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@paulorodriguesxv
Created January 5, 2021 21:23
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Como verificar se uma série temporal é estacionária\n",
"\n",
"A modelagem de séries temporais é um caso a parte dentre os modelos preditivos e difere um pouco dos modelos tradicionais de classificação e regressão. \n",
"Nesse tipo de estrutura, os elementos são adicionados de forma sequencial e devido a essa característica, importantes suposiçoes sobre a consistência dessas observações\n",
"deverão ser tratadas de maneira específica. Um bom exemplo de série temporal é a previsão diária de temperatura, preços de uma ação, e até o fluxo de vasão de um kanban.\n",
"\n",
"De maneira geral, esperamos que as observações sejam estatísitcamente consistentes. Na terminologia de séries temporáis, isso é chamado de estacionaridade. O estatísticos que me perdoem pela simplicidade, mas o que quero dizer aqui é que as observações deverão apresentar uma aleatoriedade ao redor de uma média conforme o tempo se desenvolve. E essa pré-condição é muito importante no estudo \"clássico\" das séries temporáis, pois apresentando essa consistência, poderemos utilizar diversas ferramentas estatísticas na previsão de tais séries.\n",
"\n",
"Porém no mundo real a maioria das séries temporáis não são estacionárias, isto é, apresentam tendencia ou sazonalidade. Por outro lado, muitas vezes é possível transformar, com alguma penalidade, uma série não estacionária em uma série estacionária. Com isso em mente, quero trazer nesse artigo como identificar, com python, a estascionaridade ou não de uma série temporal.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Análise visual\n",
"\n",
"Primeiro vamos ver exemplos visuais/intuitivos de uma série temporal estacionária e uma série temporal não estacionária com sazonalidade e tendência"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**1) Série temporal estacionária**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"No gráfico abaixo, que é um dataset com datas de nascimento por pessoa, observe como os valores dão a impressão que estão bem distribuídos em torno da média laranja, temo valores acima e abaixo da média, mas sempre estão em torno da média, sem se afastar em demasia. Isto pode indicar que a série é estacionária (primeira impressão)."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from pandas import read_csv\n",
"from matplotlib import pyplot\n",
"\n",
"births = read_csv('./data/births.csv', header=0, index_col=0)\n",
"births['Mean'] = births.Births.mean()\n",
"\n",
"births.plot(figsize=(10,5))\n",
"pyplot.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**2) Série temporal com sazonalidade e tendencia**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Aqui vou usar um dataset com o número de passageiros mensais"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"passengers = read_csv('./data/passengers.csv', header=0, index_col=0)\n",
"passengers['Mean'] = passengers.Passengers.mean()\n",
"\n",
"passengers.plot(figsize=(10,5))\n",
"pyplot.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Agora observe o exemplo acima. O primeiro ponto que chama atenção é como os valores estão distribuídos em relação da média (em laranja). Aqui começamos com valores bem inferiores a média e terminamos com valores muito acima da média. O segundo ponto perceptível de forma visual é que temos uma inclinação crescente nos valores conforme os meses passam, isto é, veja que topos e fundos vão ficando cada vez mais \"altos\", isso é a tendência. Por último, podemos perceber que os valores são ciclicos, isto é, há uma sobe e desce de valores ao longo do tempo, de forma bem regular - similar a uma senoide - isto é a sazonalidade/periodicidade."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Assim conseguimos ter uma idéia visual de como é uma série temporal estacionária ou não estacionária com têndencia e/ou sazonalidade. Porém não julgue um livro pela capa. Nem sempre essa forma visual será o suficiente, princilamente se você tiver trabalhando com um volume muito grande de dados. Logo, vamos dar uma olhada no que os dados nos falam de forma númerica."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Análise estatística"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Duas coisas simples e que acho bacana de serem feitas é observar o histograma da distribuição e dividir o dataset em diferentes pedaços, e para cada pedaço, calcular a média e a variância. Se estes \"pedaços\" apresentarem diferenças grandes nos valores de média e variância, provavelmente a serie temporal é não estacionária. Vamos fazer isso para nossos dois datasets anteriores."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**1) Nascimentos**"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x504 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"births.Births.hist(figsize=(7,7))\n",
"pyplot.show()"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"p1 -> Mean: 39.76373626373626 | Variance 49.48530751016939\n",
"p2 -> Mean: 44.185792349726775 | Variance 48.97628055005103\n"
]
}
],
"source": [
"sample_len = round(len(births.Births) / 2)\n",
"p1 = births.Births[0:sample_len]\n",
"p2 = births.Births[sample_len:]\n",
"\n",
"print(f'p1 -> Mean: {p1.mean()} | Variance {p1.var()}')\n",
