wNpNmzbVk9eydHOjiEjmUi23RURaVdqBdm/0Pj8xfAGhVruEuz/h7mvcPefu2939Q8BW4MQ6lnkZ8FTgqXvvvfcEslxKNzeKiGQu1XJbRKRVpRpou/t24GFgZXGYmR1MqM2+q8bZFACrY5lb3H2du6/r6Zl8t+C6uVFEJFtpl9siIq0qi5shrwA+aGbLzGwecDFws7s/lExoZieY2aFm1mVmc83sfGAJcHMG+apJ1jc31tsGXERERESmpiwC7YuAG4HfAo8B3cDpAGZ2mpn1xdKuAH5CaHLyAPDXwEvc/ZEM8lWTrG9uVBtwERERkc6Q+jU7d88D50Sv5Lirgatj3z8NfDrtPLQytQEXERER6QxqHNdgT99vHmseHeuURW3ARTqPu+MOXvxMHTemiHSgh7cMcM71a1i9YRsrD1zIpaeuUHe6DeTu5AtOvlh2ORTcKUTllxfAcQoe0hY8fC+mrTp/yieKT+ujw7zs+Ebr7qqt1Fag3WDnnng4q750O5BdG3AVRhKXDOrqnh6i6X20UBt9Z/eAsXTZk8l4tdG7F7bxSYq/NZn/+OeCl/6m+Ili9DdFv6+QOMEkpyku00fzE183yXG7WzR3eq1rRqTjFJtdAqPNLq97+3OanKvW5+7kCk4u7+QKhei99HO+EALm4nuhAPmS72NlnIyZ3qNAuyU1qg04qDBqBHdnJB8KpFyhQL5Q+r1cYFr6fWw+QFSYFYO9seCuMDo+FiAysYBORGSqaedml+7lzwvFcbko4M0VQtAbf88XiuebKE10/hmJzke5vE4EzaZAu83UWxjFA8RiTR6MBW3EawIprbUs1uaRKBxGh49+Lg7P9oCvpbY1HpjG81xtnkXJWoC8/uaLiGQuy2aX7s5QrsBQrkAuXyAfq9UtFMaaTBSi93whNj4RJJc7v3ji3FqavryNOwe5/Nb13Lexj8OWzOWs4w5hybyZqf1maRwF2lNcyYHvzhH77MGfHh97NtDT95/Phi39ZS4dhXfFiSIi0uom2+yyUHAGc3kGRwoMRe+DI/kQYI/kW+5cePmt67n3ifAMwHuf6OXyW9fz0ZOObHKuZCIUaLeQ4r/q4XyB4VzslS8wki/s1m4qX/Dd/hW/+uj9RwPtQ/aaw5nPPYjHtw824deIiIikY7xml4WomcRI3hnJFUY/56LzZjGwHs5VjqRbrQZ53cbeku/3bewbJ+XEtdpvblcKtBssly+Mfn502y4GR4rBdJ6R/O6Bc70HwuK5M0Y/n33CYTpoRETa0GjPDlGzuHI39pZvOkdJm7lyNxUnklTNx2QU845T0lNF/OZjx3l0267RadZt7GVr//Doldo0tFoN8rLFc1j/ZP/o98OWzE19Ga32m9uVAu2MDecK9A6OsHMwR+/gCA9sHjtwnuwdossq37WqA0FEpPncd68IqaYQBcPFbtCKn70Q3vPuPLJ1gAtv/DN3PbaDo/afx7kvP4K9582IrlpScgWz2E44V+ZqZrt7sndo9HP/UJ65MwoVUtevETXI9Vh17FI+9r17gHB1+qzjDkl9Ga32m9uVAu2UDY7k2Tk4Qu9gjp27RhgcSRQGdRaOOhBERNIxki/QP5Sjfzg/2i53NAgujH2O3xxe/JyVC268e7Qy5Q+P7OD8G+9WZUoTNKIGuR6NuDrdar+5XSnQnqBCIbSn3jEwMjrsT4/tTL09tA4EkfahNpGNM5TL0z+UjwLrHP1DeYZzhZbbBqpMaQ2NqEFuNZ34m5tBgXYF+YLTP5RjcCTPYC7coRxe4SYL93DiLBrJp3spC3QgiDRKvQHYRAI2NQXLxuBICKgHhvP0DeUYGM6Ne/Nbq20DVaa0hk68v6kTf3MzdHygHe5KHuvqZ8OWgdFxdz26gyXzhipMnT0dCCITU28gXG8ANpGATbWXk7drOB/VUIda6v7hXF03xLXaNlBlikh76+hA+5GtAyV3MgNs7R9uUm5EJE31BsL1BmATCdhUezk52weGuecvvdUTVtBq20CVKSLtravZGWimTrtru5yNOwe54Ma7Of3Lt3PBjXeXNIURmcrqDYSXLZ5T8r1aAFZvegi1l0WqvaxfGmW2toGINFJHB9oyVuuXdx+t9atGwblMBfUGwvUGYBMJ2FR72XzaBiLSSAq0O9xELn9PJDgXabR6A+F6AzAFbCIiUk1Ht9GWibVXbLWbiaQz6CmpIiLtq9W63kyLarQ73EQuf0+kbarIZOlKisjEqLmfTAXtWsYr0O5wE6n1081E0gy6kiIyMe0awEh7adcyXk1HpG66JC/lZH3Zr9W6ZROZKto1gJH20oplfBrnNdVoi0gqsq4105UUkYlRcz9phnqbLDWijK83T2mc11IPtM2s28wuMbMnzazXzG4ws8UV0r/czO42s11m9icze2naeZLmUvvAzpB1rZmupIhMjP6kSjPUG6Q2ooyvN09pnNeyaDpyLnAy8GxgC/BV4OvAicmEZnYw8E3gbcB1wGuBb5nZke7+UL0LHs4V2LBl7LLDY7GnPj6WeAIkwOPbBtnYWxr0be4bKvt5PJ2WfiLTXHbLfaOXg+59opfLbrmPs084rKZlSTo29w1x7R0P8+DmfpYtnsOqY5eWFGppOGDhbB7eOjD6/aDFs1P9U9Vqx0Lax85QLl/TPNpNPeX2joGRSe9TE9luWWp0fopBd9rHZtblS9brqRP3i6yXkQxS123srbjfNeI315unSue1ad1W0zLNU348opltAC50969E3w8B7geWJYNnM7sAOMHdnx8b9gvgx+5+QY3LWwQsApi+z6Fr933Tf6TxM0REGm7Dxa+8092PaXY+sqZyW0TaQS1ldqpNR8xsPrAUuLM4zN3XAzuBZ5SZZEU8bWR1NLxWZwNro5eIiLQ+ldsi0hHSbjoyL3rfkRi+PTYubo9x0h5ZxzIvA64BOGTx7LXff//xNU9YrumIpK/ey4r3berlcz8N7aaW7jmbNz7nwIrpN/cN8bHv3QPAea84ouoly6zTt2Ke4s13ILTTrNR8ZyK/uV71bud2t2D2NF54cbNz0TATKrd3DIzwwOb+kmFZ76vvu+4PFGIXfrsMPvW6Z46bvhHHTtbL+NSP1pVcLq9WXrRi+ZL1MhpxHsk6T602/3rVu5+mbVq38coayuy0A+1i45f5ieELCLXa5dLXmrYsd99CaAvOMcccw4GL5lSZYoxhUFsTG5mEJfNm8rFXH1Vz+stuuW/088NbB7j+zkf56Em1/fdaPHdG1Rso4m2/rr3j4bpuuqhl/pOdJov0Z59w2IS7KJrIb67FZLZzO1o0d3qzs9AwEy23t80cpn94/LbsWeyry5fswb1P9JZ8b/axk/Uykm3jH9o8UHEZrVi+NHIZWZfxE9FqvzkL9e6naZveU1sAmWqg7e7bzexhYCXwBxi94XEecFeZSdYAL0wMOxr4SZr5kqnloc0DJd/T7r3i2jseHv28/sl+Lr91fdsHeEvmzWy535j1dhZJw1nHHbJbENnuDlsyt+TPRbXuAFuxfJH2V+9+2ixZ9KN9BfBBM1tmZvOAi4Gbx+lF5CrgGDNbZWbTzGwV8CzgaxnkS6aI5MGS9sGjAK81ZL2dRdJQDCK/8Q/P5qMnHdn0WrxGOOu4Qzh8nz3oNuPwffboiD8XMvVMlf00i+79LgIWAr8FZgA/Ak4HMLPTgC+6+1wIN0qa2WuAfyd0A/gAcMpEuvaT9pF1DdJU+Rfc7jqxplBkKlANdfriTRaLXdx2wp+2LE2V/TT1QNvd88A50Ss57mrg6sSwHwA/SDsfMnVlffA0IsBToVrdVCkkRUSS6i3jO7HJogRZ1GiLtLRGBHgqVEVE2le9ZbyaLHauLNpoizRUsmahFR7xnnWh2oq/WUQaQ8d/89VbxuuelM6lQFumvHI1C82WdaGa9W/WiVykdbVimVePdihf6i3jp8qNe5I+Bdoy5bXiJbmsC9VmdIEoIq2hFcu8erRD+VJvGd+JvddIoDbaMuW1Yi8i9bYDr/fGmqx/81Q/kYs0SyNuhG7FMq8e7VC+6GZuqVVH12hP6zGmdevRkFNdO1ySq7eGJ+vfrPaE0oq6uoyuFi+yG1FbO9XLPJUvU1M7NPlpho6u0d53/iz2nT+LXL7AYK7A4Eg+eoXPQ7k8wzlvdjalinaoWai3hqcdukAUqdf8WdP4q4P2ZGAkz8BQjr6hHH1DI83OVolG1NZO9TJP5cvUpN60JqajA+2inu4u5nZ3MXfG7qsjX3CGcmPB92ggnssznCvgisMlBa12KXiqn8ilfXV1GXNn9DB3Rg97A92xKu6li2ax5+wZ9A3lGBjOky80voButWO5Fal8mZraoclPMyjQrqK7y5g9vYfZ03cfVyg4Q1FNeN9Qjp2DI/QN5mhC2S5TnGp4RCZv0ZwZHLhozuj3XcN5+odz9A/l6B8Kn3P5bAtoHcvSrvQncmIUaE9CV5cxa3o3s6Z3s3BOiMQLBadvOEfvYI7ewRF6B7Mv2GXqUw2PSPqK5fPiuTNGhw2O5OkfyjGcL1DwUGYX3MkXPHz38L1QGPucLzi1luJLF83mE685CndwH5unrn7KVKc/kROjQDtlXV3GvJnTmDdzGjALd2dgOE/vYKjx7h0cUbtvEZEmmTmtm5nTuhu+3GLQnY8Ce48H9VHAn3cffc8XQrBf/Fx8FQP/fDQP9/AnIPlZJG2qEJoYBdoZMzPmzOhhzowe9pkfungaHMkzMBzaeA/nCgzn8wwVP+cKanoiItJmzIxuK21TnqViYF8SiMfq5ccLxpPDa6/Ln5iSPBbC8gqxqwFO8Q9F+GOSyzsjhQIj+QIjueizzpvSwhRoN0G1GpWR/FjQXQzARwqFcWs6Ri9tqqDJRCP6xRURSVMxsIcW7w8xJfmCh+A7X2Ak70zvGfvdc2d0M72ni5G8OjCQxlOg3YKmdXcxrbuLOTOqp40rCcTdGcmHz7l8gZGCk49qAooFUi7v5KLxqg0Yn7o0EhFpbd1dRnfXWCVW7+DYCfSwJXtw4KI5JR0YFN8Hc3mGol7Fpvp5UJVCrUmBdhvp6jK6MCbS/LBQKF5eLL3MGP/3Hx9WTAuUtgmMXZ4sDounTct4cxu9POrs9jtGs1jhxqRywx/akujSaFMf82dNI1cokCsU/8xM8RJaRKTNxTswKGcolyeXj7WVH203T+yG2fh76Y2uyXNf8XO5c+LYeC8zbPQTPtquv/rvU6VQa1KgLUAogILOuMxYj2cduJA7Htxa8v1p+80rSePuY0F37OpBSQGcKGTLFc5O+NMDlNwwNfonyBltt1go1PZnqHR59f8hGJuXbrYSkfY1o6ebMo/TaAnxc0zxPFMovkfjylUKzZzWFV25VqHdLC26S4m0jkt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"text/plain": [ "
" ] }, "metadata": { "filenames": { "image/png": "C:\\Users\\randa\\OneDrive\\Documents\\Teaching\\econometria\\_build\\jupyter_execute\\teoria\\06-estacional\\02-sarima_5_0.png" }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def correlogramas4(serie, residencia, func):\n", " fig, axs= plt.subplots(2,2, figsize=[12,5], sharex=True, sharey=True)\n", " opts = dict(lags=24)\n", " if func is plot_pacf:\n", " opts['method'] = 'ols'\n", "\n", " func(serie, **opts,ax=axs[0,0], title='$y_t$');\n", " func(serie.diff(1).dropna(), **opts, ax=axs[0,1],title='$\\Delta y_t$');\n", " func(serie.diff(12).dropna(), **opts, ax=axs[1,0],title='$\\Delta_{12}y_t$');\n", " func(serie.diff(1).diff(12).dropna(), **opts, ax=axs[1,1],title='$\\Delta\\Delta_{12}y_t$');\n", "\n", " for ax in axs.flat:\n", " ax.set(xlim=[-0.5,24.5], xticks=np.arange(0,25,6))\n", "\n", " pp = 'parcial' if (func is plot_pacf) else ''\n", " fig.suptitle(f'Correlogramas {pp} de cantidad de pasajeros {residencia} en SJO', size=18)\n", " return fig\n", "\n", "extranjeros = pd.DataFrame(np.log(sjodatos['extranjeros'].values), index=pd.period_range('2011-01', '2019-12', freq='M'))\n", "correlogramas4(extranjeros, 'extranjeros', plot_acf);" ] }, { "cell_type": "markdown", "id": "fa7c6c4d", "metadata": {}, "source": [ "Al usar una herramienta de selección de modelos `statsmodels.tsa.x13.x13_arima_select_order` en Python se selecciona el modelo $\\text{SARIMA}(0, 1, 1)\\times(0, 1, 1)_{12}$." ] }, { "cell_type": "code", "execution_count": 4, "id": "6ec43002", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
SARIMAX Results
Dep. Variable: 0 No. Observations: 108
Model: SARIMAX(0, 1, 1)x(0, 1, 1, 12) Log Likelihood 194.101
Date: Thu, 21 Jul 2022 AIC -382.202
Time: 00:05:34 BIC -374.540
Sample: 01-31-2011 HQIC -379.106
- 12-31-2019
Covariance Type: opg
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err z P>|z| [0.025 0.975]
ma.L1 -0.6109 0.087 -7.024 0.000 -0.781 -0.440
