{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "___\n", "\n", " \n", "___\n", "
*Copyright Pierian Data 2017*
\n", "
*For more information, visit us at www.pieriandata.com*
" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true }, "outputs": [], "source": [ "airline = pd.read_csv('airline_passengers.csv',index_col=\"Month\")" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [], "source": [ "airline.dropna(inplace=True)\n", "airline.index = pd.to_datetime(airline.index)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "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", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Thousands of Passengers
Month
1949-01-01112.0
1949-02-01118.0
1949-03-01132.0
1949-04-01129.0
1949-05-01121.0
\n", "
" ], "text/plain": [ " Thousands of Passengers\n", "Month \n", "1949-01-01 112.0\n", "1949-02-01 118.0\n", "1949-03-01 132.0\n", "1949-04-01 129.0\n", "1949-05-01 121.0" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "airline.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# SMA\n", "## Simple Moving Average\n", "\n", "We've already shown how to create a simple moving average, for a quick review:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": true }, "outputs": [], "source": [ "airline['6-month-SMA']=airline['Thousands of Passengers'].rolling(window=6).mean()\n", "airline['12-month-SMA']=airline['Thousands of Passengers'].rolling(window=12).mean()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Thousands of Passengers6-month-SMA12-month-SMA
Month
1949-01-01112.0NaNNaN
1949-02-01118.0NaNNaN
1949-03-01132.0NaNNaN
1949-04-01129.0NaNNaN
1949-05-01121.0NaNNaN
\n", "
" ], "text/plain": [ " Thousands of Passengers 6-month-SMA 12-month-SMA\n", "Month \n", "1949-01-01 112.0 NaN NaN\n", "1949-02-01 118.0 NaN NaN\n", "1949-03-01 132.0 NaN NaN\n", "1949-04-01 129.0 NaN NaN\n", "1949-05-01 121.0 NaN NaN" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "airline.head()" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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c2Q8xyaoUsQsJYTW59JcDZpuZTSc3sfToUhqLNPQSieSCxyHs5fTo7amO1Rar\nU2HSWxRWmAirYwPw0IwfuFX7M/vjbiR5/NPw86vwyxvQbayqKNlEcsuq6Z8Urn4QQjX0PW/xaBcX\nYkCrUdiTe5ATv81nxfEVFFYVEm4Ib/RYMnQjkUgueE7b49OxwfbFWC+nOrqSX24iMrBWVk1lEb6r\nnma/SGR5/ONqHH30m+DjC989qhrqJnA0t5xio5nWoaq3TvEJMJWpHn0tzKKakISlLC94gnmH5tEn\npg/vX/U+ayauafR40tBLJJJzIresio1H8lt07wjHQmScM3SjBiNaQgYhp6TSOY6TH5+Hinxe0/2F\nkmr79wyOg6tfhvT1sOebJo0x64dDBOq1TOxrl8B2LMTGdHdrd7jwMLetuA2T32ZCTSP4eeLPvD3s\nbYYlDEOn0TV6PGnoJRJJs/gto5BJH21mwGtrmfL5VtKyiltsrNOlVei1NamIjgwYb3v0JouN3LJq\nWoX61RwsOw27/gcDH+C0Xyd3GYQ+d6qSwmv/DubGyRRsPlbAmoNnePDK9jW/HJwZN2oOfaWlknd2\nvMMt391CYVUhA/yfxnh6FKGG0GZ9L2noJRJJs/h8QzoHT5dySz9VlPBk8bnpsZyNnJIq4kIMzgXS\nIEPLbNZ9uqQKIaC1q6E/s0997TTKU+9Go4FrXoHSk7Dlwwb7t9kEM78/QOtQP6YPctlv48w+CEsC\nfSCbTm5i/NLxfL7vc65vfz1Lxi6hV9QACipMVFQ378EmDb1EImkWGQUVDEgK56mRnYGaja5bgtMl\nlc6MG1DTK8H7Hr3jYeXm0ec6Cpm6EhmoJ7+sljZ80hDoNAo2/gsqCs7a/8+Hc9l3spQnR3bGoHNZ\nRD6zn9LoLjy1/inuX3M/Oo2O2SNn88qgVwgzhDlTLJsrbiYNvUQiaTJCCDIKKmgbEUCovw6dj+LU\nbmkJVI++xvgGebl4ycEpu6FvHeZi6PMOQkAUBEQSF2Koe2u/q/8GpnJY/+ZZ+z9wqhSAkcmxNQfN\nlZQWH+decliduZoHUx9k0ZhF9IutkSGOsefb55c37x5LQy+RSJrMmdJqqsw2EiMDUBSFqEA9uWXN\nr9w8Gzab4ExplbtHb2gZj95h6N0WY3MPOmPnsSEGSqssniGU6C6QPB72LgBb/VIF6fkVxIUY8POt\n8eZLT+3g3phIDptLeGfYOzzQ8wF8fdzTOyMCpaGXSCR/MBkFFQAkRqghhahgg1Oky9sUVJgwW4Wb\n8Q3w1aJqtSEJAAAgAElEQVQo3o/RnyyuJDLQtyasYrOpuz5FqYbeMYfTpXU81DqNBmMB5KTV2396\nQYVbkdTpitNM3/ISh319+VffpxmaMLTO6yLtAmv55aY6zzeENPQSiaTJZOQ7DL1qtKKD9C0Wo6/J\noa8x9BqNKlHQEjF6t/h8SZYakrHrzzjy+E/XpTvT/kpAgaNr6+0/Pb+CpCj1nh0oOMDkFZPJri7k\n/fxShnWZVO91wQYdWo1CgfToJRLJH0VGgRGdj+I0itFBLRe6qamK9XM7Huzlrf1ADd24ZdzUUpR0\nePR1CowFRKqplkfrLmQqNpooNppJDPdnweEF3PHDHWg0Gv5bHcjgsK7OzUbqQqNRCA/wpUB69BKJ\n5I8iI7+ChHB/fDRqumN0kIEioxmTpflSuvXhCJPE1ipiUjXpvefRCyE4VVxVK+PmgPoa1cVtDqfr\nWpAF6HA1ZG+DSk/9+PT8CvCpYG3RLF7Z8gq9onsx78oP6HRyL3Soc2sPNyIC9RRUSI9eIpH8QWQU\nVJDkEmt2bIeX18zQwtnIKalC56N46sMbtF6N0RcbzVSarZ6plUGtwE8tVDLofAjz19UvGdzhahA2\nOP6Lx6mdp47h3/Yjfi/dwdP9nuajaz4i8mQaIBpl6CMDfWWMXiKR/DEIIcgsMNLW1dDb0/9y61qk\nPEdyiiuJCTag0birOgYZvBu6ceTQtw51+eWQd9BDHz42xK/uGD1A6z5gCHGGb4QQnCw/yY8ZP/Lx\nkcfQaMv56OpPmNJtChpFA0dWg38ExPVqcH6RgfpmZ91I9UqJRNIkcsuqqTRbSYr0dx5z7HvaErn0\njqrY2gT7aSnL8V7oxqNYymZVM2763e3WTs2lr8fQ+2ih3ZVwdC1rMlbz+rZZ5FbmAqAnkpCiBxnQ\nqq+9fxscWwvth6sVtg0QIWP0EonkjyLdnnHTtq7QTQsYejWH3s/jeLCX9411Fks5DH1RBliqnPF5\nB7EhhrrTK+2UtL2MpwzVPPbL40T4RfDiZS/y5egviS59nvZhLnLGObvUdMyO1zRqfhGBeirNVowm\n9eFWZbY2+rtJj14ikTQJR2plUmSNoY8I8EVRWsajV2WDPfXhgw1ayqst2GzCI6zTHE4VV6LXagh3\nrAXkHlRfa23WHRdsoLDCRJXZ6i5jAOwv2M/jmQvIDfDnoZghTB/xLjqNDiEEJ/J/pF+bml9Bahqm\nAu2vatT8Iuz3oKDchH+4lr8tP9Do7yY9eolE0iQcqZWu4RStj4aIAD15Xk6xrDJbKa+2eOrDo6ZX\nCgHlJu+Eb04VV9E61K9mZ6ncA4ACUZ3d2jkyb87U8uqXHF3C7d/fjk3x4b/5Fdxn9nVKCeeVV1Ne\nbXF7OHJktZqOGRDZqPnVFE2pD9P0/PJGfzdp6CUSSZNwpFZqfdzNR0sUTRVWqDHp2hk3oGrS6zFh\nOrgKvnsc/u9esDR/fI9iqVNpENEB9EFu7RxtXOP0s/fN5oVNL9A7pjcLblhASkwqZG93ns/IV/d7\nTXQY+op8OLm90WEbgIgA9WHniNM7+mwMMnQjkUiaREatMn4HUUF6r4duHEYtog6PPlIp43vfZ4lc\nmqPu3Wo2QnArdTOQZnCyuJIrO0fVHMjZDW0GerSLdRZNVWKxWXh357vM2T+H0YmjmTl4JjofHcT3\nh/X/gOpy0Ac6w13tIgPVTg4uU9Mwu45p9PycoZuKaowmy1nXCWojPXqJRNJohBCcKDTSNsLf41xL\nVMfm2wuEImrH6E1G+m1+kNZKPkeGfgBPpUPvO2DjO5C5ucnjVFus5JVV12ztV5EPpdkQ19OjrUOK\n4WD+Me5YeQdz9s/h5s438/qQ11UjDxDfTzXkp3YBcDy/wl5JbA937V8MER3r3DqwPiKdwmamJnnz\nIA29RCJpAhUmK0aTlZhgz3TH6GA9+eUmrDbvbSno9OhdQzc2G/zfPQQV7GaG+SEyY64BnQFGvgZh\nbWHxvVBV2qRxjuepHnebCHvoJme3+lqHoffz1RAUvZlvTj1GZmkmb17xJs8PfB4fu4SB1SY46ttJ\nbZy9zd5/eU24qzwPMjZC8jhQGr+IbND5EKjXkl9e7RSVayzS0EskkkaTbw/NRNURSokOMmC1CWdc\n3Rs4RLzcQjcnt8Oh7yi67FlW2fpRVm1PsdQHwviP1Y22d8xp0jibj6kbhvRPilAPOA19D7d2J8tP\nctequyBiKcF0Y/GYxYxKGuXW5sN1R7nmo72YQ9s74/R7skvo3ipEbeAI2ySPb9IcQf1lU1Bucqa4\nNhZp6CWSPwkLt2fxwc9HW3QMh8RBZFBdht5eHevF8E1hhQm9VkOAi367Ixyi9LgZgNJKl6ybNgPV\n+Hja19CEzcp/PVZA2wj/mhz6nN0Q2hb8wpxtfj7xMxOXTeRg4UHa2u4kpPQ+ovyj3PopMZr5eP1x\nhIDswO6Q/Rs5xUZOl1bRq419v9f9iyGyk1MorSlEBPhSUFFNen4FMcGef4P6kIZeIvmTMHdzBm+u\nOsyiHdktNobDo68rrz06yJeHfBYTufIBWHw//Pb5uY9XbiIyUF+T8giqEQ6IJiAyAYCy2kVTqbep\n0gX2B0JDWG2CrekFXNYuwmWMNGiVCoDFZuFfO/7FIz8/QkJwAt/e8C3dg6/mdInnwvNnG49TVmXB\nT+fDTmsHqMjj0CF14+9ebcKg7AxkblK9+SaEbRxEBOopKDeRkV/3gnh9NNrQK4rioyjKLkVRvrN/\nDlcUZbWiKEfsr2EubZ9VFOWooiiHFUUZ2aRvIpFImozNJjiWW4GiwHNL9nLodNNi1I3F4dFH1eHR\ntz86hyd0CwnI2w3HfoYVj8Oehec0XkFFtedC7Kk0iOuJr84Hg07jqWCZPB60BtWrrwebTTjXEvaf\nKqGsysJl7e2GvrJIrYqN60l+ZT73rr6X2ftmM7HTRP47+r/EB8UTG2Igv7zaTa2zqMLE7I3pXJcS\nx+COkfxQ1BqAssO/4KvV0C0uGH59r9lhG6gRNkvPr3DPyW+Apnj0M4CDLp+fAdYKIToCa+2fURSl\nG3ALkAyMAv6jKEr9QssSieScySmtotJsZcbwjgQZdDz4v51UWxpfIt9Y8suqURQI969lfDM2EbJp\nJt9b+zOn72J4bD8kDITvHoWCY80er6DcVFOpCmCuVDXi7YukwQadp0fvFwpdroe9C+vNq7/vfzu4\n57/bEUI44/NOj/70XgB2+Acyafkk9ubtZebgmbx42YvofdQHXKsQRy59jVzxpxuOYzRbefTqjvRL\nDOPn4igsYe24IvN9roqtwvfkVtj8AfSZ5lFt21giAlSp4oIKk/cNvaIo8cB1wGcuh8cCc+3v5wLj\nXI7PF0JUCyHSgaNA/0bPSCKRNJljuWqV5MB2ETw7ugvH8ys4cqbxlZONJa/cRESAr3uxlLEQvp2O\nEpbIKz4PkltuUsW9JnwGGi18e2ezC5kKyqudhUIAnNkPwuoMq4T66+pe/E29DaqK4fAPdfZ74FQp\nPx3KZdnuU/x6rIAO0YFE2zOJxKk05gQHcdf+/+Cv8+er675iTHv3fPeEcDUN80RhTZrjxqP5XNYu\ngo4xQfRLDMeKD7/0fg+N1cTfKl6FJQ9AaBsY8Wqz7gWoi7GOpYfEFvDo3wGeAlx3FYgRQuTY358G\nYuzvWwNZLu2y7cckEkkLcdRu6NtHBdIxWq3kdKgxepO8smpPOYLD30P5aRj/McEhETUSvqEJMOZ9\nNaa+e36TxxJCUFBRS+fGsR+r3aOPD/PnRGEd37PdMFVHfs+COvt1iK+9uuIgv2UUOr35ffn7uC/9\nG/4ZEcaVCVcx/7r5dArr5NGHo44gs8Do7DM9v4IO0WpBVHKrEAw6DR/u8+Ev5keIrjyuhoPGf+RR\nadsUXLOPvOrRK4pyPZArhNhRXxshhACalDyrKMq9iqJsVxRle15eXlMulUgktTiWV06In47IQF/i\nw9SwQnaR9w19fnm1Z3w+a5uqwd66DzG1lR273gAx3WHbJ03KggE1Z7/aYnOP0efsVjNhQtSF2Dbh\n/pwoqEDU7lvjA51Hw/F1YHH3+EsqzZisNsb3ak1BeTVGk5WUNgoP//Qwt664lQPmUp7RtuLtYW8T\n6BtY59xigw34ajVOj77IaKasyuJU9PTVauiVEMb2zCI22HpQdP2nMPYDaHt5k+5BbRwPPUVRv3tj\naYxHPwgYoyhKBjAfuEpRlP8BZxRFiVMHVeKAXHv7k0CCy/Xx9mNuCCE+EUL0FUL0jYqKqn1aIpE0\ngWN55bSPCkBRFEL9dfj7+pBd1LTqycZQp0efvR1a9wWNhrhgg/umHIoCA+6DM/sg89cmjeXMoXcN\n3ZxKg7hUZ8ZKm3B/KkxWCuoK33S4GswVkLXF4zsAXNklmqmXJaIPzOSDI39hy6ktPNzpNlaeyGJy\np4numT610GgUEsL8yLQXLqU7FT1rjG+/RDU/JSZYT1ifCdBrcpO+f1047n2rED8P5cyz0aChF0I8\nK4SIF0Ikoi6y/iSEmAIsA+6wN7sDWGp/vwy4RVEUvaIoSUBHYFujZySRSJrMsbwK2kep3qeiKMSH\n+XndoxdCeHr0VaWqymOCugwXE2Igr7was9UlypsyUfXCt37UpPEc2+aFOzx6S7UqHexSrVo7hOJG\n0hDQ6Dw263bo8YT6Q0TCzxjafEKQbyBfXfcV92oiCBSiUdLBbSMCnOM6DL6rRn+/pHAAeiWEnfWh\n0RQcFcJNCdvAueXRzwKuURTlCHC1/TNCiP3AAuAAsBL4ixDC+8v/EokEUEMReWXVtI+uCTPEh/lz\n0suGvqzaQrXF5h4zP7kDEKq2C+ruS0LU2oBE56fq0BxaAcVZNBaHRx/p8OhzD4LN7FyIhRpDf6Kw\njkpRfZBaQHV0rdvh3LIqfPyPMXP3PXyy52NGJ42qicUf+wnCEiG8XYPzaxPuz4lCI0IIMvIr0CiQ\nEFbj0fdqE0awQcuQTo2TIW4Mof6+aDVKyxp6IcQ6IcT19vcFQojhQoiOQoirhRCFLu1mCiHaCyE6\nCyHqXvaWSCRe4VieuhDbIcrV0Pt5PXRTUyzl4tFn/wYoEK9uj+cQ/PLYaq/fXYBokjSBIxzjjNHX\nWogF9YGmKHCioJ6HWofhatioVM0bKaoq4uvj/8C/7acoio2Pr/mYWUNmqbF4qxkyNjR6I5C2Ef4Y\nTVZVZKzASOswP3y1NSY1UK9l87PDubVfm0Z/54bw0Sj8+7be3HtFww8iV6RMsURykeNIrXT16FuH\n+lFaZaGk0kyIn84r4zhCKW6hm6xt6sYcBlXHxSHh67F5dmgbSBysevXDX2jUeI60SWceffZ2MIRC\nWJKzjUHnQ2ywgcy6PHqADldTvfZltu76lNVaM2sz11JuNmItvIrFt83CT+eiP5/9G5jKm2ToQf01\nUZ90c4De+yZ2VPfYJl8jDb1EcpFzLE+VwE0IqzFa8fYQwsmiSq8Z+rzaHr0QqnHseoOzjcOjr1Mr\nvdMoWPVXKMpUVSYbIL+8miC9tmbRMXOTmrVSK97dKtzGoaLdLDt2gpLqEspMZZhtZiw2C78X/s6O\ntglUZywkUBfIsIRh5GZdzhFzoLuRBzVso2ggcUij7kebcNWwZxYYSc+vYHyvCzeLXBp6ieQi52hu\nOYkRAW5FTI4Uy5PFlXRrFeyVcfJryx8UHFWLkhJq6iFD/XXotRpOl9QRSuk4UjX0R36E/vc0OF5B\nuakmbFOaA4XHKe01mbm73mfB4QVUWioRQmAyqJ7/cxtrrtUqWjSKhoSgBCbqW3P56aMMeGgbvjo/\nbv1kC1FBNs8Bj/2kZg/5hTbqfsSH+aEoqjKla2rlhYg09BLJRc7xvHI6x7oX4dTk0nsvTp9XVo1G\ngTCH/EGWPZkuvsbQK4q6l+zpurYUjOygLnL+vqpxhr6imvAAX4QQHDz0LSvCQ1l8YiFlFiPD2wyn\nTbAa+z6ULVi7R2HFg2OJC4wkUBfo1IYH1GKtw/dB4XGISSavvJqO0bXy442FcHInDH260ffDETb6\n5Xe1Dsg1tfJCQxp6ieQixmSxkVloZHSKe9w2PMAXg07j1RTL/PJqIgL1+GjsoZPsbaAPUSV3XYgJ\nNtTt0YMavvntczBVgG8AJdUlFFQVUFxVjMmmeuaV5kpyjbkct25FG5DLNd++xBnjGbTBQQyLG8h9\nqQ/QJbyLs8vl2lP8uHkXmKMI0dfx68XxiyNrK8Qkk1taxeXtI9zbHPoOENB5lMflZ6NNuD9b09U8\nFOnRSySSFuFMaRVWm6BtuLuRUXPpvZti6VEslfkrtBkAGvfkvbgQAztOFNXZh7HdUNbtncOm1X9h\nV3UuWWVnSbfUawjStKJ3TG/6HVzLCL94Qq5616OZo0I0s8BIl9g6DH1YEgREQdY2qnreQWmVxamd\n72T/YjWtMi7V8/qz0DZCNfS1UysvNKShl0guYhxpjI5sF1fiw/zILvZe6MatWKo8F/J/h1TPas+Y\nEANnSqqx2QQajYIQgt9O/8bC3xeyLutnqqIjCSvYQ6/4IUzoOIHYgFjC9GHotWrfeh89UYZoLn9t\nG3cM7cgTfSLhp49h+G11zsuZ/VJX0RSoi7cJAyBrq3NB2S1zyFgIx3+BQY80WSPe4cXXTq280JCG\nXiJpQYQQXquKrAuHTG5cHYa+dagfaVnFXhvLrSgrc5P6mjjYo11csAGT1UZOWSmbTq/iywNfklGa\nQbBvMGM7jGNU+nZ65/yO5vZ36jWsRRUmrDZFXYw9YZdOaDuozrah/r4EG7T1p1iCGr459B1Feaoa\nS3SQy/06uFxVxOw2rp6L68fxa6Ipm4CcD6Shl0haiPu+3E6Yvy+zJvRouHEzOX0Wj75tsA/3mr7E\n9MN6fONTIWkoBDZPV0qVPzDV7BWbsQl0AXVunh0ZpEEXvoFJ379BqamIbhHdmDl4JiPajsCgNYDP\nZ3D4/6mLoxHtAcgqNBLiryPYoKaCFlSonnd4gK86ltYArXrXOz9XOYI6sS8YmzO3AaHuHv3+xWp4\np47v0hCOXxPS0EsklyjbM4ooq7bw7LVdvZbLXpuckioC9VqCDLX6t1Qz9venifLZAL/pYKsJAmPh\nvl8gqOkFN6VVFkxWW42BzNykesk+NeMKIVhzYg1vH3wTQ0wOsYbe/GvYW/SL7ef+q8aRp565yWno\nb/tsC51jgvnsDrXC9pff8wHUmPvmDarEgtZz+0IHbSL82XeypM5zOSWVbM2NYpxGhz5nO3B1TYy+\nogDS18OgGc3a2i8xMgA/nQ/dW3snhbWluHCDShLJRYzRZKGgwoTJYmPlvpyGL2gmp0uqPL15qxm+\nnU7MmfU8a7mbdTfuhDuWQ3UpLLxTPd9E3IqljIWqkFliTSglvzKfx9c9zuPrHifQNwDjiemMj/s7\n/eP6e4auIjupi6MZauK70WQhq7CSNQfPkJ6vSg5/tTWT3m1C6aw5qUoYdB591vm1DVcXni1Wz/z4\nD9cd49FFh6mK6k5owU40iouu+5b/qGGb5KaHbUDd4Wr9U1dyU5+EhhufR6Shl0haANdsl//b6aHS\n7TVySqs84/NpX8Oh7yi7cibfWK8kq9QKSVeom4Cc+BVWv3jWPoUQjH53A++tPeI8lmuvdI0K0tfI\nDbdV4/O/nvqV8UvHsz57PY/1eYyFNyyAys6eMggOFEWtcM3YBEK4hVzmbEpn87ECjudVMGVgW9j9\nNSg+qgLmWUgI98diE5wp88zf33hU/XWw36crMWUHiPbXqCmiG9+BDW9ByiSIbX54LSrIJeX0AkUa\neomkBXDkr1/ZOYqt6YUtstsTwOmSSqfsgJPfV0JIGwKHPIheq6kpmkq5CQY8oHqx6Rvq7bPYaOZg\nTilvr/6dtQfPUFpl5u/fHSBQr6VTTJAactEaoHVvvjn0DQ+ueZAo/ygW3rCQ6d2no9fqiA7S1y2D\n4KDtYCjNhuJMp8Rv17hgFu7I5sNfjhHqr+Pa5Gh1h6iO10Bg9Fnvg7NArNA9Tn+quJLjeaqy5PLC\neHTCxEs+X8Ciu2HNS9B9Aoz7sFlhm4sJaeglkhbAYVwfuqoDAEt2ed+rN1tt5JZVu3v0lmo1VbDj\nNSgaDa3D/NwfMle/BMGtVSNXz45PjpRNg07DY9+kcffc7RzNLefDKb1Vjz5jIxXxfXh52+u8uvVV\nBrUexJejv6RdaI2iYkztDUhq4wj7ZGxyevQvXt8No8nKhiP5TOwTjyFrPZTlQM9bG7wXDm2f2gVi\nm+ze/JSBbVlenEQpAVxjWqNq1PeeCuM/Ufe3/ZMjDb1E