"print(f'p2 -> Mean: {p2.mean()} | Variance {p2.var()}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Observe que apesar dos valores de média e variância entre as duas amostras não serem exatamente iguais, estão muito próximos. Temos o histograma que se parece muito com a famosa \"curva em formato de sino\", indicando uma distribuição gaussiana. Estes dois fatores podem indicar que a série é estacionária."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**2) Passageiros**"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 504x504 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"passengers.Passengers.hist(figsize=(7,7))\n",
"pyplot.show()"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"p1 -> Mean: 182.90277777777777 | Variance 2275.6946400625984\n",
"p2 -> Mean: 377.69444444444446 | Variance 7471.736306729265\n"
]
}
],
"source": [
"sample_len = round(len(passengers.Passengers) / 2)\n",
"p1 = passengers.Passengers[0:sample_len]\n",
"p2 = passengers.Passengers[sample_len:]\n",
"\n",
"print(f'p1 -> Mean: {p1.mean()} | Variance {p1.var()}')\n",
"print(f'p2 -> Mean: {p2.mean()} | Variance {p2.var()}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Por outro lado, aqui no dataset de passageiros temos um histograma cuja a distribuição é não gaussiana (não apresenta curva de sino), podemos ver que é uma distribuição achatada diagonalmente. Também podemos observar a grande discrepância entre os valores de média e variância das amostras p1 e p2.\n",
"\n",
"Um ponto interessante que podemos observar nesse dataset é que a distancia vertical entre os topos e fundos vão ficando maior conforme o tempo passa, isso pode indicar que nossa série contem um fator periódico de crescimento com escala logaritimica. Geralmente quando isso é identificado, podemos aplicar uma transformação logarítimica nos dados e observar se o histograma passa a apresentar um comportamento gaussiano."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Um exemplo de como aplicar essa transformação logartimica e o resultado disso:"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x504 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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ASimllFKuGByLUhnw4fXIrGMVft+q3C9QAyullFJKuWIwPElVoCDlMStjpVOBSimllFJpGQxHZ7VacFT487VBqFJKKaVUugbHorOagzoq/D6CkSli8USOR7U0GlgppZRSyhUD4cmUKwLBylgZA6MTq2s6UAMrpZRS6pfA6MQUR7tG3R7GtMlYnFAkNndgFXCahGpgpZRSSqkVJJ4wvPuup7j1jifcHsq0oentbOaeCoTVt19gntsDUEoppdTyuvPR0zx1ZhiAiWicIp/X5RFd6Lo+d/G6df9qK2DXjJVSSim1hrX1hfm7H7dQXGDlUlZKbyhnn8DquQIreyPm1dZyQQMrpZRSao2KxRN8+FvP4fd5+eiNOwFWzP5701OBc/WxcjJWKyQQTJdOBSqllFJr1L893M5znSN8/q0HqC8rBFbO1NpCU4F+nxef18PwKgusNGOllFJKrUHByBSf/WkrN11Sz+v3rZ/OAK2UQGVgbBJfnmd6ivJiIkJFIH/FZNjSpYGVUkoptQadG5ogGk/w+kvXA1AZWFnF4IPhKNUBHyKz9wl0VPh92m5BKaWUUu7rC0UAqC21apjKivIRWTl9oQbDk3O2WnBU+H2rrt2CBlZKKaXUGtQXslbd1ZZYtVVej1BWtHKm1gbHotNZtLlUBFbffoEaWCmllFJrUL8dWNWUXMgKVfp9K2aV3XwbMDusjNXKyLClSwMrpZRSag3qC0YoLcyjMP9CM9CKgG9FZKyMMQyEJ6lOYypweDxKImFyNLKl08BKKaWUWoP6QpPUlhbOuK/C71sRU2tj0TiTscSCU4Hl/nwSBkKRWI5GtnQaWCmllFJrUF9oktqSmRmhykD+ipha6xm1CuvXlRXOe970SsYVMn2ZDg2slFJKqTWoLxSZFVhV2DVWxrg7tXZ+ZAKA9eVF85630npvpUMDK6WUUmqNMcbQF0wxFRjwEY0lGI/GXRqZpSvdwMrOWK2EurB0aWCllFJKrTHBiRiTscTsqUD/ymgS2jUygUegrmSh4nVrI+aV0nsrHRpYKaWUUmuM0xy05uKpwMDKmFo7PzJBfWkhed75wxBnvKupSagGVkoppdQac3FzUEdlYGVkgLpGJmiomH8aEKCkII88j7ieYcuEBlZKKaXUGnPxdjaO6WJwlwOV8yMTC9ZXgbURc7k/3/VAMBMaWCmllFJrTF/QyVilDqzczADFE4ae0UhagRXYTUI1Y6WUUkopt/SFJinK91JckDfj/tKifDzibo3VQHiSqbjJLLDSGiullFJKucXqul6AiMy43+sRyl3uvu70sGoon785qKMikK+BlVJKKaXc0xec3RzUUeF3N1A5P+wEVv60zrcyVlpjpZRSSimX9IcmZ60IdFQGfAyPuReoXGgOmm7GysfICugWny4NrJRSSqk1pi80OauHlcPtmqWukQlKCvMoKcxP6/xKv4+puCG4SjZiTiuwEpEzIvKCiBwRkcP2fZUicr+ItNrfK5LO/5iItIlIi4jcsFyDV0oppdwUiyf4t5+fot/uG7USjEdjhCdjs1otOCpcr7GK0JBm4TpAY6V1bsfg+HINKasyyVj9ijFmvzHmcvvnjwIPGGO2AQ/YPyMiu4FbgT3Aa4Eviog3i2NWSimlVoRvPX2Ov/nhCX50tMftoUy70Goh9VRbRcDKWLk1tdaVZg8rx5aaYgDa+kPLNaSsWspU4C3AXfbtu4A3Jt1/tzFm0hhzGmgDrljC8yillFIrTmQqzmd+ehKAkRXUZ+lC1/XUGavKQD5TcUN40p2ptfMjExllrDZWBfB6hFN9Y8s4quxJN7AywE9E5GkRea99X50xphvA/l5r398AdCY99px9n1JKKbVm3PXYGXqDk4i4v0VMsrm6rjucJqEjLow5PBljdGIqo4yVL8/Dxko/bX3hZRxZ9uQtfAoALzfGdIlILXC/iJyY51xJcd+sfKMdoL0XoKmpKc1hKKWUUu4bnZjiiw+d4todNbT2hlfUJsELTQVWBi50X2+sTK/lQbZ0Z7gi0LGltphT/asjsEorY2WM6bK/9wHfwZra6xWRdQD29z779HNAY9LDNwBdKa55hzHmcmPM5TU1NYt/BUoppVSO3fHwKUYnpvijG3asuAaWfaFJ8r1ChT/1qrsKJ7ByYcwXmoOmn7ECq87qzOAYsXhiOYaVVQsGViISEJES5zbwGuBF4D7gnfZp7wTutW/fB9wqIgUishnYBhzK9sCVUkopN/QFI/zHL87whn3r2bO+bMU1sOwLRagpnt113eHmRsxdI9Y0ZSZTgQBba4uZihs6hlb+ysB0pgLrgO/Yv6A84L+MMT8SkaeAe0TkdqADeBOAMeaoiNwDHANiwO8YY+LLMnqllFIqx770SDtT8QQfun47AOV+H+fsbuIrQV9wkprSuafaKl3ciPn8yDhej1A3z/hS2VITAKCtL0yzvUpwpVowsDLGtAP7Utw/CFw3x2M+DXx6yaNTSimlVpjnOke5rKmCTdXWh3150UqbCoywsSow5/GSwjy8HnFlzF0jEepLC/F6UmfT5rKl1gqmTvWv/JWB2nldKaWUykDH0DhNVReKviv8+YxOTBFPrIwtV/pCk3O2WgDweMTeLzD305eZtlpwlBbmU1tSsCpWBmpgpZRSSqUpMhWnJxihKWk1XbnfhzEQnHC/zmoyFmdkfGrOFYGOCr/PpRqriYxXBDq2rpKVgRpYKaWUUmlyaqmSA6uKgLX6biVMBzpb68zVw8pREcj9tjbxhKFnNEJDReYZK7BWBp7qD6/4zZg1sFJKKaXS1GmvSmu8KGMFK6NJ6EJd1x3WVGBuA6u+UIRYwmS8ItCxtbaYUCS2ovZlTEUDK6WUUipNznL/GRmr6U7m7mesnOagC626qwz4GBrLbSDYNd0cdPEZK4C2FT4dqIGVUkoplaaOoXGK8r1UF/um7ysvsqYC3dgi5mL9znY2C2asfIzkeCPm83YPq8UUr4OVsQI4tcIL2DWwUkoppdLUMTROU6V/RvPN6YabKyFjFZrEI1BVPH9gVRnwEUsYQjnciHmpGau60gICPu+Kb7mggZVSSimVps6h8Vn765UU5uGRlZGx6gtOUlVcsGCfKDe6r5/qC1NamEdxQbrbFM8kImypLV7xLRc0sFJKKaXSYIyZzlgl83iEcr9vRWSsOofH05pqS96IORdeODfK/zx7nhv21C/pOltrVn7LBQ2slFJKrShDY1G+/3w3z3YMuz2UGQbHooxH4zRVzg5cyv35KyJjdXZwnE1V/gXPK/fnrkXEZCzOh791hOpiH5+4efeSrrWltpju0QjhHE5hZmpx+TillFIqiyZjcb7wYBs/a+njaFcQY6z94R748LVuD23a9IrAFIFLxQrIWEWm4nSNTrCpesOC5zoZq+EcrAz85/tbOdkb5ivvOkiZHdAtlrMysL0/zKUbyrMxvKzTjJVSSinXPXZqkM8/2Ea+18Mfvno7N+6t59zwxIpqBtmZotWCw60tYpJ1DI1jDGyunnufQEdFIDcF9890DHPHw6e49WAj1+6oXfL1ttZe2Ix5pdLASimllOtaekIAfOW2K/jgdds4uKmSyVgi593B59MxaAVWGypmB1ZlRT5GXc5YnRmwVsvNtwGzo6Qgj4I8D73ByLKNZzIW5//e8xzryor4k5t3ZeWaG6sC5HlkRddZaWCllFLKdSd7QqwrK5yeKnK2PekaWb4P/kx1DI1TV1pAYb531rGVkLE6M2gFVpvTCKxEhMZKP51DE8s2niMdI7QPjPHxm3ZRUri0KUBHvtfDhooiztpB7kqkgZVSSinXtfSG2F5XMv2zs7Lt/MjyffBnKtWKQEdFwMfEVJzIVDzHo7rgzOA45f78tOuYmir903Vjy+GEnYV8ycaKrF63rrRwWTNtS6WBlVJKKVfF4gla+8LsqL8QWK1fgYFVqh5WDmeVnZsrA88MjLEpjWyVo6nST+fQ+LLVsZ3oCVFWlE/dAhtCZ6qutJAeDayUUkqp1M4OjRONJWZkrCr8+RTme6a7dbttMhanOxiZO2O1ArqvnxkYS6tw3dFY6Sc0GVu2YLClJ8jO+pIZXeqzob6skN7g5Ipa2JBMAyullFKuOmlPGe1MyliJCA3lRSsmsDo/PIExqVcEQm77QqVitVqIsDGNHlYO57Usx3RgImFo6QnN+J1mS11pIdFYYkX0DUtFAyullFKuaukNIXJhk13H+hUUWHXM02oBoLzIyli59WHvjC+TjNVyBlbnRyYYi8bZUV+a9WvXlxYCrNjpQA2slFJKuaqlJ8SmqsCs1XYN5UUrpsZqvh5WABUBdzNWmbRacDTaHeSXI7ByCtd3rst+xqq+zKrZ0sBKKaWUSsFaEVg86/715UUMhKOurrRzdAyNU5DnoaYkdSG2U2PlVsYqk1YLDr8vj+rigumgMZtOdAcBZtTNZUudnbHqHdXASimllJohMhXnzMBYyikjp+VC9wr4AHVaLcxViF2Y76Uw38OISxmr0wPjVGTQasHRVFm0PBmr3hCNlUUUF2R/57zaEp0KVEoppVI61R8mYWBHisyG03JhJdRZdQxNzDkN6LD2C3QnY3V2cCyjaUDHcvWyOtEdZOcy1FcB+PI8VAV89AYnl+X6S6WBlVJKKdc4W9nsqJ89FbhSmoQaY+btYeUo9/tcy1hl2mrB0VTpp2tkgql4ImtjiUzFOTM4viwrAh0ruUmoBlZKKaVc09Ibwuf1pMy21JcVImK1OnDT8PgU4cnYghmr8iJ3trVxWi1k0hzU0VjpJ2GymxVs6wsTT5gZDV+zrb6skJ4VMEWcigZWSimlXHOyJ8SW2mLyvbM/jnx5HmpLClyfCnSKuxfKWFUE8l1ZFehM5W2qTr+HlWM5Wi5MrwhcpqlA0IyVUkoplVJLT4gdKVYEOtaXF9E16m5g5RRJrysrnPc8ayow9xmr03arhcVkrJqqsh9YtfQE8eV52JRBs9JM1ZcWMjgWZTI2c8XoR7/9PJ/+/rFle950aGCllFLKFcHIFF2jEbbPM2VkNQl1NzPRZwdWtQvseVfhz2dkPEoikdutVs4OLj6wqispxOf1ZD1jta22mLwUWchscfYf7LuogP1nLX0Mht3bVgg0sFJKKeWS1t7ZW9lczGkSmutgJVlPMILXI1QHFgqsfCQMhCZjORqZZbGtFgA8HmFDZVFWe1md6Akta30VQJ2dPewLXQi6R8aj9AYnl/25F6KBlVJKKVe09ISB+ZtINpQXEY0lGBxzLwvRG5yktqQAj2f+zYTLp5uE5nasZwfH2LSIFYGObLZcGBqL0h+aZNcy1ldB0rY2oxcyVhe6vS/vcy9EAyullFKuaOkJEvB5p9sqpLISeln1BiPT3b7nUzG9EXNu66zODIwtahrQ0VTpp2MwO4HViR6r4/pyZ41S7RfodHtfzjYP6dDASimllCtO9obZVlcyZzdzgPXl1geo+4HV/NOAAOX+3O8XuJRWC46mSj/BSIzRLASEJ7oXnt7NhnJ/Pr48z4yVgS29Icr9+dTOse1QrmhgpZRSyhXnRsbZuMDKsZXQJLRnNDKdIZmPG1OB7f124foiWi04GrPYcqGlJ0RlwDfnnorZIiLUlRbM6GV1oifEzvr5A/Vc0MBKKaVUziUSht7RSdaVzT0NCFBWlE/A53UtsJqIxglGYtSmNRVoBVbDY7mbCnzoZB8AV26uWvQ1Mu1lde+R8zzS2p/y2LOdw+xZX5qT4KY+qZdVImFo6Qkta++sdGlgpZRSKucGx6JE44kFe0OJiN1ywZ3AyvngTqfGqqwoHxEYmchdYPWTo71cuqGM+gXex/lkkrE61hXkQ/c8x6e/f3zWsb5ghJO9YV6+tXrRY8lEcpPQc8MTjEfjrq8IBA2slFJqTfvPJ89y96EOt4cxizOFs1BgBe72snI+uNOZCvR6hNLC/JxNBfYFIxzpHOE1u+uWdJ3igjyqAr4FA6t4wvDx77xAPGE40ROaFew+emoAgKtzFFjVlxbSE4xgjJkumne7cB00sFJKqTXtMz9t5aP/8wLfWGHBVbfdTX2hqUDA3YxVyFrOn07xOlgrA3O1KvD+470AXL+7fsnXaqz0L9jL6huHOjjSOcIHrt0CwM9PzpwO/C0R7v4AACAASURBVEXrIOX+fHbnqN1BfVkhkakEwYnYdKuF+Vp35IoGVkoptUb1hSL0hyYpK8rn4995ge893+X2kKZ12xmrdKawNlQUMTgWZSIaX/DcbOu1x1mX5lRbmd+Xs4zV/cd6aar0s32eLYHStVAvq75QhP/3oxO8fGsVH7lhB+vLCnmopW/6uDGGR9sGePmW6gX7fWVLXVLLhZaeEE2VfgIFeTl57vmkHViJiFdEnhWR79k/V4rI/SLSan+vSDr3YyLSJiItInLDcgxcKaXU/I51WdMjn711P5dvrOAPv3lkVpbBLd2jEXxeD1UB34LnTrdccGHPwN5ghKJ8LyVpfmBbGavsBlbxhOGxtoEZ3efDkzEeaxvkNbvrslIo3lTp5/zIBFPxRMrjf/W940xOJfjLW/YiIrxyRy2Ptg0SjVnnn+ofoycYyVl9FcwMrE70BFfENCBklrH6fSC5Wu2jwAPGmG3AA/bPiMhu4FZgD/Ba4Isi4s3OcJVSSqXrqB1YXbaxgi+/8yDbakt4/9ee5txw9rYvWazu0QnqyhbuZg6wvsy9JqE9wQj1ZYVpBy8Vfl/WVwU+0trP2778JP/ys7bp+37e0k80nuD6JdZXOTZXB4gnTMqs1eEzQ9z3XBcfuHYLzTVWduzaHTWEJ2McPjsEwGM5rq+CC3VvHYNjnB4YW12BlYhsAG4Gvpx09y3AXfbtu4A3Jt1/tzFm0hhzGmgDrsjOcJVSSqXrWFeQxsoiSgvzKSvK5x/etI+JqThPnx12e2h0j0bSqq8CaKiwzjs3nPvAqs/eziZd1cU+BsKTxLO4t6ET7PzzT0/yZPsgAPcf66HCn89LNlbM99C0bbOnE539G5M9YT/nu1+xefq+l2+tJt8r/LzFyoD+onWAxsoimhboS5ZNzqbYj7YNkjDub2XjSDdj9RngI0ByjrDOGNMNYH+vte9vADqTzjtn36eUUiqHjnaNsmdd2fTPW2oDiFxoKumm7tGJtFYEgpWZyPNIVjcKTpeTsUrXlppiJmMJzmcxCDw/MoHP62FjVYAP3v0sfcEID57o47pddeR5s1MqvaXGCazCs46d6AnRWFlESeGFTZ6LC/I4uKmSh1r6icUTPN4+mNNsFUBhvpcKfz6PtlnZspXQagHSCKxE5HVAnzHm6TSvmSpfOit0F5H3ishhETnc378y5vyVUmqtCEWmODM4zp71F/4VX5DnZUNFEacH3A2snOag6QYseV4P68uL6MxxxsoYk/Y+gQ4n83MyReZnsbpGIqwrL+Tzbz3A8NgUb/63xwlGYlmbBgQIFOTRUF5Ea9/swOpkb4gdKVbbXbujhpbeED851ksoEstpfZWjrrSQ0GSMgjzPkrb1yaZ0Qt2XA28QkTPA3cCrROTrQK+IrAOwvzvLA84BjUmP3wDMWopijLnDGHO5MebympqaJbwEpZRSF3OWn+9pmDk90lxdTPvA7A/PXBoat5qDrk9zKhCs4upcZ6xGJ6aYjCUyCqy21loBSKoAZbG6RiZYX1bE3oYy/vR1uzgzOE5BnodXbMtuILO9rnhWQBiNJWjvH0vZxuDaHdZE1f/70QkAXrYl94GVE5xvryvBm6PViAtZMLAyxnzMGLPBGLMJqyj9QWPM24H7gHfap70TuNe+fR9wq4gUiMhmYBtwKOsjV0opNaej50cB2LO+bMb9m6sDnO4fw5js1QBlqnsk/VYLjsbKopwHVr3BzHpYgdV9va60gNa+7GWsukcmWG/vmfj2qzbytiubePtVG/H7sttaYFtdCe0DY8SSVgaeHhgjljApp9m21RazvqyQs3ZmtDKNFZ7ZVldi/Q2tlGlAWFofq78FrheRVuB6+2eMMUeBe4BjwI+A3zHG5L75iFJK/RI72hWkKuCbVXi9pSbAWDROn9340g1Oc9BMMlYbKvwMjkUZm4wt17BmyWQ7m2TbaktS1iotRiyeoCcYocFuOSEi/PWvXsKfvm53Vq6fbGttMdFYYsaUa4udwUoVuIgI1+60sla5rq9yOP3FVsqKQMgwsDLGPGSMeZ19e9AYc50xZpv9fSjpvE8bY7YYY3YYY36Y7UErpZSa39GuILtTbIa7udqqAXKzgD2T5qAOZ6PgXK4M7MlgO5tk2+qKaesLz+g7tVi9oUkSBtaVpx+ELpYz3Zc8HdjSEyTPIzRXp25Cev0uq87rlTvcKelxfjcrYfNlh3ZeV0qpNSYaS9DaF5o1DQjQXGMV+LpZZ9U9GiHfK2k1B3VkslFwtvTZgVVNBu0WwMpYTUzFOZ+FvltO7671OQisttZawVNbUn1YS0+YzdUBfHmpw4Vrd9Twgw++wpX6KrACulv2r+eyjeWuPH8qGlgppdQa09oXYipuZqwIdNSXFlKY7+G0ixmrntEJ6ssKM9r6xMlY5bLOqicYocKfT2F+Zj2up3tCZaHOygmsnKnA5VRckMf6ssIZvaxO9obYPs80m4iwO8XfWa40lBfx2VsPZL3ebCk0sFJKqTXG6bieKrDyeITN1cW0u9hyoWs0wrrSzDIwFf58Aj5vTjNWvcHJjOurwCrqhtQ9oTLVZRf6p9tMdam21ZVw0h73eDRGx9A4O1fAxsariQZWSim1xhzrCuL3eefs69NcHXC1l1XPqNWXKRMiQmOlP6fb8WTaw8pR7vdRU1KQlZYLXSMTlBXl52xz4W21xZzqDxNPmOkAa76MlZpNAyullFpjjnaNsmtd6ZxTbc01ATqGxqc30M2lRMLQM5pZN3NHY6WfzqHcFa9bgVVm9VWObbXFWQusclFf5dhWZ3WOPzc8zkm7F1qq5qBqbhpYKaXUGpJIGI51BVNOAzqcDXc7XdiM2WkOum4RmaDGCj8dQ+M56cEViyfoD01mvCLQsb2uhLbe0JLH2jUayUl9lWPb9MrAMC29IQrzPdMLB1R6NLBSSqk15OzQOGPR+IKBFbjTcsFpDrqY9gFNlUVMTMUZHItme1izDI5FSRioXWRgtbW2mLFonC67tcRi5Tpj5awMbO0LWYXrK6ij+WqhgZVSSq0hx7utwvXd62a3WnA4PYlOu9BywWkOmu4GzMly2XKhZ3RxzUEdFwrYF78yMDwZY3RiKmeF6wClhfnUlxbS1hvmRE8o5VY2an4aWCml1BpydtAKOjbXzL0hbZk/n6qAz5WMldN0czHBQi5bLvQusjmow5lSW8rKwO7pHla5mwoEq87q0Jkh+kOTWl+1CBpYKaXUGtIxNE5VwEfxAqvImmsCrrRc6BrJvDmoY0NF7rqv94Yy3ycwWWXAR3Wxb0m9rJxpxIYcTgWC1eDUeY91RWDmNLBSSqk1pHNoPK1i480utVzoGZ2grjSz5qCOIp+X6uICOgZzkLEajeD1CFXFiwuswKpXWsrKwFx2XU/mNDgFXRG4GBpYKaVUhqbiCZ4/N+L2MFI6OzQ2PWU2n+aaYvpDk4QiUzkY1QVdo5GMNl++WFNlUU5WM/YGI9QUFyypcHtbbQltveFFrwzsGpnAI8zaSHu5bbcDq7Ki/EVn7H6ZaWCllFIZuu9IF2/4wqM8dWZo4ZNzaCqeoGskklZg5awMzHXWarE9rByNlf6sBVYtPaHpYvqLnRueWHJQsb2umNBkbLquLFPnRyaoLy0kz5vbj+qtNVaWakddyaxNvNXCNLBSSqkMtdgrvf7jF6ddHslM3SMR4gmTVmC1pSb3LReMMYvqup6sqdJP10iEWHzpzU3f/dWnuP0rh0kkZmaU2vrCPHF6kJdtXdrGwltr0y9gn4jGeeB474zsVvdIJOfTgGAtbtheV8wVmytz/txrgQZWSimVofZ+64Pyx0d7crop8EKcNgTp1Fg1VvrxCDktYB8cW3xzUEdjhZ94wtC9xP5QwcgUnUMTHOsO8r0Xumcc+8KDrRTmeXn31ZuX9BxOrdLJNFou3PnYaW6/6zCPnxqcvq9rdGJR/b6y4bu/dzV/eP12V557tdPASimlMtTeP8b+xnJEhK8+fsbt4UxzAqumqoUDq4I8L42V/ukgMVv6Q5N841AH8cTsuiKnN1T9EmqsNlRaj11qLysni1SQ5+Eff9LClJ0Ba+8Pc99zXbzjpRuXVLgOUBXwUVaUn1bw+sMXegD4+pNnAauDvpWxym2rBUdBnlcbgy6SBlZKKZWBqXiCjqFxXralihv31nP3U52EJ2NuDwuwgo18r6Tde2k5VgZ++5lzfOx/XuAT//virKLtnxzrBZbWPiBbvaycxp0fv2kXZwfH+eZTnQB84cE2CvK8vOea5iVdH6yNo5trAgsGr51D47xwfpTqYh8/OdpLbzDCwNgk0Xgi560W1NJpYKWUUhnoGBonljA01xTzW1dvJhSJ8e2nz7k9LMD6gN5Q4U870+AEVtnce+/soBWofeNQB3//4xbAqq36p5+08LkHWrn50nXzbrezkHVlReR5ZMkF7C29IYryvfzmVRs5uKmCzz3QyvHuIP975Dxvv6qJ6iVmqxzN1cUL1rH9+KiVrfqnN+8nljDcfaiTLnvrn6WsoFTu0MBKKaUycNr+kGyuCXBZUwX7G8u589HTswqg3dCRZg8rR3NNMePROL3ByayN4ezgOPsby3nblU188aFT/OvPT/EX3zvG5x5s4y2XN/K5Ww8sqoeVw+sRGiqK6BhaWpPQ1t4w2+qK8XiEj7x2J32hSd7+5SfJ93p47zVblnTtZM01AfoWaGvxoxd72LWulGu213DN9hq+cahjOiO3lEJ/5Q4NrJRSKgPt9v56W+z99n7r6s2cGRznZy19bg4LsAKrpsr0MxzN05sxZ6/OqmNonI1Vfv7ylr287tJ1/O0PT3Dno2e4/erN/O2vX5KVup3GCv+SpwKdDYYBDm6q5LqdtQyORfmNKzdSk8W+Uc7qyzMDqcfbF4zwdMcwN+6tB+A3r9pITzDC1x63aq10KnD10cBKKaUy0N4/ZhUl+/MBuHFvPXWlBdxzuNPVcY2OTzE6MZVWqwVHs9NyIUt1VtFYgq6RCTZWWtOR//Tm/bz1ikY+duNOPnHzrqz1RGqs9HN2cPFTmCPjUfpCk9ONMAE+fvMuXrWzlg9cm71sFVhZQbgQkF/sx0d7MIbpwOpVO2tZX1bIoTND+H1eyoryszoetfw0sFJKqQy0949NN9cEyPd6eNmWap7pGMlqrVKmnJqjTAKrupJCivK9Wetl1TUyQcJcaPfgy/PwN792Ke975ZasNprcXlfM8PgU/eHFTWGetFcEbkvarmVLTTH/cdvBrGarADZW+RGBU3O8xz98sYctNYHpsXg9wtuubAKsrWy0Qefqo4GVUkploH0gPJ3pcexvLKc/NLnk3kpLkUkPK4fHI3YBe3amAs/aY9hYFVjgzKXZYW8M3NKzuA2Onb5S23OwD15BnpcNFUUpp1uHxqI8eXqI19rZKsebDzaS7xXWLaFDvXKPBlZKKZWm0YkpBsLR6ekdx77GcgCOdLq3f+BiAiuAzTWBrE0FdtgrAjem0UdrKXbWW6sKT3TPHVgZY3iopY9b73ice4+cn3GstTdEcUEe63MUuMy1MvD+Yz3EE4Yb966bcX9tSSF/cctebl9ig1Lljjy3B6CUUquFk3Vorp6Zkdm1rgSf18NznSPcdMm6VA9ddh1D41T48yktzKwmZ0t1gB++0E00lsCXt7R/a3cMjVOQ56EmS60K5lIZ8FFbUsCJOTJWRzpH+NsfHueJdmsvx+BEjFv2N0wfP2mvCMzVNFtzTYBDp4dIJMyMFZE/erGHDRVFKdtPvPWKppyMTWWfZqyUUipNTjPNizNWBXledq0vdTVj1Tk0nlF9lWNzTYCEgY6hpWetzg5aY1hKO4V07agvoaU3OOv+e4+c543/8iitvWE+9YY9fPTGnRzrDs6YijvZG2J77fJPAzqaa4qZmIrTG7owVTwejfFo2yA37KnXOqo1RgMrpZRKU3v/GF6PpAxg9m8o44Xzoym3csmFTHtYOZrtthHZKGDvWGRwtxg760s42RuetRnzd5/rprGyiJ9/5Fd458s2ccv+9QB8/3lrP8DB8CSDY9HpffxyYUv17A2vnzw9RDSe4NodNTkbh8oNDayUUipN7QNhGiuKUk6Z7W8qZzwap7VvcQXVSxGLJzg/PLGooGaT/aG/1K1tjDFWYLXM9VWOnfWlRGMJzgxe6A+VSBgOnx3ipc1VFBdYlS7ryoo4uKmC79sbLTsrAp0C+FyYbrmQlDV7+GQ/BXkeDm6qzNk4VG5oYKWUUmlq7x+bNQ3o2LfBKmB/zoXpwO7RCLGEWVRgVVaUT3Wxb8kZq4FwlPFoPGcZq1QrA1v7woyMT80KVm6+ZB0nekK09YVyuiLQUVdagN/nndFy4eGT/VzZXEVhvjdn41C5oYGVUkqlIZEwnB4Ym1W47thcHaC0MM+VOiunC/lig5rm6uIlZ6w6plst5Caw2lpbjNcjnOi5UGd16IxVrH7l5qoZ5950yTpErGnCk70hSgvzqM1yv6r5iFhtLZzVl+dHJjjVP8Y126pzNgaVOxpYKaVUGs6PTDAZS8yZsRIR9jWWc6RzNMcjW3yrBYf1ob+0XlZO8XtT5fL2sHIU5nvZVOWfsTLwqdND1JUW0HjRtj61pYVcsamS77/QTWtvmO11JTkvGG+uKZ7uF/bIyX4Artmu9VVrkQZWSimVhvaBC5svz2V/Yzkne0OMR2O5GhZgBVZ5nsU3lGyuCTAQjjI6MfdGwQuOYXACEdhQkbu97XauK52eCjTGcOj0EFdsrkoZNL1u33ra+sI82znM9hzWVzmaqwOcG54gMhXnkdYB6ksL2VabuwJ6lTsaWCmlVBpOOz2sFgis4gnDi+dntwFYTh1D4zRUFJHnXdz/0jdnoYD97NAY9aWFOa0Z2llXQsfQOOHJGOeGJ+gJRrhiU0XKc1+7px6PwFTcsN2FgKa5JoAxVp3eL9oGeMW2am2zsEZpYKWUUmloHxijuCBv3uaXTgf2XBewL7XNgTO9uZStbToGF9fuYSmcAvaTvSGePG3VVx3cnHqVXU1JAS/dYtVe5bJw3bHFfo/vPXKe0YkpXqHTgGuWBlZKKZUGa0VgYN4sQ3VxARsqirJewG6M4be+8hR//N/P0zUyMX3/6PgUH/rmEZ4/N8rehrJFX7+p0o/XI0taGdgxNM7GHAdWztY2LT0hnjo9RFlR/ryNP998eSMBn5fdKTqdLzcnK3j3U52IwNVbtXB9rdItbZRSKg3t/WGumCMbkmxfYzlHOrIbWJ0bnuDBE30AfOfIed71sk3sayznU989ykA4ygev28bv/srWRV/fl+ehsaIo7T0D73j4FD852svX330lhfleJqJx+kKTOVsR6NhQUUTA5+VEd5CnzgxxcFPFvF3fb9nfwA176l1pcRAoyKO+tJCeYIRLN5RRGfDlfAwqNzSwUkqpBYQnY3SNRtiaRm3O/g3lfP/5bvpDk9RkaUn/sW6rZusLbzvAz070c8cj7RgDO+pK+PI7DnLJhsVnqxybqwNpZax+8EI3f/2DEwDc9dgZ3vfKLXQOL21V4mJ5PML2+hJ+0TZA+8AYt17RuOBj3Owbtbk6QE8wwjXbdBpwLdPASimlFtDWZ9UebU1jfzmnzur5cyNct6suK89/rCuICLxqZy2vu3Q977lmM0+fHeb/vGQDBXnZCRSaa4p5on32RsHJXjw/yofuOcJlTeX4fXl88aFT3HpFE2cHnR5WuWm1kGxnfQnfONQJsOK7mDfXBHi8fZBXaP+qNU1rrJRSagGt0926F85Y7VlfighZXRl4vDvI5uoAfp/1b+Gd9aX8xpUbsxZUgZVNmZiK0xOMpDzeF4rw3q8eptLv419/8yV89MadjE5MccfDpzg76PSwym3GCi7UWRXle5dUZ5YLr9pZyxWbKrlsY+qVi2ptWDCwEpFCETkkIs+JyFER+ZR9f6WI3C8irfb3iqTHfExE2kSkRURuWM4XoJRSy62tL4zP60krcAgU5NFcHeCF89lrFHqsO8iudctbcN2cYqNgRyJh+MDXn2F4fIo73nE5tSWF7G0o4w371vMfvzjDMx3DlBTkUeHPX9YxpuKsDLxsYzn5i2w3kSvX7arjnve/dMWPUy1NOr/dSeBVxph9wH7gtSJyFfBR4AFjzDbgAftnRGQ3cCuwB3gt8EUR0