ma.S.L12 -0.7632 0.117 -6.520 0.000 -0.993 -0.534
sigma2 0.0009 0.000 6.349 0.000 0.001 0.001
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Ljung-Box (L1) (Q): 0.05 Jarque-Bera (JB): 0.23
Prob(Q): 0.83 Prob(JB): 0.89
Heteroskedasticity (H): 1.56 Skew: 0.09
Prob(H) (two-sided): 0.21 Kurtosis: 3.16


Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step)." ], "text/plain": [ "\n", "\"\"\"\n", " SARIMAX Results \n", "==========================================================================================\n", "Dep. Variable: 0 No. Observations: 108\n", "Model: SARIMAX(0, 1, 1)x(0, 1, 1, 12) Log Likelihood 194.101\n", "Date: Thu, 21 Jul 2022 AIC -382.202\n", "Time: 00:05:34 BIC -374.540\n", "Sample: 01-31-2011 HQIC -379.106\n", " - 12-31-2019 \n", "Covariance Type: opg \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "ma.L1 -0.6109 0.087 -7.024 0.000 -0.781 -0.440\n", "ma.S.L12 -0.7632 0.117 -6.520 0.000 -0.993 -0.534\n", "sigma2 0.0009 0.000 6.349 0.000 0.001 0.001\n", "===================================================================================\n", "Ljung-Box (L1) (Q): 0.05 Jarque-Bera (JB): 0.23\n", "Prob(Q): 0.83 Prob(JB): 0.89\n", "Heteroskedasticity (H): 1.56 Skew: 0.09\n", "Prob(H) (two-sided): 0.21 Kurtosis: 3.16\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n", "\"\"\"" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mod_extranjeros = SARIMAX(extranjeros, order=(0,1,1), seasonal_order=(0,1,1,12)).fit()\n", "mod_extranjeros.summary()" ] }, { "cell_type": "markdown", "id": "b9eb49b7", "metadata": {}, "source": [ "El modelo estimado es\n", "\\begin{align*}\n", "(1-\\Lag)(1-\\Lag^{12}) y_t &= (1-0.611\\Lag)(1-0.765\\Lag^{12} )\\epsilon_{t} \\\\\n", "y_{t} - y_{t-1} - y_{t-12} + y_{t-13} &= \\epsilon_{t} - 0.611\\epsilon_{t-1} -0.765\\epsilon_{t-12} + 0.467\\epsilon_{t-13}\n", "\\end{align*}\n", "\n", "Los resultados de la tabla anterior muestran que:\n", "\n", "- Los coeficiente estimados son significativos.\n", "- Los residuos del modelo...\n", " - parecen no estar autocorrelacionados: el valor $p$ del estadístico $Q$ de Lung-Box es 0.19.\n", " - parecen ser normales: la asimetría es 0.09, la kurtosis es 3.16, y el valor $p$ de la prueba de Jarque-Bera es 0.89.\n", "\n", "Por ello, podemos pensar que el modelo estimado es una buena representación de los datos.