0gJkF1U6t5PrlxjG4l0nPbe7O0fyyqoR\nAmJDXMS5TmxWd1XqeA2gGkA346fzgyv/qurIH1hKXThSNt+Y0AMBbEsv5PUbUxjSMQrKzvBb8e9M\n0BXyf0f+j7u638V7V75HgM496ySu9paCtYnqCn7hkLmJjAIj4QG+XNY+ggH2zTpuG9AW0uapapUN\nxOcBWoWqD7usWpIPG4/mExnoy4zhHSnWhNKz6mOe7fYTPJ2hhrIuASMP0tBLJC1CdlEl8aF+aDQK\no7rHcTS33LmzkbdweN5xoS4e/ZHV4OOrxuRRc+k9ZBB63grR3WDt3+tcmHX0OyApgv9O78+/b+vF\nxL4JVFoqeWPdk0yPi8bHN4i5o+fyaJ9H3XVl7LQKVfXw6324aTT2OP0GMgsqnGmKr47rzj8n9iQp\nwKzKEnSfAFp93X24oNf6EBOsd/uuQgg2Hc1nUIdIIgL1XN4+AoGGqNqhrksAaeglkhYgu0jdiAKg\nW5yaenfodJlXx3CERtxCN0dWq4VFvqqHHR/mR2GFCaPJUtNG4wNXvwyFxyDtK49+c0oq8dEoRAXp\n6dUmjGtTYll7Yi2Tlk/if4W7uLVaYeHYJfSK7lXv3BIjA6gy2zhTl7iZs9FgKD5BdV4Gbe2FRx1j\ngpjQJx5+nqmGofpMa+ztsP96qfHoD58pI7/cxOAO6g5PN/RoBeApf3AJIA29RNICZBVVOuPGXezK\nkodPl3p1DGdVbLA9dFOUCfmHnWEbcJErru3VdxwBMSl17viUU1JFTJAesLEyYyU3Lb+JR39+FJvN\nwqdnCvhr4lj8fc9eIJRkLyA6nl/udry0yswLS/bx0Nc7oeMIhEbH/6t6l6Qwlxz5rN9g26fQ/16I\na3w2TO19cjceUePzg+yGflRKLMM6R3FZe+9t7XexIA29ROJlKqotFFaYSAhXjWxYgC/RQXoOny5v\n4MqmcbqkCj+dD8F+9jjz0dXqawdXQ1/3IiWKAr0mw6ldcOaA26lTxUYCIvZy47IbefKXJ7HYLLw2\n+DWWdriDgcYKt41G6iMpSjX0Gfk1HvaGI3mMeHs9X27J5Ls9OWSIWM5c+U8u1xxgfNbr6uKwxQTL\nH4HgVo3eiarmu/qRU1LlzKXfeDSfdlEBtApV/w7BBh1z7uzvIel8KSANvUTiZRxZLvEuaoadY4M4\nfMbLHr09h95ZkHRkDYS2hciOzjZn1aVPmQgarZqrDtiEjXVZ6zjk8zdO6z9Ho2h4c+ibLB6zmBva\n34D20Aq1urZ13wbnFhdsQK/VkG736G02wUNf78Jf78O7t6gKkeuP5LE/chRvmifRJns5/LML/LOz\nWox13T/Vzb2bQHyYP1ab4LRd0XNHRhED20U0fOElwKWx5CyR/IE4jGq8y9Z+XWKD+O/mTKw24bXi\nGreqWHMVpP8Cqbe55YRHBerx9dGQXVcef0AkdBrF3v0L+C7YjzUnfiK3Mhdhi2BQ0Aw+HDMdjWL3\nBc2Vakpiz1s9ZInrQqNRaBvhT7rdo88oqKCk0sxz13ZlbGpr/vnj76z/PY/L20fygXUsD17TnYCi\nQ6rMQVxqozJtalPzUKukvNpCWbWFvm3DmtzPnxFp6CUSL+MIk7ga+s6xwVRbbGQUVNA+KrC+S5vE\n6ZIqBrRT0xE58SuYjW5hG1ANbuswz8wbk9XEqoxVfK0tZF+4Hv3v3zIo/gouj7uKp+cqDOiaUmPk\nQS3CMhuh6/WNnl9SZADH8tRiqL12HZpkuybM0E5RLNqZTVSQgSC9Dv+hTZcIro1rmOpYnvpLoo80\n9IA09BKJ18kuqkSv1dQoPQKdYxwLsmVeMfRWm+CMq/zBkTXgo4ckz42tXVMsT1ecZsHhBSw6sojC\nqkKSghP5a6mJMVEpBFz1LvtPlQAbPWUVtn6shoWShjZ6jomRAfx8KA+rTbD/VCm+Wo1aWQtc0SmK\nL7dk8v3eHNpG+ntFytmRS59dZOREgZHIQL1TRvhSRxp6icTLOFIrXY1Xx5hANIpq6K9NiTvnMQrK\nq7HYRE2x1JEf1WrTOrJhWocaWJ2+mcfXLeKnEz9hEzaGJQzj1i63MjBuIMrKZ2H751BZTE6xmg4Z\nF+pShHVyp1qINfJ1NTWzkbSLDMBktXGquJK92SV0jQ1CZ9/A/LL2EWg1CiWVZgaHeycLxjWXfseJ\nIvq0DW3RvQAuJqShl0i8TLZLaqUDg86HxIgADnspl95ZLBVsgKIMKDgCfae7tbHarCw7towtps8x\nR2eyNSeYqd2mcnOXm2kd2LqmYY+JsPVDOLiMHJPqsbt59Fs/At8g6DWlSXNMdKZYVrDvVAk39Gzl\nPBeo19I3MYwtxwudxVLeICHMn7SsYjILjEwe0MZr/V7sSEMvkXiZ7KJKurcO8TjeOTao2UVTZqsN\nrUZxeqiOzJ7YEAMcWaY26jjC2f63078xa9ssfi/6nVhDO6oyJzB/2kMkx9XhPbfqDeHtYe9CcmL6\no9UoNXvDlubAvkXQ7x4wNE1zPSlSNfS/HM6jrMpCSq17ckWnKLYcL/Tqph3xYX5sz1T3q5Xx+Rpk\neqVE4kUcOfSuC7EOOscGkVFQQaXJ2qQ+y6rM9H11DVNnbyO7yMj2jEJeXLqPED8diZEBajVsWCJE\ntMdsM/P61teZvmo6ZaYy3h72NjP7z8Zc0o+8Uk+tdoCCChPFHcZC+gYq87OICTbUZAZtehdsVhhw\nb62pnqMAACAASURBVFNvBVFBegJ8fVix9xSAh6Ef3T2OuBADvb1okB2/pHx9NCS38nzYXqpIj14i\n8SI1GTee4Yiu0Qbu1Synev48/KpPqdvbjXjFbZemujiSW05JpZmNR/MZ8a/1mK024sP8+XRqHwIV\nk7pDUq8p5FXm88QvT7AzdydTuk7hkd6P4Kf1c1bQehRNoW76MeHDXwmrTGQxgna5q4gLuVE9uesr\nNaTTZxqEt/O4tiEURSExMoD9p0rR+Sh0jHFfhE6KDGDzs8Ob3O/ZcDxgU+JDMOgav57wZ0caeonE\nizi01dvWke0x8Oi/GKmbR/npeIiIV41owVGYNLfORVQHx3LVVMEvpw9gzq8Z+GjgHxN6EuKvg93f\nICyVrIpszcxlN1JtreaNIW9wbbtrnddHBxnQ+Sh1auK/8cMhMgqMZBBJYUwyA8vWcChqFBxaoVao\ntrsSrn2r2fcjyW7oO8cGode2vOF1PGBl2MadBkM3iqIYFEXZpijKbkVR9iuK8jf78XBFUVYrinLE\n/hrmcs2ziqIcVRTlsKIoI1vyC0gkFxIn7BtfeCww7phDyJ7ZzLZdx/vdv4W7VsEN78KxtTD3Bqgs\nqrfP4/kV6HwUBrYL57M7+vLx7X1VIw+U7ZrL/2vdhicPzSY+MJ55181zM/IAPhrFribpqdU+d3Mm\ndw5KpGtcMAuqL6OjLZ2ZxybA/NsgqgtM+m+DvzjOhiNOXzts01J0jg0ixE/H8C5n36jkUqMxHn01\ncJUQolxRFB2wUVGUH4AbgbVCiFmKojwDPAM8rShKN+AWIBloBaxRFKWTEKJpgUmJ5CIks8BIsEFL\nqL+LSFf2DljxBLQfzrf59xBr99DpM03dO3XhNPjvOJi6BPw8PdHjeeW0CfdH6+Pulx3P/IUZ5uNk\n+/oyo/cjTEuehlZT9//SrUP9yHLZfclmEzz17R7aRQXw9KguLN99iue/HcwJH8H1KbFc3iUeOo1q\n8gJsbRyGvq7F6ZYgKkjP7pdGNNzwEqNBj16oONSYdPb/BDAWmGs/Phdw7K47FpgvhKgWQqQDR4H+\nXp21RNIMdmcVn33XIy+QWWikbe0skq0fgT4Qbvqc9rGhHMl1ybzpch3c/D9V3+XL8VBV4tHn8Tz3\nalohBEuOLuG2Xx6l