c2QlFKr1sneEM01gbT7RF3SUMaLWQqsRiemODc8we5lDqycppnJW8Q42vrDPH12mI/euHNGVuhD129nKp7gBy/00Fjpd6Uv0676UvK9wsu26PSaWhkW/L+EsTjNTfLtLwPcAtxl338X8Eb79i3A3caYSWPMaaANuCKro1ZKrUl//YPj/OCFbreHMUtrX5htGfQ+2ttQRk8wQn9ocsnPfcIuXF/uFgHVxQU0lBfxbIpWEc4qx6svqg3aVB2YLhjP9YpAR5k/n+/+3tXcfvVmV55fqYul9c8vEfGKyBGgD7jfGPMkUGeM6Qawv9fapzcAnUkPP2ffp5RScwpGprjj4XZ+/+5nOWxvprsSjEetrt6ZbD/iZHVe7Fp61spZEbjcGSuwOsenam565NwIJYV5bE5RnP7BV20j4PNO1zq5YWd9qaur/ZRKllZgZYyJG2P2AxuAK0Rk7zynp8oFm1knibxXRA6LyOH+/v70RquUWrOOdVkBRJ7Hw/u+9jTn7CX8bnNWBKZTuO7YY2eXXjy39MDqeHeQqoCP2iy1bpjP/sZyzg1PMBCemWk70jHCvg3lKVcL1pYW8rM/upb3X9u87ONTajXIqILOGDMCPIRVO9UrIusA7O999mnngORmIhuArhTXusMYc7kx5vKaGu3podQvO6cm6SvvOkg0nuA9X32ascncbmacSmtv+q0WHCWF+VkrYHcK13NRv5RqS56JaJyW3hD77WOp1JYUZnWFolKrWTqrAmtEpNy+XQS8GjgB3Ae80z7tncC99u37gFtFpEBENgPbgEPZHrhSam052hWkvrSQK5ur+PxbD9DSE+RD9xzBmFkJ75xq7QuT75WMa4j2ZKGAfSqe4GRPOGdbsOxtKMXrkRmB1dGuUeIJMx10KaXml07Gah3wMxF5HngKq8bqe8DfAteLSCtwvf0zxpijwD3AMeBHwO8YY+LLMXil1Nrx4vlR9jZYAcS1O2r5w1dv58dHeznZu/iNgbOhtTdEc3VxxkvkL2kopWs0wmB48QXs7f1jROOJnNRXAfh9eWyvK5lRwO7se7ivcWX3iFJqpUhnVeDzxpgDxphLjTF7jTF/Yd8/aIy5zhizzf4+lPSYTxtjthhjdhhjfricL0AptfqNR2Oc6g+zZ/2FD+/X7VsPwLMdw24NC7AyVlszqK9yXChgX3yj0GPdVsZruXtYJdvfWMZznSPTmcIjnSM0lBdRW1KYszEotZpplzKllOuOd4dIGGb0SNpU5afcn8+zWd7QOBMT0Tidw+MZrQh0OEHiUqYDj3eH8OV5aK7J3VYx+zaUE4zEOGNvU/PcuRHNVimVAQ2slFKuc4IPZyoQQEQ40FjOs53uZaxO9YcxBrZn0MPKUVaUz8YqPy9ksDJweCw6o6bsWFeQ7XWZT0Muxf4mq5bqSOcwg+FJOocm5i1cV0rNpIGVUsp1L54fpSrgo7505nTTgaYKWvvCBCNTroyrtc/aI3AxGSuwMnDp9LIyxvDlR9p5yV/dzwfvPsJUPIExhmPdwZzVVzm21Zbg93l5rnOU587Z9VUbNLBSKl0aWCmlXPdiV5A9DWWzWgocaCrHGHi+M3v77mWitTdMnkfYmKIxZjouaSjj3PAEw2PROc+JTMX50D3P8VffP87u9aV897ku3ve1p+kYGmdoLJrzwMrrEfY2lPFs5whHOkbwCCt+c2OlVhINrJRSropMxWntDbE3RUuBfY3liLhXwN7aF2ZzdQBf3uL+V3nJAh3Ye0YjvOlfH+c7z57nQ9dv577fuZq/euNeftbSx1vveALIbeG640BjOce7ghw6M8T2uhICBXk5H4NSq5UGVkopV53sDRFLmJRZkdLCfLbWFKfcvy4XWntDbFvEikDHXruAfa5GoX/3oxO09YX50jsu54PXbcPjEd5+1UY+85b99Nr7DO7KUQ+rZPsay4nGEzzRPqT1VUplSP8ZopRy1YvnrXYEl8wx3XSgqZz7j/VijMlJ93FHZCpOx9A4b9i/+K1Oy/z5NFYWzbky8Pnzo7x8azXX766bcf8t+xuoDPho6QlRWpi/6OdfrORgSgMrpTKjGSulfsn8rKWP7tEJt4cx7cWuUUoL89hQUZTy+IGmCobHpzg7mNu9A9v7x0iYzPYITOWShrLp4DFZZCpOe3+Y3etSrzh8xbYa3v0Kd/bfW1dWSI29N6F2XFcqMxpYKfVL5GuPn+Fddz7F5x5oc3so046eH2VvisJ1xwF7+X8u2i7EE4Zzw+M81jbAPYc7AWuV3FLsbSijY2ic0fGZKxtbe8MkDOx0oYZqISLCvg3lFOV7F70iUqlfVjoVqNQviXuPnOfP7juKyIVtStw2FU9wvCfEbS/bNOc522pLCPi8PNsxwq8e2JDV5zfG0NoX5pHWAX7R2s+Tp4cYj17YgWtdWSGbq5fWnDO5gP3lW6un7z/eY2Wx3ChOT8cf3bCDt17RSF4Oe2gptRZoYKXUL4EHT/Ty4Xue48rNlVy6oZx//8VpxqMx/D53/xfQ1hcmGkuwZ54Cba9H2NdYviwd2L/40Cn+/sctADRXB/j1yzawe30pGyv9NFX5WVdWhNeztLqu5AL2GYFVd5CifC9NlZlt7pwrO+pL2FG/tGydUr+MNLBSao070jnCB77+DLvWlfKld1zOodND3PFwOy+eD3LF5kpXx3ah4/r8fZIONJXzbz9vZyIap8jnzdrz//xkPzvrS/j32w7SUJ66xmupKgI+GspnF7Cf6A6xo75kyYGbUmpl0RyvUmvcF3/WRklhHl9510FKCvOni5GfWwHTgc90DFNS/jnGggAAIABJREFUmMfmBRpwHmisIJYwaXUxT1csnuD5cyO8dEvVsgVVDquA/cLYjTEc7wmya47CdaXU6qWBlVJr2Oj4FA+19HPL/gaqiq1VXtXFBWyoKFoRdVZPtg9xxaZKPAtkbZz967LZKPRET4jIVIIDTRVZu+ZcLtlQxpnB8emteXqDk4yMT63Y+iql1OJpYKXUGvaDF7uJxhO88aJeTPsay10PrPqCEdoHxriquWrBc6uLC2iq9HP4TPYCK6fp6IEctBNwasicrNXxbqtwfWe9BlZKrTUaWCm1ht175DzN1QH2Nsz8AN+/oZzzIxP029293fDE6SEArmxOr87ris2VPHVmiETCZOX5n+0Yns7eLbfplYFOYGWvCNTicKXWHg2slFqjukcnePL0ELfsb5jVI8qZWnOzzuqJ9kFKCvLS3mT4quYqhsenONkXysrzH+kY4UBTeU66uVcVF7C+rHC6Uejx7hAN5UWUFeW+q7pSanlpYKXUGnXfkS6MgVv2r591bO/6Mrwe4blz7gVWT7YPcvmmirT7JF1pr2B8sn1oyc89PBalfWBsuvloLuxNKmA/0a2F60qtVRpYKbVG3Xuki32N5WxK0eCyyOdlR12Ja3VWfaEIp/rTq69yNFb6aSgv4on2wSU//5FzTn3V8heuOy5pKKN9YIzB8CTtA2NauK7UGqWBlVJrUGtviGPdQd6YIlvl2NdYznOdI1mrWcrEoen6qvQDK+v8Sg6dHsKYpY352Y4RPAKXbpi/f1Y2Ob26/vdIF/GE0cJ1pdYoDayUWoPuPdKFR+B1l84dWO1vLCMYiXF6cCyHI7M82T5EwOdl7zwd11O5anMVg2NR2vrCS3r+ZzuG2VFfSqAgdz2SncDqW/YehDoVqNTapIGVUlmQSBjGozG3hwFYY7n3ufO8fGs1NSUFc563354Gc6OA/Yn2QS7fVJnxPnTO1GEm04HxhGEydmH/v0TCcKRzJKf1VQA1JQXUlxZyoidEYb6HjQs0RVVKrU4aWCmVBX/xvWNc83cPEYsn3B4K33+hm86hCd58eeO8522tLSbg8+Y8sBoIT9LaF067zUKyxsoi1pUVTrdqSMfvfeMZrvvHn0+3lmgfCBOKxHLSv+piTtZqR32pbmWj1BqlgZVSS/RMxzB3PX6GgfAkJ3qy0wpgsabiCf7xJy3srC/h5kvWzXuu1yNcsqEs5wXsTn1VJoXrDhHhquYqnmwfTKvO6uGT/fzghR7ODU/wvq8dZjIW5xl7M+dcdFy/mNNPbJf2r1JqzdLASqkliMUT/Ml3XpzuR/RMFrdcudjwWJRnO4YZDE/OGVR886lOzgyO85HX7lhwmxiwCtiPdQeJTMUXPDdbnmwfxO/zTjfNzNSVmysZCEc51T9/bVgsnuAvv3eMjVV+PvOW/TzTMcLH/+dFnu0YprQwj+YUqyWXm/OadUWgUmuXBlZKLcGdj57heHeQv/nVS6grLeCZs8sXWH3k28/zq198jJf81U/Z+8kfc/PnHuHBE73TxyeicT77QCsHN1XwKztq07rmFZsqmYqbrG4VE5mK876vHebxU6nroJ5oH+IlGyvIz7C+ynFlmnVW/3Wog9a+MB+/aRdvPNDA71+3jW8/c45vP3Oe/U0VaQWe2XZVcxW/dqCB1+ypy/lzK6VyQwMrpRbp/MgE//zTk7xqZy2v3VvPSzZW8PQyZqye6xzhZVuq+OTrd/Pmg41EYwluv+sw//KzNowx3PnYafpDk3zktTvT7ib+0i1V+LweHmrpy9o4j3YF+fHRXt5911Oz6re+9HA7Lb0hXrGtetHX31Tlp660gCfnqbMaGY/yT/ef5KXNVbxmtxXE/P5127jpknqisYQr9VUAgYI8/ukt+1lXtvzb6Cil3JG7tcZKrTF/ft9REsbwqTfsQUS4rKmCH7zQQ18oQm1JYVafayA8SV9okvde08y7Xr4ZsDJUH/2f5/n7H7fw/LkRHj81yHU7azm4Kf2icL8vjyubK3noZD+fyNJYT9mtEArzvdx25yHued9L2VpbzD/df5LPP9jGzZeu47aXbV709UWEKzdX8YRdZ5UqiPzsA60EJ6b4s9fvnj7u8Qj/8KZ9NJQX8euXbVj08yul1Hw0Y6XUIvzkaA/3H+vlD169ncZKPwCXbbSKoZ85m/1i8OPd1h5zyfvqFfm8fOYt+/mTm3Zx/7FeQpMx/u8NOzK+9iu319DWF+bc8HhWxnqqP4zP6+Fb738peV4Pv/nvh/jot1/g8w+2cevBRj536wF8eUv7X89VzVX0hawO5hc7NzzO1x4/y1sONs2qZfL78viTm3fTVOVf0vMrpdRcNLBSKkNjkzH+/L6j7Kgr4farL2Re9qwvxef1LEsB+7EuK7C6OFAQEd5zTTPfeM9VfOYt+xdVFH2tXY/1UEv/0gcKtPWF2VwdoLmmmK/+1hWMR2N883Ant1+9mb/5tUv+//buPLrq6tz/+HtnHiFzCElISAgJc5hSBCwIjkUFq61Yp9virbbW2/b6s3rtvcvW1rar061DnW61tepVabWFixOTgIAgU5gCgYQ5cwIZSMh49u+PJBhMYk5OTgbI57UWK+d8h7P3+bJWeNj72c92S5mB2aOapxI3HGrf59VZRTQ6LPd+OanH7YiIdJemAkW66Q+rD5FfUcvb35h8QQK2r5cnE+KGsqMXEtgPFFQSM9SP0ECfDs93d2uYtpIjA4kL9WdddjF3zEhw+XNa5ZacZdzwz1a/vXXvZWQXVrEwfbjTuV9dGREeQFJEIOuyS85PjbZad6iEpIjADvdIFBHpbRqxEumGrPxKXt50jNsy4pma0D6XaWpCKHvzKi6o9O2WdgsqL5gGdCdjDFekRrE5t6zH/a5taOLE6RqSIz8LasbEDGHR5Fi3BVWt5qRGsuVIGefqP+tzbUMTn+SWMSc10q1tiYg4S4GViJMcDsuP/7mXEH9vHr42rcNrpowIob7Rwf6WqTt3qG1oIrekmrHd3FevO+amRlJT38S2oz0bbTteVoPDQnJUkJt61rm5qVHUNTouKLvwyZEy6hod56c3RUT6mgIrESct3X6SXSfK+fGCMYQEdDwlN2VEawK7+6YDDxedpclhe7WopLvKLrRujpwc2fuB1ZdGhuHnfWGf12eX4OftwZdGdn+7HBERd1BgJeKkFXsKGB0dxE2TYzu9JmqIH3Gh/m5NYO9oRaC7tS270BO5JX0XWPl5ezIzOeKCPq/LLuaypHD8vD17vX0RkY4osBJxgsNh2X2qnOmJYV3mCk1NCGXH8TNO7WXnjKyCSgJ9PBkR1rslAuamRpFTfJaTp10vu5BTfJbYEH/8ffomsJmbGsnxshqOllZztLSaY2U1mgYUkX6lwErECUdKq6mqbWSSExW7pyaEUlRZR175Obe0nZVfSVrMkF7fgmVuS8J3T0atckvOMqoP8qtazR3dHER9dLD4/JTgXCWui0g/UmAl4oTWrVmc2QrlfJ7ViZ4XCrXWcqAXVwS2lRTRXHbhYxcDK4fDkltytk+mAVudL7twqIR12c1lFhLCVWZBRPqPAisRJ+w+VU6QrxdJTgQNacOCCfbzYu2Boi6v7cqpM+eoqmvs1cT1VsYYZiSFs93Facz8inPUNjj6dMQKmqcwtxwpY8sRlVkQkf7XZWBljIk3xnxkjDlgjNlvjPl+y/EwY8wqY8zhlp+hbe75D2NMjjEm2xhzTW9+AZG+kHmynAmxQ52qGu7l6cHNU+J4b28hZWfretRuVmviei+WWmgrIzGM09X155PQu+OzFYF9O2I0NzWS+kaHyiyIyIDgzIhVI/CgtXYMMAO43xgzFngEWGOtTQHWtLyn5dxiYBxwLfCsMUZLdOSiVdvQxIGCStJHdD0N2OqOGSOob3KwdPupHrWdlV+Jh4HU6OAefY6zpreUKdh69HSH5621bDlSxgNv7GLy4ysvWP2YW9K8b19fj1hljAzD39tTZRZEZEDoMrCy1hZYa3e2vK4CDgCxwELglZbLXgEWtbxeCLxpra2z1h4FcoAMd3dcpK9kFVTS0GSZFOd8YDUqKpjLksJ5fetxmhyurw7MKqhkZERgn62ySwwPIDLYl20dBFars4q48vfrWfziFtZnF9PYZHl6zeHz53NLzhIS4E1YJ9vu9BY/b09umRrHLVPjVGZBRPpdt/YKNMYkApOBrUC0tbYAmoMvY0zrGHwssKXNbadajol0aVNOKf/YlXf+vZeH4Ttzk/s1Ibk1cT3dicT1tu6YkcD9/7uT9YeKmZcW7VLbBwoqmTwitOsL3cQYQ0ZiGNuOXViHq6HJwcNv72Govze/uWUi108czp8+PsLvVh3iYGElacOGkFN8llGRQW7fusYZP1s0vs/bFBHpiNPJ68aYIOBt4AfW2i/ar6Oj36rt/stujPm2MWa7MWZ7SUnPihLKpeNnK7J4d08Bn+SW8UluGW/vPMUv3zvYr33KPFnOsCF+DBvq1637rh4XTWSwL69+ctzpe4qratmfX8H+/Ap2HD/NqTPnGBPTN9OArTJGhpFXfo5TZz6rZ7Uxp5Sy6noeuS6Nr02Lx9/HkzsvSyDAx5MX1h8B4EgfrwgUERmInBqxMsZ40xxUvW6tfaflcJExJqZltCoGaN1X4hQQ3+b2OCD/859prX0ReBFg2rRp7qmkKBe1g4WVHCys4qc3juPumYkA/H7VIZ5ac5gDBZV9sjKuI7tPljMpfmi37/P29OC2jBE8vfYwJ0/XEN9BgU9rLR8fLmVddgkbc0o4VNQ+aXxibPdGynpqemJzntK2Y6eJC23u8/LMfIb4eV2w6i4kwIfbMkbwl83HWDJ7JKVn6/s8v0pEZKBxZlWgAV4CDlhrf9/m1HLg7pbXdwPL2hxfbIzxNcaMBFKAT93XZblULcvMx9PDsGBizPljS2aNJNjXi6fXHv6CO12XX36Oh/62m8KK2g7Pl9fUc6yshvR416bjbsuIx8MYXt96osPzy3fnc9fLn/La1uNEBfvxyHVpPH/HVF64s/nPq0symDUq3KW2XZXaUi7i05Y8q5r6Rj7cX8iCiTH4el2Yw7Rk9kgM8ON/7gMgOUo1pERkcHNmxGoWcCew1xiT2XLsUeBXwFJjzBLgBPA1AGvtfmPMUiCL5hWF91trm9zec7mkOByW5Zn5XJ4SQUSQ7/njQwO8+ZdZiTy9NofswipSh7l3Wuzn72bx3t5CKs418OJd09qdz2zJr3JlxAogZqg/V42J5q1tJ/jhVSntApN3duYRF+rP6n+fM2ASrz09DNMTw84HVquyiqipb2JhevtUyeEh/ixMj+Xtnc2rH0dF9u20pYjIQOPMqsCN1lpjrZ1orU1v+fOetbbMWjvfWpvS8vN0m3uesNYmW2tTrbXv9+5XkEvB9uNnyCs/x8L04e3OLZk9kiBfL55y86jVliNlvLe3kNToYFZmFbEqq31Bz90nKzAGJsS6FlgB3D5jBGdqGli5/8LPP1Ndz6acUhZMjBkwQVWr6Ylh5JZUU3q2juWZ+cQM9SMjseNSBvfNSQLAx8uD2FD/vuymiMiAo8rrMiAsy8zD39uTq8cOa3cuJMCHu2cm8N7eAg4XVbmlvSaH5Wcrshg+1I+/f+cyUqODeWzZPqrrGi+4LvPkGVKiggj283a5rVnJEcSG+PPmtgunAz/cX0ijw3LDxPbBZH/LaKkHtSqriPWHSrhx0vBO9ypMiQ5mwcQY0uNDnCqgKiJyKVNgJf2uvtHBu3sLuGpsNIG+Hc9O3zM7iQBvT55am+OWNv++4yT78yt5+Lo0gv28+cVXx5NfUcuTbeoyWWvZfaqiW/WrOuLhYbh1ejybcso4UfbZSrt39xaQEB7AuD6qqt4dE2KH4uftwe9WZtPosNzYwUhiW3+4NZ3Xlnypj3onIjJwKbCSfrfhUAnlNQ0dTgO2Cg304fYZCby7J5/SHm4TU1XbwG8+PMSUESHcOKm5zakJYdyWEc9LG4/ywb4CXlify50vfcrp6nomdbN+VUdumRqHh4Gl208CUHa2js25ZVw/MaZf6j51xcfLg8nxoZSerSclKqjLTaC9PT3w8dKvExER/SaUfrdsdz6hAd58efQXb6B70+RYHBY+2FfYo/ae+SiH0rN1PHbDuAuCmoevTSPE35v7XtvJL98/SHFVLffMHskNk3o+VTc8xJ85oyP5246TNDY5+GB/IU0Oy4IJA28asFXr9jaLJscOyOBPRGQg6lbldRFn/d/ufMICfZg1KuILryupqmNVViG3TI3D2/OL4/y0YcEkRwby7p4C7piR4FK/VmcV8eKGI3x9Wly7kaiQAB/+8s0MckqqmJkcQfSQ7hUE7crijBHc++oO1h8qYcXuApIiA/u8+Gd3XDd+GO/vLeCrU7RxgoiIszRiJW7X2OTg0Xf28oO3Mqlt6LzSxr68ChY+sxFr4baMEV1+rjGGBROHs/VoGcVVHded+iLZhVV8/81djB8+lJ/e2PEWKBPihnLT5Di3B1UA89KiiAjy5dl1uWw9Wsb1EwbmNGCrMTFDWPXvc4gZqpV+IiLOUmAlbrcnr4KqukZKqup449OOC2Muy8zj5uc2A/D2d2Yybrhz5QxumBiDw8L7e7s3HXi6up57/rqNAF8vXrxrap9tatyWt6cHt0yNY8fxMzgsXO+GKUYRERlYFFiJ2206XArAuOFDeH59brtRqz+sPsT338xkUnwIyx+Yzfhu1IhKiQ4mNTqYd/cUOH1PfaOD776+g6LKOl68c2q/jsDcOr15t6eUqCBGRw/caUAREXGNcqwGgbKzdTzwxq4LajTNTongoWvSeqW9jTmljBs+hB9/ZQzf+NNWlm4/yV2XJQLw9x2n+MPqw9w8JY5f3Tyhy7yqjiyYGMN/rz5EYUVtlxsjZxdW8eDfMtmXV8l/3zqJySNc25rGXUZGBPLAvFFdrrITEZGLk0asBoF/7Mpjc24ZQwN8CA30wRjDHz/K7bDSeE/V1Dey88QZZo+K4LLkcKYnhvLculzqGpvYcfwMj76zl5nJ4S4HVdAcWFkL7+3tfNSqscnBHz/K4fqnP6agvJbn75jKTZPjXP1abvXg1alcNyGm6wtFROSioxGrQeCfmXlMihvKX7+VAUBDk4Prn9rIY8v2MTM5vNOinK749OhpGposs0ZFYIzh+/NHc8dLW3lqzWHe2naKmBA/nr19istBFUByZBBjYoawYk8+35o9st15ay3femU7Gw6VsGBiDI/fOI7wNvsPioiI9BaNWF3icorPsi+vkhvbbKDr7enBEze1rzTuDptySvHx9GB6y75ys0aFMzUhlD9+1Jxr9ae7phES4NPjdq6fGMPOE+XklZ9rd25/fiUbDpXw4FWj+eM3piioEhGRPqPA6hK3LDMPD9O8mq6taYlhLJ7eXGn8QEGl29rbmFPG1ITQ86vujDE8dE0qYYE+PH3bZFLclLB9fcv3WZ6Z3+7c2ztP4ePpwZ2XuVbrSkRExFUKrC5h1lqWZeYzMzmCqA7qMj1yXXOl8Uf/sReHw/a4vdKzdRwoqGR2yoVFQWckhbP9x1dyRVpUj9tolRAeyGVJ4byy+Rj1jY7zxxuaHCzPzOfKsVFuGRkTERHpDgVWl7BdJ8s5cbqm0z34QgJ8+PGCMew6Uc67X5AI7qzNuWUAHVZb9/BwfyHMe+ckUVhZyz8z884fW5ddQll1PTdPGRiJ6iIiMrgosLqELduVh4+XB9eOH9bpNYvSY4kM9uWD/T3bfw+a61cF+3kxoRt1qXpizuhIxsQM4YX1uedH3P6+4yQRQb5d7jsoIiLSGxRYXaIamxys2FPAlWOiCPbz7vQ6Dw/DvNQoNmSX0NDk6PS6rlhr2ZhTyszkcDx7YXSqI8YY7puTRG5JNasPFHGmup61B4tZlD68R6sORUREXKV/fS5RG3NKKauuZ2F61xvozhsTRVVdI9uOnXa5veNlNeSVn2N2F5suu9uCCTHEhfrz/Ppclu/Op6HJcvNUTQOKiEj/UB2rHig9W8eeU+Xn3w/x82ZqQuiA2Fh3eWY+Q/y8mJva9ZTY7FER+Hh6sPZAMTOTux8YtVY3NwYuT+nbKTgvTw/+9fIkHlu+nxOnaxgbM4QxqmouIiL9RIGVi87