\n", "\n", "\n", "\n", "La expresión\n", "\\begin{equation*}\n", "y_{t} = y_{t-1} + y_{t-12} - y_{t-13} + \\epsilon_{t} - 0.611\\epsilon_{t-1} -0.765\\epsilon_{t-4} + 0.467\\epsilon_{t-5}\n", "\\end{equation*}\n", "puede utilizarse recursivamente para generar pronósticos." ] }, { "cell_type": "code", "execution_count": 5, "id": "4853be80", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "filenames": { "image/png": "C:\\Users\\randa\\OneDrive\\Documents\\Teaching\\econometria\\_build\\jupyter_execute\\teoria\\06-estacional\\02-sarima_9_0.png" }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_forecast(modelo, serie, residencia, ax):\n", " fcast = modelo.get_forecast('2020-12')\n", " ci = np.exp(fcast.conf_int())\n", " np.exp(fcast.predicted_mean).plot(ax=ax)\n", " ax.fill_between(ci.index,'lower y', 'upper y', data=ci, alpha=0.5) \n", " np.exp(serie).plot(ax=ax, legend=False)\n", " ax.set(title=f'Pronóstico de pasajeros {residencia} en aeropuerto SJO')\n", " return ax\n", "\n", "fig, ax = plt.subplots(1,1, figsize=[9,4])\n", "plot_forecast(mod_extranjeros, extranjeros['2015':], 'extranjeros', ax)\n", "ax.set(ylabel='miles de pasajeros');" ] }, { "cell_type": "markdown", "id": "70d62f17", "metadata": {}, "source": [ "{{ termina_ejemplo }}\n", "\n", "\n", "\n", "## Pronosticando un modelo SARIMA\n", "\n", "Si expandimos los polinomios del proceso $\\text{SARIMA}(p,d,q)\\times(P,D,Q)_s$\n", "\\begin{equation*}\n", "\\notation{\\Phi(\\Lag)}{$p$}\\notation{\\varPhi(\\Lag^s)}{$P$}\\notation{\\Delta^d_{\\phantom{D}}}{$d$}\\notation{\\Delta_s^D}{$D$} y_t = \\notation{\\Theta(\\Lag)}{$q$}\\notation{\\varTheta(\\Lag^s)}{$Q$}\\epsilon_{t}\n", "\\end{equation*}\n", "\n", "el resultado será un polinomio de grado $p+Ps+d+D$ del lado izquierdo y uno de grado $q+Qs$ del lado derecho.\n", "\n", "Para horizontes de más allá de $q+Qs$ períodos, la dinámica de estos pronósticos estará gobernada únicamente por la ecuación en diferencia homogénea\n", "\\begin{equation*}\n", "\\Phi(\\Lag)\\varPhi(\\Lag^s)\\Delta^d\\Delta_s^D \\hat{y}_{t+h} = 0\n", "\\end{equation*}\n", "\n", "\n", "![sarima-forecast-paterns](figures/sarima-forecast-patterns.png)" ] } ], "metadata": { "jupytext": { "formats": "md:myst", "text_representation": { "extension": ".md", "format_name": "myst" } }, "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": "3.9.13" }, "source_map": [ 17, 23, 33, 49, 56, 196, 219, 224, 228, 254, 268 ], "substitutions": { "empieza_ejemplo": "
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Ejemplo:  \n", "fin_titulo_ejemplo": "
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