1EfDp4P/wd0pd9dr5AHaRQVwLK/cqQ9/otDIyeJK7hnSDoPOhxt6tiIoMJCv\nrcMp7X67KqXgH35uNwPolxhOu8gAhnSIOue+JM2nUVk3iqL4KIqSBuQCq4UQW4EYIYRje/vTQIz9\nfWsgy+XybPsxieS8IYRg2hfbuGP2NqotLffjMqvQSBvXsI2lWpUP6HId+IXRMTqQ7KJK98ybTiNh\n0peQsxvWv+nWn8Wqyia0sxv64yXHmb5qOi9seoHOJjPf6DrSt/2oBufVOTaYsioLp+wPOkeap0NC\n2aDzYfKAtgBOtUdvkBDuz09PDHO/J5I/nEYZeiGEVQiRCsQD/RVF6f7/27vv8KqK9IHj37npvTdS\nCWkECC0U6VWlKKioWFhsC4pt1V1X/emqu7qLveyuInYFdEURBVGk994hkN57gfR67/z+ODcNgiTh\nphjm8zw8uTn3lJkA7z2ZM/O+570v0e7yW00IsUAIcVAIcTA/P78thypKm+WXVnO2opbY3FLe2hDf\nIdfQGyQZZyuaL7tP3g7VJdD3egBCPe2RkoZcLA3Cr4V+N8DBz5rd1WecraRWLwlws+C9o+8x58c5\nxJ6N5fk+t/BpRjreQ+5uVdvOz4kfl6sF+vqUBAALxwfz2pyoThtPVzpPm+bRSynPAVuAa4FcIYQP\ngPFrnnG3TMC/yWF+xm3nn2uplDJaShnt4aF+rVM6VoJxXDzC24Gl2xM5lFpk8mtkndOCcrMZNzE/\ngJUjBE8AaJhiWN+eZkY9AjWlcPDThk1JBWXobFL5NOVh3j/2PlcHXc2Ps39kTvJhdPZerc7yGNaQ\na6fM+LWUAFdb7Kwah3tsLc25OdpfpQ3ogVoz68ZDCOFsfG0DTAXOAD8C8427zQfqKw3/CMwVQlgJ\nIXoDocB+UzdcUdoi3hhY/3vHEHo52/DUdydMfo36GTcNwxT6Om2aYtg1DXVPA93sMNeJ5uP09XoN\n0pKG7X0f6qqp1lfzxZn3sA1cAqKOD6Z8wOKxi3EvzoHEzTBiYavqqQI42VjQy8m64Y7+TE7JFVmA\n40rVmjt6H2CLEOI4cABtjH4tsBiYKoSIB6YYv0dKeQr4BogBfgEeVDNulK6WkFeGg7U5we52zL8q\niPi8MorKa0x6jdTC+qmVxoexabuhsqhZRSYLMx1B7nbE516k2tToR5FlOWza+TKzVs/iUPEqdOUj\nWD37e0b5jtL22fMfsLCDoa0btqkXZkzBUFWrJ6WwomE4R+n5Ljm9Ukp5HLigCrCUshBocVmblPJl\n4OXLbp2imEhCXhkhnvYIIehbX6w7u4RRIaarH5paVI6lmQ5vR2NCsJgfwdwGQqY02y/U0/6iyc2S\n3IJYHBDMntTvCXHqQ0DNY9joIrCzMH54FGfCiZUw7L42z4oJ93ZgV0IBsTml6A1S3dFfQVSuG+WK\nEJ9XRohx5kqEjxbgTpsok2S9tMIK/FxttDwxUmrDNiGTL1j1GuppT0phebPZPxW1Fbx64FVuWjOH\n4+bmPFVYxEq/WeTmBhDs0eT43e+CNMDIRW1uX4S3A7V6yc8ncxq+V64MKtArPV5xRS0FZdUND0Ld\n7a1wt7fiTLZpa7imFlY0PojNPgalWRA+/YL9QrwcMEhILtDSJezP3s+NP97IsphlRDlPITfuCSLP\n+VC7aTGlZU0KlRz8RJuTP+QP4BLY5vaFe2m/yaw5loWluc6kWSOV7k0FeqXHS8jX7txDPBsXHfX1\naX/K4JZIKUlrulgq7hdANEsdXC/U2I4tyYd4fOvj3PvrvZgJM+4MfIVtuycwOqg3KxzmY1OZw51m\nGwlxtYAjy2Dt4xB6Tbtzz/TxtMNMp+W8CfGwv2ClrdJzqaRmSo9X/+AzxKNxqKK+WHed3mCSgFdU\nXkNZdR3+9Xf0sevAbxjYXzh1WGdZgI3/J7wXF4eDpQMLohYwK2geE17dxfgwDz6YN5TC8ij2vrOS\np81XYPbdckBC0FgtAVo7c89YmZsR7G5HfF6ZGp+/wqhAr/R4CXllWFvo8G2SI76vT2Ox7hDPyw96\nDcnMXG2hJEsbupn8fLN9avW1LD2xlI9PfIyFrTlBulv5as5j2FnYsSuhAIOEBeO0lAS+zjZU3/I2\np7a8zYC+fRFuIdrqWovLW7Ua7u2gAv0VSAV6pcu9uOYUReU1vDP3gsldJhGfV0awu31jMQ0gwlsb\nrz6dXWqSQJ+Yb0xP7GYLcSu1jU0WM6WVpPHk9ic5VXiKGcEzyEqaSk6BecNsmiTjeH3TB6/BfYdA\n3y8uu21NhXs5sJZsFeivMCrQK13qfwfS+HRXClbmOvQG2SwYm0pCXtkF+cn7eGoLl87klDSrZdpa\nZ8tr2HA6l/UncziWUUxBWTUWZkIbutn4CzgHaml+gTWJa3hp70uY68x5e8LbTA6czCvlZ9gTl0St\n3oCFmY7k/HJsLMzwcrC+xJUvz8QIT9adzGGIv8rXfiVRgV7pMqeyinnuh1M4WptTUlVHSmHzLI2m\nUFFTR+a5Sm4d5t9su5W5GX087DmT3fYHsrklVUx9cxslVXX4OtswIdyDMC97ooNcsZZVkLQVou+m\nvK6Cl/a+xNqktQzxHMLisYvxsfcBtAeytXpJamEFIZ72JBeUEeRuh64DPuia6u/rxM+Pju3Qayjd\njwr0SpfQGyQPrTiCq60li28awF2fHiA2p9TkgT4xTxsSaTrjpt4I90rCUz6G722gulQbAx90+yXP\neSj1LCVVdSy5cwjX9PNunhvm0OegryY1aCQPrZ1LWmkaiwYu4o9Rf2yWRjjUOFyUkFdKiKc9SQXl\nnZazXbnyqECvdIljGedILijnrVsHMjLYDSG01LnTB/iY9DqnsrRMkJE+TQpoSAmHPuP/Up5F1FVi\nSO6FTgBn1kL2cbjmZdBdvOzdmewSdAImhHs2D/JSwr4POOATwZ+Ovo5O6Pjo6o8Y5j3sgnP08dTG\n4uNzy5gUYSC9qILr2zGEpCitoSbSKl1iy5k8dAImhntibWFGkJtdQ8ItUzqWUYyjtXnz0n7bX4O1\nf6LCfQCTa15n/+xt8MhRGPGAVsf1q7lQU3HRc57OKSXYw/6C4tN1KdtZWp3OAusq3G3cWTF9RYtB\nHrRMkX4uNsTnlZFWVIFBNlZjUhRTU4Fe6RKbz+QxNNCloeReuJfDRfO/XI4TmeeI8nNuvPM2GLTh\nlT6TqLtjNenSi5OZxWBmDtMWw4w3IH4DLJ8DVS1/8JzOLrkgfUBsUSzzdzzJv12dmRo4hS+nf4m/\no3+Lx9cL9bQnPq+MJGNuehXolY6iAr3S6XJLqjiVVcLEJgWcw70dSC2qaF556TJV1eo5k13KAL8m\nY9/pe6EkAwbejoejNb2crDme0aR837D74KaPIH0ffDHrgtJ+JVW1ZJytbEiMdrrwNI9ufpQ5a+aQ\nXFfGK87DeHXCGzhaXrrWaoinPUn5ZSQYA32wu2mfTyhKPRXolU63NVarUTMxvDHQR3g7ICUt52lv\npzM5pdQZJAObBvoTK7WMksY57gP8nDiReV6d1gFzjKX9jsLGF5q9FWf8rcPHtYbndj3HrWtv5UDu\nAR6wDeHnzGymj3+x1e0L9XSgus7AjrgC3OwscbJt34pXRbkUFeiVTrf5TB4+TtaNwx/VpUTJM1yl\nO0X+6R3aQ00TOJFxDoABfs7aBn0tnFoNEdO1Yt1AlJ8zyQXlFFfWNj84YjoMX6hVe8o41LB5V9oZ\nrLx+4J8n5rM2aS139buL9ZM+YNHpHTgNvBOcf3u4pqkQY5K1/SlFathG6VBq1o3SqWrqDOyML2DW\nYN/GcfOVd+GbsJGvLIFdQPZEuO6ddmVobOpYRjFudpb0cjIuQkrcohUCGXBzwz5Rxrv9k5nFjD4/\nN/3EZyBmNaz9EwV3ruSNI++wNnktli5mXBM0g/uj7tfG4VfepeWfmfhMm9pXP+VTb5DNUxEriomp\nO3rlAodSiziSdrZDzr03qZDyGj2T6odtMg5BwkYYuYinHf/FF04PQMYBeO8qLZ/7ZTiRUUyUn1Pj\nB8qJlWDtDH0a6+XUF8I+Zrz7b8bakZqpf2d5RRIzV81gfcp6XGuvJbT6FV4e87IW5DMOwqnvYdTD\n4ODdpvY5Wls0FCnprcbnlQ6kAr3STFl1Hfd9fpBnV5/skPMv25uKi60FY0KNd887XteC78RnqPUf\nzbvlU2DRXvAIg1ULoTCxXdepqKkjPq+0cdimukz74IicBeaWDfs521oS6GbLiYzm4/RVdVV8F/cd\n0858yGI3VyIryvhs9H8pSJvMAG9fbaeaClj3Z7Dz1AJ9O9TnyFdDN0pHUoFeaebTncmcraglPreM\nmjpDu85hMEiS8suoqKlrtj2tsIINp3O5Y0SgNgc954SWznfkIrByIMLbgYKyagrNPeHWZdqUx5Xz\nobaqzW04lVWCQdL4IDbmB6gtb3Hl6wBfJ45nFFOrr2Vf9j7+vufvTPpmEi/seQF9rT0OaTfwXnYh\npd/8i/IaPRE+jtp4/8r5kHVUm5Jp1b4kYfXDN33U0I3SgVSgVxoUV9by4Y4kHK3NqdEbSMy/SAHr\nS1h/KodJb2wj8m/rGfPKZlYdzgDgs90pmAnBvKuMY+873gBLBxixAGhcvXo8oxic/OCGD7QPg5+f\n/M0HtNnFlcz7eF+z9h5Lr38Qawz0R1eAax/wH9H82LJsdI57KbT/gNFfj+G+X+9jTeIaJvhP4N0J\nH1AYt5BBwbM4Fng3o6u2MU53jEFWOfD9Qoj/FWa+CZHXt+vnBDC1rxcjg10bC5YoSgdQD2OVBh/v\nSKKkqo535g7i0a+PEpNV0jBfvC1OZhVjphM8OjmUzWfyePybYxSV1/DNwXRmRvng5WitBfBTq2HM\nY2CjZVIcFOCMmU5wIKVIm2Mfdg2MeRx2vgnuoRcdHtmfXMSO+AIeWHaI1Q+O5lyF9oHVx8MOTwdr\nKEqG1J0w6TlqDLUczjvMzoyd7MzcSWKxNjRkZuXMENfJ3NpvKiN8RmBrYct7WxMorT7LogkhRLi/\nSOYra/nC8hX4/hXtwpOeg+h72vfDNhoV4m7SAuWK0hIV6BVAS7v7ya4UpvX3ZsYAH5789jin21lT\nNSm/nEBXWx6ZHMqCccE8sOwQL/10GoB7xvTWdtr4Alg7wehHGo6ztTSnfy9HDqY0eRA86TkoSoJf\nnwVHX+h/4wXXSyvU0hXE55Xxl2+Pk5BbRkW1ns/vGa7tcOxrEiwsWFqTwtavx1BZV4mFzoKhXkO5\nIfQGhnpcxXVvxdG3dzgTA0IBbbHVJzuTGRvq3pBszGbup2QcXIFf5EjwGw7uIe36+ShKZ1OBXgFg\n6Y4kymvqeGxqGOZmOsK9HYhpZ6BPzC9rmC5obWHGknlDeeq7E9TqDUT5OUPSNm2mzdR/NNzN1xsW\n5MoXe1OprtNjZW4GOp02hFOaQ/X3C8mzdaLA3hVrM2s8bT1xsXYh/WwFHg5WzBsZyJsb4jDXCT6/\nZzgBbuZsS9vCTwkr+MXPB9u8g1wXfB1j/cYy3Hs4thaN+W9CPLI5kt74AbMnqZCCsprGDybANWwk\nrmEj2/UzUZSupAK9QkFZNZ/tSuG6qF6EeWkPFSN9HFl/KgcpZfMMjZegN0hSCiuarXq1MjfjrVsH\nad8YDLDhb+DoB8MXXHD8kEAnPjmYwr92/xeDWQF5FXnkVeaRZ1tGcYA37PjThReVAuFrxk9nPekd\n5YCdpRmLT7xP1p4sagw12JobuNtzDHdPfAVna+cW2x0d5Mra41kNxU8OJBdhrhOM6O3a6r4rSnel\nAr3Ckq2JVNfpeXRKaMO2vj6OfH0gnZySKnycWl+nNPNsJTV1hosvADpiTC0w+32waKymFFMYw6r4\nVaxL+hm73iV8lwyeNp542HrgZ+/HEM8heJ7LxvPk93hEL6Cq91hyKnIori7m452JeDubE+WlI7ci\nF53Q4WTpxwTfsYw6sJyh0grLq//zm0W1h/d24av9acTmlBJpHD7q5+uEraX6L6L8/ql/xVe43JIq\nvtybyg2D/ZoV/YjsVV9TtaRNgT6xwJigq6UCIrmntBk0vcdD1K2U1ZSxLnkd38Z9y+mi01iZWTEl\ncArbj3rQx2EwX94yqfnxUkJWEuz7DIY9DHZu1OoNvP6/n7k9LIQnxoY333/nW5CfAneu+s0gDxAd\nqN25H0wtoo+nHUczzjH/qstbmaso3YWaXnmFW30kk+o6A49Mbv5gsT4PTUxW28bpE/PqMzGed0df\nXQbfzAdrJ3Km/ZPXDr3J5JWT+cfef6CXep4e/jSbbt7E4rGLGddrKsdSajEYzptSKYQ2nbG6FLZp\nM1+yzlVikGi1WpsqyYZtr0H4dAiZzKX4udjg7WjNgZSznMgopqbOQHSQGrZRegZ1R3+F0+7YrS+Y\nx+1gbUGAqy2n62uqVpVoi4IuMV6fVFCOs60FrnaWzbZXrPszm6qz+Tl8LHt+mYdEcm3va7kj4g76\nu/dv9hwgOsiVrw+kE5dXSoT3edM7PftquWqOLIOJz5BepC3K8ndpEuilhF/+CoZarVpUKwghGNbb\nlQPJRfT10T7kogNVAW2lZ1CB/goXm1tGuHfLqzqnuuYTlvIZvBcPeafAwQdCr9ZWlwa0PPskKb+M\nYHe7hsAtpWTDvjdZXLSNfA9XfKqLmBc5j7kRc+ll33LpvGFBWoA9kFx0YaAHGHE/HPsKjnxJuvks\nAPxdmwwvnfxOWwk76TlwDW7lT0K77ppjWfxwJIs+Hna42Vu1+lhF6c5UoL+C1eoNJOaVMS7svAU7\naftg8z94LmMH1dKcOptRmE94GvJi4OQqOPw5DL0bpv4drJsH4sT8csaHeQBQUFnACzufZVvWLvoK\nC16Z/D7RvqMuOYsnwNUWd3tLjqYXM++qFnboNQgCR8O+paRHTMRcJxqfI5TmwE9PgN8wGN3CDJ3f\nMMw4VBObW8ptw1ufblhRurtLjtELIfyFEFuEEDFCiFNCiEeN212FEBuEEPHGry5NjnlaCJEghIgV\nQlzTkR1Q2i+loJwavaF5WbzyAlhxCxQmkh79FMOq32PtoCUw4Sm45Qv4c5y2QvXw51qGydxTDYeW\nVtWSX1pNsIcdu7N2M+fHOezN2sNfCs+yYuJ7DPMb3aqpmkII+vs6NRT2btHIB6A4Dde0Dfi62GCm\nE5B9TEsZXFcNs5douXLaIMzLAQdr7Zj6h7OK0hO05mFsHfCElDISGAk8KISIBJ4CNkkpQ4FNxu8x\nvjcX6AdcC7wnhDBr8cxKlzpjrJZUP3cegA3PQ00ZzPse3+lPYevoztrjWY3vW9rC1S/BvRtBGuDT\nadpvAGgrYoVZGUfKP+L+DffjLMz4KiOLP4TfinnvMW1q2wBfJ+LzyqiqbSwtWFFTx4fbkxjzymY+\nK+wLzoHMyXmb/9a9CB9Ogg/GQfZx7YFtO1atmukEQ43j8sPUg1ilB7lkoJdSZkspDxtflwKnAV9g\nFvC5cbfPgdnG17OAr6WU1VLKZCABGG7qhl8JyqrrKCirpqCs+sIZKCYQm1OKmU40ZFAkbS8cXQZX\nPQieEeh0ghlRPmyLy6e44rwKTH5D4d71YOtO4bLZbDrwb94//g52fV7nQOEv3Bl4DV8lxBDqOUD7\nYGijfr2c0Btkw+rc1MJyxr26hZfXneZseQ1Ld6Siv/YVTskg7M2MWTKvfgkej2kxQ2Vr3RLtz7X9\nvJuP+SvK71ybfrcVQgQBg4F9gJeUMtv4Vg7gZXztC+xtcliGcdv551oALAAICAhoSzOuCEn5ZVz9\n1nbqjAH+5qF+vHbzQJNe40xOKb3d7bRUA/o6WPu4tmJ13JMN+1w3sBcf70xmfUwOt0Q3jluX1ZSx\nseAwa0MGsD+vFhmzFB06DJVhfD39YSK+vx+sXWDuCrBoe9Cszzp5KrOYIQEurDqcSWF5Dd8svIq8\n0ioeWnGEDXVDuL/qSZ6cEM6iCabJOzN9gA/TB/iY5FyK0l20OtALIeyB74A/SSlLmo61SimlEKJN\nt5xSyqXAUoDo6GjT367+zq0/lUudQfLsjL7sTSpk9dFM/jotAncTzgSJzS3Rcs8A7P9Am1lz67KG\neqqg5XP3d7Vh7fFsbhziw+6s3axNXMuW9C1U6auwFV64lo7i5dJ12NU486NVfyL+d6eW6uDun9pc\ndaleLydrXO0sGwp3b4nNY7C/M8N7u1Jdp8fZ1oK3NsQD2sNbRVEurlULpoQQFmhBfrmUcpVxc64Q\nwsf4vg+QZ9yeCTSdsuBn3Ka0wZYzeUT6OHLf2GCemhZBrV6y8mBGu861N6mQB1ccprqucby7rLqO\n9KJKIrwcoCQLtvxTmzoZMbPZsUIIRvetY3/x50xeOYUHNz3Inuw9DHSeSnnyIkrin6CvywJSA55n\nIOn8rfpNcOkNC7eBT/t/AxFC0K+XIycyS8grreJ4RjGTIrT8OVbmZswe5EtsrvaModkcekVRLnDJ\nO3qh3bp/DJyWUr7Z5K0fgfnAYuPXH5psXyGEeBPoBYQC+03Z6J6uuKKWQ2lneWB8HwBCPB0Y0duV\nFftTWTguGJ2u9UnGpJS89FMMJzNLGNnblXlXBQEQZwyS4d4OsP4prWLStFcaFkTllOewPmU965LX\nEVMUg7mLDnfzETw/cS5jfcfy8IrjeFmdY/MTE7CxNAOGwmErKMnUcsibW16kRa03wNeJpduT+PVU\nLoCWo97olmh/PtudAqg7ekW5lNYM3YwG5gEnhBBHjdueQQvw3wgh7gVSgVsApJSnhBDfADFoM3Ye\nlFLqLzytcjHb4/PRG2SzwHbnyEAe/uoI2+Lzm2WGvJQd8QWczCzBwcqc/2xJ4OZof6wtzIg1zrgZ\nVH1IK2494RlwDSapOInXD7zOjswdAPR17cuTw55k6TonbPVeTAoYQa3ewK6EAmZE+RiDvNGQeab5\nARgN8HWiziBZuj0JL0erhgpUoOXi6e/rSEpBBc62v53HRlGudJcM9FLKncDFbiFbTCIipXwZaN3a\nc+UCW87k4WpnySD/xpS61/Tzxt3ekuV709oU6N/fmoiXoxWvzRnIHz7Zz/J9adw7pjexOaX4WFbg\nseU5cA8je9CtfLH/Fb4+8zU25jYsGriI6cHTCXTUEntlpJ7m4x3JFFfUEpdXSml1HeOMC6M6Sn3B\nj7SiCuYO879gDv6L1/cntbC8TWmUFeVKpFbGdjN6g2RrXD7jwzy0RUAA6QewjPuF5Q4HqUjMoO4j\nd8ytHbSFS8HjL3quI2ln2ZNUyP9N78u4MA9G9XHj/a0J5JZU8cORDN6z/oSY2mI+jLyKLT9qqQRu\nCLmBhwc/jJuNW7NzTevvwwfbkth4OpfkgnLMdILRHVwCz8/FBicbC4ora5v9dlNvaKBLw7x3RVEu\nTgX6LmIwyBbH2o9lnKOovIYJ4ca75exj8NkMMNQR4BjEAWnLuWqJe8lp+OJ6uOohmPw3MG8+G0dK\nyTub4nGyseC2Edr01cenhjFnyR4+3ZXA3T6bWCVi+cXeHafieO7udze3hN9y0fwzUb5O+DhZ8/PJ\nHPJKqxjk74yTTccOmQghGODrxL7kwg7/UFGUnkwF+i6wZFsiK/alsfHx8ViaN058qtUbWLI1ETOd\n0PLFVJVoS/ptXWHhDixs3HjwHxuY5uXNq9eHanVU9/xHS/AVMROiboWg0QCsPprJ1th8/jqtD+ll\n8cSkxhBTGMOgESdIL43nK1mHDfYsHPBH7up/N/aWLeSPb0KnE1zTz5sV+9KoNRh4bEpYR/6IGjww\noQ/X9vfG3kr9U1WU9lL/e7rA5jN5pBVV8MupHK4fqN1B19QZeOSrI/wak8uzM/ribGMB3y6EfAAr\n5AAAE+FJREFUs6lw11qw98AcGBvqzva4AqRFFGLmmxB5PRz+QsvYePhzGHE/acP+wt82Lscr7CAf\npiXyXoq2qtXBwoG+Nh6MPXeOvna9GH7TMtyde/9GS5ub1t+7YaZLR4/P1xsd4q7u5hXlMqlA3wZ6\ng8QgtbVdFmbtq9lSpzdwPOMcAMv3pnL9wF5IKXn06yP8ciqHv82M1ApSH1kOp1bB5OchcFTD8eNC\nPVh3Ioe4+vTCwRMgeAKypoIT6x9nXfz/WJu9DjzB3saH6cF30M+tH5HmTvgd+hLdsa+g1xC4YxVY\nO7Wp7dFBrrjbW6I3SAb4tu1YRVG6jgr0rXQ84xxz3t9Djd4AwGNTwprVWG2tMzmlVNUajGPPRcTn\nlnIw9Sw/n8zh6WkRWpA/lw6/PAWBYy5ItVt/J709Lp9wbwcKKwtZk7iGVQmrSC5OxszRiTEVldxS\nWsKY4Gh0FQaIWQIpO0HoYPhCmPh0m4M8aEm/np7Wl1q9ofFBsaIo3Z4K9K209ng2EskTU8PYmVDA\nkm2J3D4iAA+HtqUkOJKu3c2/NLs/Ny/Zw+u/xrIzvoBRfdz449hgLXXAD4u0zJCz/wu65r859HK2\nIcTTljXxm4jR/5ut6Vupk3VEukRhX3o7+TlhjLs6lHE138O+JdpvBZ6RMGIhjFwEThekHWqTm4b6\nXdbxiqJ0PhXoW2nzmTyG93bl4cmhzIjyYcqb21iyLZHnZka26TxH0s7ibm9FlJ8T0wZ488PRLOyt\nzHnt5oHaLJwdb0HydrjuHXAJanZsemk638d/T4nHd+QaijiX68Idfe/gxtAb+WhLOcdyM1h+z3BG\nBLsBUTDmT2DQaw9zFUW5YqlA3wrpRRUk5JUxd5iWwifYw54bh/ixbG8qC8YF4+Vo3epzHU07x+AA\nZ4QQ3DUqiF9O5vDC9f3wdbaB/R/Cpheh340wZD4A1fpqNqZu5Pv479mXsw+d0BHhFM2hk2G8NusO\nru3vh8Eg2RiziYnhnsYgb9SO4RlFUXoeFehbYUuslq9tUpNFO49MCmX1kUz+uyWBv8/q36rznC2v\nIamgnDnR2vDH4AAXjv7tai2NwOEvYN2fIXwG3LiU2LNxfBf/HT8l/URJTQm+9r48NOghZoXMwtXK\nk5HHN7HmWB7X9vfjRGYxeaXVTI30ukQLFEW5EqlA3wqbz+QR5GZLsEf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "airline.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# EWMA\n", "## Exponentially-weighted moving average \n", "\n", "We just showed how to calculate the SMA based on some window.However, basic SMA has some \"weaknesses\".\n", "* Smaller windows will lead to more noise, rather than signal\n", "* It will always lag by the size of the window\n", "* It will never reach to full peak or valley of the data due to the averaging.\n", "* Does not really inform you about possible future behaviour, all it really does is describe trends in your data.