VN7HwmU3t6ij95Iax/Mus9kUr+1JDk4NVB4q4ZtwwfL263mw40NeLGcnhrDlYzH9eP9bpdhqbHLyw4QhPrj5MsJ8Xz90+lcSIwJ503SVfnxbPk2sOU3q2nu/OHdXn7YuIiLTSVKCLXtxwhLzyczy5OJ1l989i2f2zuDwlgt+ubN7Drj9tPXKaqtpGrh4b7fQ9V46J4mhpNUdKzjp1fU5xFTc/t5nffJjNVWOjWfnDL39hknxv8vfx5J7LRxLg48mNnayAFBER6QsKrFxQUHGO59fnsmBCDAvTY5kUH8Kk+BB+vmg8DU0OHl+xv1/7tyqrED9vj25Ny12R2lxjau3B4i+8rslheWF9Ll95aiMnTtfwzDcm88fb+7+6+XfmJLP5kXlEqMq6iIj0IwVWLvjNB9k0Wcsj16VdcDwhPJAH5o3ivb2FfNRFgOKKj7KLmf+7dWzKKe30Gmstq7KKuDwl8nz1c2fEhwWQGh3MmgOd97uospavPb+ZX75/kCtSI1n5wzlcP3FgjBAZY1QQVERE+p0Cq27adeIM7+zK457ZI4kPC2h3/ttfTmZUVBD/tWwf5+qb3Nauw2H55XsHyC2p5q6XP+WljUextn219P35leRX1HJVN6YBW80bE8W2Y6epONfQ4fnn1uWyL7+SJxen8/wdU4kM1uiQiIhIWwqsusFay+MrsogM9uW7V3ScJO3j5cHPF43n1JlzPL3WfRscv7+vkENFZ/nFTROYnxbFz1Zk8eDfdlPbcGHwtjKrCA8D813YPmZ+WhSNDsvHh0s6PL8uu5hZyeEsTI8dECsfRUREBhoFVt2wYk8Bu06U89A1qQT5dr6gckZSOIvSh/PnTccor6nvcbsOh+WpNYdJjgzk1unxPH/HVH5wZQrv7MzjO6/tuGCfv5X7C5mWEOZSztPkEaGEBHh3OB14rLSaY2U1bt3vT0RE5FIz6AMra5uDlpc3HqWipuMpMGguYfC7ldmkDQt2ah+6e+ckc66hiTe3nexxHz/cX0h2URUPzEvB08Pg4WH4wZWj+emN4/gou4T/+fgIACdP13CwsMqlaUAATw/DFalRrD1YTF3jhSNh67Kbg625oxVYiYiIdGbQB1brDpXw+1WHeHxFFhm/WM2DS3ez+2R5u+uWbj/JsbIafnRtqlNbtoyJGcLM5HBe2XysR1vFOByWJ9ccJikikBsmXZgoftdlCXxlwjB+/WE2O46fYVVWEYDLgRXAosmxVJxrOP9ZrT7KLiEpIpAR4e3zykRERKTZoA6sHA7Lrz/IZkRYAMvun8UtU+P4YF8Bi57dxLLMvPPXnatv4snVh5meGHq+LIEzvjVrJAUVtXzYgw2OV2YVcbCwiu/NG9UuoDPG8KubJzI8xI9/e2MXyzLzGB0d1KMinbNHRRAb4s9bbUbaahua2HKkjDlOVHEXEREZzAZ1YPV/e/I5UFDJg1ePZlJ8CE/cNIEtj85nemIYDy7dfb5kwl82H6O4qo4fXZvWraTteWlRJIQH8PLGoy71r7HJwZNrDpMYHsCNkzouazDEz5tnbptCcVUtu09V9Gi0CpqnA782LY6PD5dy8nQNAJ8cKaOu0cHcbgSVIiIig9GgDazqGx38buUh0oYFc0ObWkzBft786e5ppMUEc99rO1idVcRz63KYnxbF9MSwbrXh4WH45sxEdp4oZ9eJM93u4wsbjnCgoJKHrknDy7Pzv6pJ8SH8x3VjMAauGx/T7XY+7+vT4jGmefoTYH12CX7eHnxpZPe+v4iIyGAzaAOrt7af5MTpGh6+Ng2Pz02xDfHz5pVvZhAb6s89f91OVV0j/++aVJfauWVaPMG+Xvx507Fu3XewsJI/rD7EggkxLJjYdbD0rdkj+fTRKxkfO9SlfrY1PMSfOaMj+dv2UzQ2OViXXcxlSeH4eTtfcFRERGQwGpSBVU19I0+tOUxGYhhzO8kbCg/y5dUlXyIhPIDbMkYwJmaIS20F+Xpx6/R43ttbQEHFua5voHkF4oNLdzPU35ufLRrvdFvuLNi5eHo8hZW1vPLJcZVZEBERcdKgC6zqGpv4z3/so6Sqjh9dm/qFOVOxIf6sfXAuT3QjuOnI3TMTscCfPm6fa1VR08C8367jzpe28sG+AhqaHDyzNof9+ZX84qYJhAX2zzYt89KiiQjy4dcfHARUZkFERMQZnVe5vAQVV9Zy32s72HminO/PT2GaEzlTzpRW6Ep8WACL0mN5fetx7puTfMHI0nPrczlaVk1NfRP3vbaTyGBfzlTX89XJsVw9bliP23aVj5cHN0+J44UNR1RmQURExEmDZsRq54kzXP/0Rg4WVvHs7VP44VWj+7T9780bRX2jgxc35J4/VlhRy583HWVReiybHpnHS3dPY0LsUFKHBfPYDeP6tH8d+fr0eACtBhQREXHSoBixOlZazeIXthA91Je/LplJ2jDX8qV6YmREIIvSY3l1y3HunZNMRJAvT609jMNafnjlaDw9DPPHRDN/TM/KJbhTcmQQry7JYPzwnifEi4iIDAaDYsQqMSKQ/7phLMvvn90vQVWr1lGr//n4CEdLq3lr20m+kTFiQE+zXZ4SSWg/5XmJiIhcbAbFiBXAnTMS+rsLJEUGceOk4bz6yXEOFlTh6+XB9+al9He3RERExE26HLEyxrxsjCk2xuxrcyzMGLPKGHO45Wdom3P/YYzJMcZkG2Ou6a2OX6y+Ny+Fcw1NrD9UwpLZI91aIkFERET6lzNTgX8Brv3csUeANdbaFGBNy3uMMWOBxcC4lnueNcaoqmQbo6KCuCk9lvBAH/71y0n93R0RERFxoy6nAq21G4wxiZ87vBDOwIqcAAADv0lEQVSY2/L6FWAd8HDL8TettXXAUWNMDpABfOKe7l4afnnzBGrqmhji593fXRERERE3cjV5PdpaWwDQ8rN1PX4scLLNdadajrVjjPm2MWa7MWZ7SUmJi924OPl6eSohXERE5BLk7lWBHVXTtB1daK190Vo7zVo7LTKy421lRERERC4mrgZWRcaYGICWn8Utx08B8W2uiwPyXe+eiIiIyMXD1cBqOXB3y+u7gWVtji82xvgaY0YCKcCnPeuiiIiIyMWhy+R1Y8wbNCeqRxhjTgGPAb8ClhpjlgAngK8BWGv3G2OWAllAI3C/tbapl/ouIiIiMqA4syrwtk5Oze/k+ieAJ3rSKREREZGL0aDY0kZERESkLyiwEhEREXETBVYiIiIibqLASkRERMRNFFiJiIiIuImxtsPC6H3bCWNKgON90FQEUNoH7VyM9Gw6p2fTOT2bjum5dE7PpnN6Np0baM8mwVrb4bYxAyKw6ivGmO3W2mn93Y+BSM+mc3o2ndOz6ZieS+f0bDqnZ9O5i+nZaCpQRERExE0UWImIiIi4yWALrF7s7w4MYHo2ndOz6ZyeTcf0XDqnZ9M5PZvOXTTPZlDlWImIiIj0psE2YiUiIiLSaxRYiYiIiLiJAisRERERN1FgJSIiIuImCqxERERE3ESBlYgMeMYYa4x5tc17L2NMiTFmhYufF2KM+W6b93Nd/SwRkbYUWInIxaAaGG+M8W95fxWQ14PPCwG+2+VVIiLdpMBKRC4W7wMLWl7fBrzResIYE2aM+acxZo8xZosxZmLL8Z8YY142xqwzxhwxxvxbyy2/ApKNMZnGmN+0HAsyxvzdGHPQGPO6Mcb01RcTkUuHAisRuVi8CSw2xvgBE4Gtbc79FNhlrZ0IPAr8tc25NOAaIAN4zBjjDTwC5Fpr0621D7VcNxn4ATAWSAJm9eaXEZFLkwIrEbkoWGv3AIk0j1a997nTs4FXW65bC4QbY4a2nHvXWltnrS0FioHoTpr41Fp7ylrrADJb2hIR6Rav/u6AiEg3LAd+C8wFwtsc72jarnW/rro2x5ro/Pees9eJiHRKI1YicjF5GXjcWrv3c8c3ALdD8wo/oNRaW/kFn1MFBPdKD0VkUNP/yETkomGtPQU82cGpnwB/NsbsAWqAu7v4nDJjzCZjzD6ak+LfdXdfRWRwMtbarq8SERERkS5pKlBERETETRRYiYiIiLiJAisRERERN1FgJSIiIuImCqxERERE3ESBlYiIiIibKLASERERcRMFViIiIiJu8v8BGi84u1+U+aEAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 720x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from numpy import log\n",
"\n",
"passengers_log = log(passengers.Passengers)\n",
"passengers_log.hist(figsize=(7,7))\n",
"pyplot.show()\n",
"\n",
"passengers_log.plot(figsize=(10,5), title=\"Passageiros COM Transformação log\")\n",
"pyplot.show()\n",
"\n",
"passengers.Passengers.plot(figsize=(10,5), title=\"Passageiros SEM Transformação log\")\n",
"pyplot.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Observe como o histograma fica mais parecido com uma distribuição normal e os dados, apesar de ainda possuirem tendência e sazonalidade, o range de variação exibe um crescimento linear.\n",
"Após essa transformação logaritímica, se realizarmos a divisão do dataset em amostras, calcular-mos sua média e variância, provavlemente veremos valroes bem próximos entre as amostragens. Mas isso garante que nossa série se tornou estacionária? Bem, sinto lhe dizer que não. Este é apenas um método \"rápido\" que pode nos levar a cometer vários enganos.\n",
"\n",
"\" - Mas depois de toda essa demonstração você diz que isso não funciona?\".\n",
"\n",
"Nao se desespere. :-)\n",
"\n",
"O que fizemos até aqui é muito útil para uma primeira \"impressão\" sobre nosso dataset. Mas existem algumas formas mais robustas de verificar se uma série temporal é estacionária. \n",
"Eu diria que um dos métodos mais utilizados é o teste de Dickey-Fuller Aumentado, e é sobre ele que vou falar a partir de agora."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Dickey-Fuller Aumentado\n",
"\n",
"Aqui eu deveria trazer alguns conceitos de base para você. Como esse artigo pretende ser curto, vou deixar apenas os tópicos que valem a pena você pesquisar para enteder melhor o Dickey-Fuller:\n",
"\n",
" - Hipótese nula\n",
" - Hipótese de raiz unitária\n",
" - Student t-test\n",
" - p-vlaue\n",
" - Modelos autoregressivos\n",
" \n",
" \n",
"Bem, para não ficar massante e longo, vou trazer apenas as considerações gerais sobre o teste de Dickey-Fuller. \n",
"Este é um teste do tipo Hipótese de Raiz Unitária no qual ele vai determinar o quão forte (confiança) de que há ou não uma tendencia dentro da série temporal. \n",
"\n",
"Bem, é mais facil mostrar do que falar. Vejamos:\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**1) ADF test para nascimentos**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Para utilizar o Dickey-Fuller, iremos precisar do pacote python chamado sklearn"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ADF Statistic: -4.808291\n",
"p-value: 0.000052\n",
"Critical Values:\n",
"\t1%: -3.449\n",
"\t5%: -2.870\n",
"\t10%: -2.571\n"
]
}
],
"source": [
"from statsmodels.tsa.stattools import adfuller\n",
"\n",
"result = adfuller(births.Births)\n",
"print('ADF Statistic: %f' % result[0])\n",
"print('p-value: %f' % result[1])\n",
"print('Critical Values:')\n",
"\n",
"for key, value in result[4].items():\n",
" print('\\t%s: %.3f' % (key, value))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Basicamente vamos ter uma tabela que apresentará o que chamamos de valor critico, que é o nível de confiança que o modelo propõem. Em nosso exemplo são exibidos níveis de 1%, 5% e 10%. Se o resultado do ADF for menor do que o valor critico para um determinado percentual de confiança e o o p-value for significante (menor que 0.05), a série é considerada estacionária. Do contrário a série é não estacionária. \n",
"\n",
"Para o dataset de nascimento, o valor do ADF é -4,8 que é menor do que os valores tabelados (Critical values) e o p-value é menor que 5% também. Logo temos um alto grau de confiança em que a série é estacionária.\n",
"\n",
"Vamos fazer o mesmo exercício para o dataset de passageiros"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ADF Statistic: 0.815369\n",
"p-value: 0.991880\n",
"Critical Values:\n",
"\t1%: -3.482\n",
"\t5%: -2.884\n",
"\t10%: -2.579\n"
]
}
],
"source": [
"result = adfuller(passengers.Passengers)\n",
"print('ADF Statistic: %f' % result[0])\n",
"print('p-value: %f' % result[1])\n",
"print('Critical Values:')\n",
"\n",
"for key, value in result[4].items():\n",
" print('\\t%s: %.3f' % (key, value))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Aqui a coisa já ficou feia ;P\n",
"\n",
"temos um ADF positivo!! Sem falar no p-value, que apresentou um valor de 99% \n",
"\n",
"Logo, certamente essa série não é estacionária.\n",
"\n",
"Será que se aplicarmos a transoformação logaritmica nela seria o suficiente pra torna-la estacionária? Vamos ver:"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ADF Statistic: -1.717017\n",
"p-value: 0.422367\n",
"Critical Values:\n",
"\t1%: -3.482\n",
"\t5%: -2.884\n",
"\t10%: -2.579\n"
]
}
],
"source": [
"result = adfuller(log(passengers.Passengers))\n",
"print('ADF Statistic: %f' % result[0])\n",
"print('p-value: %f' % result[1])\n",
"print('Critical Values:')\n",
"\n",
"for key, value in result[4].items():\n",
" print('\\t%s: %.3f' % (key, value))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Apesar do valor do ADF ter melhorado, ele ainda não está abaixo dos valores criticos e o p-value também não ficou dentro da nossa margem de 5%. Logo, mesmo com a transformação, a série ainda é não estacionária"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Bem, esse foi um resumo relâmpago. Apesar do eufemismo, quero realmente frizar que a idéia não foi explicar a teoria por traz do Dickey-Fuller, mas apenas demonstrar que as séries temporais podem apresentar várias pegadinhas e também mostrar um dos mecanismos em python que possibilta a detecção da estacionaridade de uma série temporal. \n",
"\n",
"Vejo muito o pessoal de certas metodologias agéis fazendo estimativas de entrega com base no fluxo de consumo do time, sem levar em conta a estacionaridade do fluxo. Não é a toa que muitas das previsões acabam sendo equivocadas. Aquela do tipo: garanto a entrega em X dias com Y porcento de certeza. Estatisticamente falando, nunca vi coisa mais furada que essa. Talvez se levassem em conta a sazonalidade e a tendência, isso seria melhorado. Também é por esse motivo que geralmente não se estima preço futuro em ações, mas sim o nível de oscilação. Enfim, esse assunto dá pano pra manga.\n",
"\n",
"Se você leu até aqui, não esquece de dar aquele \"like\" \\o\n",
"\n",
"Num próximo artigo eu mostrarei como remover a tendência e a sazonalidade de uma série não estacionária.\n",
"\n",
"Abraços!"
]
},
{
"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",
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"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
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"pygments_lexer": "ipython3",
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