\n", "* Extreme historical values can skew your SMA significantly\n", "\n", "To help fix some of these issues, we can use an EWMA (Exponentially-weighted moving average)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "EWMA will allow us to reduce the lag effect from SMA and it will put more weight on values that occured more recently (by applying more weight to the more recent values, thus the name). The amount of weight applied to the most recent values will depend on the actual parameters used in the EWMA and the number of periods given a window size.\n", "[Full details on Mathematics behind this can be found here](http://pandas.pydata.org/pandas-docs/stable/computation.html#exponentially-weighted-windows)\n", "Here is the shorter version of the explanation behind EWMA.\n", "\n", "The formula for EWMA is:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$ y_t = \\frac{\\sum\\limits_{i=0}^t w_i x_{t-i}}{\\sum\\limits_{i=0}^t w_i} $" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Where x_t is the input value, w_i is the applied weight (Note how it can change from i=0 to t), and y_t is the output.\n", "\n", "Now the question is, how to we define the weight term w_i ?\n", "\n", "This depends on the adjust parameter you provide to the .ewm() method.\n", "\n", "When adjust is True (default), weighted averages are calculated using weights:\n", "\n", "### $y_t = \\frac{x_t + (1 - \\alpha)x_{t-1} + (1 - \\alpha)^2 x_{t-2} + ...\n", "+ (1 - \\alpha)^t x_{0}}{1 + (1 - \\alpha) + (1 - \\alpha)^2 + ...\n", "+ (1 - \\alpha)^t}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When adjust=False is specified, moving averages are calculated as:\n", "\n", "### $\\begin{split}y_0 &= x_0 \\\\\n", "y_t &= (1 - \\alpha) y_{t-1} + \\alpha x_t,\\end{split}$\n", "\n", "which is equivalent to using weights:\n", "\n", " \\begin{split}w_i = \\begin{cases}\n", " \\alpha (1 - \\alpha)^i & \\text{if } i < t \\\\\n", " (1 - \\alpha)^i & \\text{if } i = t.\n", "\\end{cases}\\end{split}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When adjust=True we have y0=x0 and from the last representation above we have yt=αxt+(1−α)yt−1, therefore there is an assumption that x0 is not an ordinary value but rather an exponentially weighted moment of the infinite series up to that point.\n", "\n", "One must have 0<α≤1, and while since version 0.18.0 it has been possible to pass α directly, it’s often easier to think about either the span, center of mass (com) or half-life of an EW moment:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\\begin{split}\\alpha =\n", " \\begin{cases}\n", " \\frac{2}{s + 1}, & \\text{for span}\\ s \\geq 1\\\\\n", " \\frac{1}{1 + c}, & \\text{for center of mass}\\ c \\geq 0\\\\\n", " 1 - \\exp^{\\frac{\\log 0.5}{h}}, & \\text{for half-life}\\ h > 0\n", " \\end{cases}\\end{split}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Span corresponds to what is commonly called an “N-day EW moving average”.\n", "* Center of mass has a more physical interpretation and can be thought of in terms of span: c=(s−1)/2\n", "* Half-life is the period of time for the exponential weight to reduce to one half.\n", "* Alpha specifies the smoothing factor directly." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": true }, "outputs": [], "source": [ "airline['EWMA12'] = airline['Thousands of Passengers'].ewm(span=12).mean()" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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PKa9v1gy1lPD8cZrBdwVfS1G1JjGckxQOC+dCbXFbA5Eekhyt3ey8Hr13zJ6g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\nWxA1vMY+X+DfmkFRgXy74yj3jothw8FcAn296eZUMkEppZp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "airline[['Thousands of Passengers','EWMA12']].plot()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Great! That is all for now, let's move on to ARIMA modeling!" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }