{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimating or specifying parameters in state space models\n", "\n", "In this notebook we show how to fix specific values of certain parameters in statsmodels' state space models while estimating others.\n", "\n", "In general, state space models allow users to:\n", "\n", "1. Estimate all parameters by maximum likelihood\n", "2. Fix some parameters and estimate the rest\n", "3. Fix all parameters (so that no parameters are estimated)\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "from importlib import reload\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "\n", "from pandas_datareader.data import DataReader" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To illustrate, we will use the Consumer Price Index for Apparel, which has a time-varying level and a strong seasonal component." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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dmU7hfUMibQQC4QMhGqOxb3gB//1KD94ZtfKet3qCmLT5cHljATbWGLCjZx63P34IkzYvb+zxqUVIRBQuqGbS9JpL2Fq1pUX5sMWTJC5Ymou1iKVEfE5MMVG5FQliAgCq89UIRWKYXmSiU2zULTXSBjARJ4ARiwBTUzdi8aA5QbRV56sRo8GLIA3Mu6GMp2MCwIW1TL1dl0CtmCcYwd7hBVzdUshF70YsHl7PsmGzB5W5Kq4urq5QDZlYxB1fKrEYjW2n5rGh2oDV5dnonOILweOTi+go00Oc4ADZVMQIzdR5D4/Z4Q1FcWW8xq9EnwVdlpQX5ewxOdFSnCy46go0kEtEvLq23QNmrCjLRrZKBgCcoE29ngBTzyaXiLi56ws1aSNtJ6cdEIsoNBfr0FioxZDZjaiAIQlN0/ja893YN2zFt1/pydhuAABsnuA/XeN1AoFAIPxjIKKNQCB8IHzzpVP45O+O4MmDk/jDgQne8/1zzGL+0xsr8OjtK/DqlzchGqOxZ5DvkNhncqG2QMNFqwq1CmQrpVytGk3TTO2ZQESsqUjHzcHSNe2ARiFBVYolfm1cnA2ZmcX+SDy1sTqPb53fUKSBVExxTorDZg8iMZp7P+Z1wo6UA/Mu1BdqOJfLugINZBKRoMHH3qEFhCIxXNPCRhl1iMRoxjAlgRGLO0lcyiViNBSlN/jonHbA6gniY2tKcWFtHsZtXngT0k29wQgG5l1JqZEAYxxSV6DhOUh2TTtAUcCaSibySVEUmoq06Jtbuu4WdwBmVxDNKW0QpGIRmou1SULQ4gqgZ9bFpUYCgFouQa5ahmk7X7Qdn7SjvVTPGcY0ZBBjJ2ccqC/QIEsmRl2hBsFIDFMCcz55cBK7+s24pqUQ03Y/njkyxb+QCfx05xA++puDGEgT4SMQCAQC4f1CRBuBQDjjWNwBvHBiBretMuKKpgJBe35WtLHuhpW5KpQblHh7iC/aek2upBooimKiJL1zzCJ/zhmALxQVjIiV5mRBI5egb25JEHROOdBRquf1EGso1EImFnHRkv45Nwq1CmgUyX1cAEYU1RdqOKHBzp8UaRMQbTRNY2DejYaEqKBULEJTkVZQYB0Zt0MhFXH1d+z8vQltDALhKKbsPtTkJ0caW0t06DE5BW3td/aZIRFRuLg+P6H+bElsnJx2IEYDK8uzea9tK9Ghe8aRNG/PrBOVuSrOZRJgUlMH5lyIRJkIVe8sM39LMd/Rss2oR4/JyYkstnl5omgDgLIcJS/SFo7G0D/nxoqEdNf6Qg0C4RgvckvTNE5OO9BeGo/IxXvyCX1G//jOBNZW5OBXH1+J9VU5+L/dwzxjlUQOjdkQjdF48NX0rR52D5jxzJEpXqSUQCAQCIRMENFGIBDOOH89Mo1wlMa/XVKDthIdpuy+JNMQgBFEBVo5cuKpbwBTu3Rw1Ja0oLW4A7B6gkliCGDEy9C8B+FojDP7EIq0URSFxgQzEl8ogsF5Fy81EmAcJFeW67Fv2Mqld26o5tvrs7SW6HFq1gmaptFrckEtl6AsR5k0X4k+K0m0mV1BOHxhNBQmn0+bUYeeWb7A6pxaRLtRz6U9luUooZKJkyKH41YvYvRSpDBxTncggkmBKNIbffNYV5UDXZaUqz9LTGVkhavQdVpfnQOHL5wURes1uXhpj83FWgQjMYxbGeHEOkc2CYo2HXyhKHetdg9YUKRTJIlbACg3qHhRsSGzG6FoLCmC1xi/vqlibMLmgysQ4QxraguYVg9sdJXFF4pgwubFxppcUBSFezZXw+oJ4cSkcLsDizuAsQUvGgo1ODRmx9/TtCb4/mv9+MaLp3DJI3uShDeBQCB8EJycduC2X79zxlxy021IEd4b7+c6EtFGIBDOKOFoDH85PImL6vJQmatCQzxClrooFuohdlFtHvzhaJLRBiskUhf6TcVahKIxjFg8GWvPACYy1GtyIRiJomuKiSClOkeyXFibh/45F3b2meHwhXFpY3rziTajDk5/GNN2P3pNLjQWaXjRu5p8dZKDJBvNSq2/aynRwRuKYsy6FBnyh6LoNbmwKiHaJRJRaExJOxyOn39tQfL5t5Yw55jauHp0wYOxBS+uaGTqz4p0yemmAHB43I76Ag10WfwoI9vzbv8IU6to94Yw6/CjpYT/NwKWmpsfHrejrkAtGLlsMy4dazASxf5hKy5pyAdFJV/PshwlTE5/krAXiuDVFqghooD+FNHGnmNLXOApZYzQHkz5fA6ZPaDppb8T+1kds/LdQAHg6DjzmX3oIy2oymN676USiqdhXt6YD3cwgj8KpA0TCIRzB6H067ONPxwYx9GJRa6W+3RQKBSw2WxEuJ0mNE3DZrNBoVAsPzgB4h5JIBDOKG8NWGB2BfHQTUxfEjZSMjDn5lwEgxEmonJJSurbBdUGSMUU9g4tcMKgL41oY/t8nZhaxIjFA62CqXcSYnVFDp7YP45TM04cnVgERSFJCCWysSYXj+wYxI9fH4BYROHC2ry058qakRyZsKN/zoXbVvGbNNfkq3F43IZYjIZIRHHmGKkRJNZBsSfurggwAiYSo3nH2lysxfPHZ7g5R8xuiCgmxTSR2gJ1vFbOmdTg+/AY46LFuiFSFOP2yArkYCSKY5N23L6mTPC88zUK1BdocGDEins2V3MRtNRIW02eGtlKKfYMLuCq5kIcGbfjXzYI96upylVBI5dwrpTeUBSXCrg1lhuUoGmmhxwbWe0xOaGSiVFhWDp/hVSMilwVBuaS68sm4umSiS6VdQUaXkSOdZ5sLNLEz1kOlUzM9cNL5fC4DUqZGG1GPTpK9Tg4auONmbJ7EY3RuLatCHKpGG/HW0akClMCgXD2s7PPjPuf7cKbX9mMAu17W3yng6ZpzCz6UZrDdxF+P3iDEezoNQNgfltYJ973i9FoxMzMDNeTjPD+USgUMBr5a4ZMLCvaKIr6PYDrAFhomm6JP/Z9ADcCiAGwALiLpmkTxfzyPApgCwBf/PETwjMTCITzka64M99F8R+HEn0W1HJJkv36iIUx7UiNtKnkEqwuz8FbgxZ8Y0sjAEa0leZkQZsSnanOU6HCoMTfu+cQo2nU5KvTLn7XVDCi5+jEIo5N2tFQqOXNx9JaooNWIcGY1Yt1lTmCkSaWugINZGIRvvq3kwCA9VX8VMrqPDUC4RhmHcwP8YlJxoJfr0wWmDV5aiikjIPiTSsYgXV8SjhFsalYC+9Bpo6tNEeJrd1zaDXqk9oKAAm1cimmIUNmN1QycVIqZ3OxDn98ZwLhaAxdUw4EwjHOrVOIjTW5+MvhSQTCUS6S1pwi2iRiEa5sKsTfT81h75AVoWiM+1ykIhJRaInXyknEFGQSETbU8N8/sVcbJ9pmnWgu1gnUKGrQM5ss2qZsPuSqZUm1d/UFGuwesCS1ZuifYxw+S+PtHCiKQlWeWrDvHsDUHq4qz4ZULEJVrgovnpiFPxRNam0wGhd8VblqbK6j8ffuOQzMu3nfAwKBcPazZ9ACTzCC7afmcNfGyjMy55MHJ/G91/qw498vSps58l7Y2WeGPxzlNu9OF6lUisrKM3OuhPfOu0mP/COAq1Mee4Sm6TaapjsAvAbgv+OPXwOgNv7f3QAeO0PHSSAQzhFGFzwoNyg5Fz+RiEJdgTopTa1/ju1Txrfov7ypAENmD8bii+O+OReai3S8cRRF4Yb2Yhwcs6Fn1iVYz8ZiUMtRlafCoTEbTkwuciJOCLGIwoZqJsqXaoKRikwiwj2bq/DR1UY89dl1uKa1iDeG/eEdWfDAFQhjz9ACrmwu4I2TiEVoLtbh1OxSCsuJSQeqclVJdX/AkjjaP2LFa90mjFu9+MLmasFjbI/XyrFmIABT51VbkJzK2VSkRSjC1AceHLOBooD1lelF26ZaA4KRGI5PLqJ3lhHWOiVf4F7TWghPMIIf7xiAQioS7MPH0mbUoX/OjV39ZlxQZYBSxt9XLI9H09g6uWiMZj4jJXzhU1+gxfSiD/7QUirlpN2bJFYBoK5Qg2iMToqiDc67UZdyjaryVIKRtkVvCAPzbqyLO2eyUbyJFBMUVvBV5alwUTyCK2S8QyAQzn66ppl79bae+TMyXyxG4/cHxhGN0Xipc+aMzPlS5yxK9Fm4oqkAp2ZJDe25zrKijabpvQDsKY8lbl2qALDJrTcCeJJmOARAT1EUfxVDIBDOWXpmnQhH0/erGrF4UJMioBqKGBdBNg++f84FmUTES+cDgKtbCgEA23vm4Q6EMWHzChpXAMD17cWgaaaX2XK7kmvKc7BveAHeUJRryJ2OSxvyQVHAZY18cZXKf1xZjx/f2o5N8V5rqdQXMj3IXu0yYWevGaFIDNe3FwuO7SjVo3vGiUA4CpqmcWJqUdC9saFQg45SPb67tRcPb+tHfYGG64+WyqqKHPhC0aQauCGzm5eeyRq97B1awMFRG5qLtYIijGVdpQESEYUnD06gc2qRlxrJsqE6FxqFBGMLXqyvMnANzoVoM+oRisYwbfenFcy5ajnyNXIuJXNswYNAOCb4/jX5atA0kqJjUzYfJ/xY2GvB1l0yDp8u3jWqylXD5PQjEE52fmT767GfK/ZzPW5NFm1jC14UaOXQKKQojJus7CWijUA45/CHohiYd0Mjl+DohB0Wd+C059wzZMGkzQddlhQvd5oEXX/fCw5fCPtHrLixoxhtJTrMOvywe0OnfZwfFEfG7Vj38K4zci3PV963EQlFUQ9RFDUN4ONYirSVAJhOGDYTf4xAIJwH7BtewHX/tx9f+9tJwULkcDSGSZuPJ6AaCjVwBSKYdzE3486pRTQXayER829BJfostJfq8XrPPP5wYAI0vWR8kUptgYZbWGeKtAHA6opssL+BmSJtAHDrKiN23r/5jKSn6LKkuGtjBV7umsWv3x6FMTsryZo+kY01TPTqxOQiBs1u2L0hrBYQbRKxCH/6zFrUF2pgdgXxpUtreKmBLImpoQDT1NzmDaGuIFmQ1OSrsSlez3diahEXCKR6JqKSS/DxdWXY0WuGyRngjD1SkUlEuCIuKJerp2Dr+oDMUc72Uj0nlNjUzFYj//1ZYxbWqCYYiWLOFeBF2ioMKkjFS/WGC+4gFn1hvmjLU4Gm+WJsJt6MnRVrFQZh0Ta64EFV7tJnanNdHo5O2JP64xEIhLMftj3JFy6pBk2Dqxs7Hf5wYAIFWjm+dW0jZh1+HJtcXP5FGRhdYGpoV1dkc/XXZ3O07fnj0zC7gklGZIRk3rdoo2n6mzRNlwL4C4AvxR8WWjUIbhVQFHU3RVHHKIo6RgoaCYRzg8f3jkEiovBylwm/2jPKe37S5kMkRvMEFGtv32dywROM4OSMM6Mo2NJSiFOzTvzirRFc21qU1jQEAGewkerGmMraeOqaMTsLRbqsjGNFIuqMCDaWf9tcA41cgmGLB9e3F6etvVsbj17tH7Fi+6l5UBTSulfqsqT4y2fX41cfX4lrBdIyWYp0WSjRZ+HYBJMwwRpupF4viqLwyztXojRbiXCUzljPxvLdG1tw4L8uxY9vbcMn1gkbjADAbatKoZKJcfkykUtjdhZyVDLU5KszFuK3G3UYW/DC6Q+jc8oBhVTEa5QOMOJJLKIwbGHOeWbRD5peqotjkUlEqMpVYyh+bfq5a5Qc4a2KN1lPTZE0OfyQiinkqeUAGEFboJUniTaaZtIvq/OXjnNDTS7CUaZvXDomrN4zlipFIBDODF1xJ8aPri5FdZ4K29O0+Hi3zDsD2DdsxZ1ry7GltQhZUjFe6pxNOz4QjuLTfziCh7f1p3VynFlkWqOUZiu5dig9Z0i0BcJR7Bs+c2v3aIzGm/1Mb84zKSynbD7c/2xXxv6aLMFINKmM4GzkTFj+Pw3glvj/zwAoTXjOCMAk9CKaph+naXo1TdOr8/JOz82GQCB88PTPubBv2Ir7r6jDDe3F+Mkbg5hz+pPGpLPeby3RQSkTY1e/BUcn7IjGMouCa1oYESKigG9sach4XJ/dVIm/3XPBsm5bZTlKGLOzsLFaOGr3QaJTSvFvl9SAooAbO4RTIwFALZdgRZkeB0aseL1nHmsqcpCvSe9KplNKsaW1KG2UjWVtZQ6OTiyCpmlOtKVG2tj5/vDpNfjspkqurm85Sq4t9tQAACAASURBVPRZ+Ojq0oyplBdUG9D7vauX/RtRFIVvbmnEA8v8zdvjkcqT0w680WvGhbV5glFbmUSECoOS+1xOxZtyp4o2gKlrY23/WdOc1EgbG0kbSzEjmXP4UaBVJP0dKgyqJNFm84bg9IeTIm3s/CNpzE0A4Fd7RnD/syd570kgED48OqcXYczOQq5ajk01ueiecZ6WDT6bmr2uKgcquQSXNxVgZ59ZcE6apvHtl3vw1uACHt87JriBCixlAJRkZ0GXJUW5QXlGzEgA4KG/9+OTvztyxkRg59QibN4QKOrMCUsAeOztUbzUOYuT05nndPrCuPp/9+FzTx5b9u8YjdF4J97u5h/N+xJtFEXVJvzzBgAD8f9/FcCnKIb1AJw0TZ/e9gOBQDgr+O2+MShlYnx8XRk+f2EVaJrJQU8k0Wghkax4lGV7zxz2DVkhFVNYXZ6+rqzMoMTHVpfiW9c2wZideaEvk2Q2t2ChKAovfmEDvn1907JjPwjuvrAKu/5jM6+pdioba3JxcsaJQbMb18Tr+06X1RXZsHqCmLT5MGR2I0clS9seodygwreva8pYe/ZBcssqIy5tyByRa4v3n3vy4CTmXYGM16kmX831sZuMG4OU5fCjcvUFasws+uEJRtA55UCJPgvZKQYwSpkExTpFUi89ADA5AijWJ0dvq/JUmEgYx0bnqhM2NPI1cmgUEgyb0wsy1uzguWOZo200TWNnnxlO35lpoEsgENLTNeVAR3zzqCpPDU8wggV3UHAsTdP43f5xwTYgLOwGD5sxsKpMD6snCLOLP+fzx2fwt+Mz+PKlNbipoxiP7BgUrI2dtjNOuayhU0uJDr1zpy+Ijozb8edDkwCAQ2Ppz+m9sLPPDKmYwpaWIpyaPT0BzOIKhPFyPFo5aRNu1QIwBjD3P9eFcasXewYXsKM3s7HMs0encecTh8+ouHy3LCvaKIp6BsBBAPUURc1QFPVZAP9DUVQPRVHdAK4EcF98+DYAYwBGAPwWwL99MIdNIBDOJE5fGGZX+uLfcDSGbafmcGNHCfRKGRqLNFDJxLzc81GLB4VahWDz5Bvai+HwhfH0kUmsKM1OskIX4ke3tuET69On3L0f8rWKJKv3fyQiEbVs3R0AbEqo37v6DIk2VtQenbBj0OxGfYHmnO4NplNKUZmrwq5+5oc+k2FMbb4GkzYfgpEoJu0+KGViQcHKRh6HzG6mIL5SeCNAyPbf5PSjWJccEa0wqLjoGpCwoZGQxklRFGrz1Vz6ZiquQBjDFg9EFLNQS2cARNM0frxjEJ9/8hh+tGNAcAyBQHh3vDVowUia7yQAWNwBmJwBTrRxEXgrXxjEYjS+/UoPvv9aH77wl+OweoSF3bjVC5VMjDwNk2LdkiGd8bXuOVTnqXD/5XX40a1tyFXL8MyRKd64mUU/ShI2PSsMSpgcgbQNwUcsbnzhqeN4+jB/LpZINIb/eqEbxmwm7f7QmD3t2PfCzj4z1lcZsL7aAIcvzEUJ0+ENRpZtbP7SiVn4w1FQFDARz7IQ4s+HJrF7wIL/vq4J9QUa/ODv/TyzqURe7mKEYLr2Lx8k78Y98g6apotompbSNG2kafp3NE3fQtN0S9z2/3qapmfjY2mapr9I03Q1TdOtNE0f++BPgUAgnC73PduJLY/uS+ss1T/nQiAcw8Z43yyJWISV5dk4OsGPtKWrBbuwLhdahQSBcAzr30W91D8r7aV6Lk1yudq7d0tNnhq6LCl+vnsY/XOuZev/zgXa48YjG2tyM/bSqy1QIxqjMWH1YcrmQ1mOUlCwshHQ7afmYPOGsK4qnWhjbP/ZneBojMa8M4CilEgbu5Bjo23DZg8UUhFKUsbV5mu49M1UuqedoGngUxdUwOoJcjUfqTy+dwyP7RmFRiHB9lNzGd1dCQRCeqbtPnzuT8dw528PpxVYbJo1GzVP5xYLMOnNTx2awq2rjPAFo3jw1V7BOcesXlTmqbh7U1OxFhQlXN81ZHajzaiHSERBLhHjurZivDlggSuQHGWfXvShNHvpflOky0I0RgtGBF89acLV/7sP23vm8bOdQ2nvISMLHoxZvbjvslpsrDHg6IT9tF0uTQ4/xqxeXNqQzxmm9JqEo1ivdM1iww/fRPN3duA/X+hOOydN0/jzoUm0l+pRlavKGGl7sXMWbUYdPr2xAt+5oQkzi368cEI4s2HW4ecyjKYyCMEPijNR00YgEM5h5p0B7B1agM0bwve2Cv+gHI+7WCUagqwuz8Gg2c1FEmiaxuiCF9V5/NQzAJBLxFzkaAMRbWmRikX4+R0d+P6NLWdsTpGIwk9va4dBJUcgHMto7HKu0GZkdrm3tGTuKsP1ybN4MGn3CdazAYwJSpZUzKUhrk3To64qV5WUCmX1BBGJ0bz0yNSFXK/JicYiLa/+sCZfDasnhEWBDZOuaeZ7d+9ltSjQyrlUn1SePz6DtZU5+Mlt7Vj0hXHgQ6q3IBDOdX6zdxQiCnD4w/jKcycFBcmsI14rFv/Ol+izIJOIeHWnNE3juWMzuLA2F4/c2oYvXVqD17rnBL+fYynOskqZBNV5ap54cfrCmHMGkjbebuwoRigSw+sJ/eKiMRomhz+pjpg9Xvb4E3npxAyK9Vn48a1tsHqC2D0gvEE0Hk/zbizSYl2lAU5/mKsFTsexCTv+dmwar3WbknpmsrD1fM3FOjQUaiARUWnNSJ48OAmKorC6PBvbTs2ljYjNLPoxYvHglpUlqDCo0kbarJ4gumccuLyxABRF4YIqA3LVMnROCZtDbT3J2HRkScWYtBPRRiAQ/sG80jWLGA18ZEUJXu4y4S2Bm/WJKQeKdYqkyM+aimzQNHBiillYzrsCy/ZLu/uiKtyxtgwry8590fBBcmlDQVoL/ffL5U0FePmLG9Hz3atwXdu53z7z2rYi3LbKiGtaM6eQVuepQVHAm/1mTNn5PdpY2CbwTn8Y+Ro5KtKIu6p4iutofPHCLoBS0yPLDEpIxRT65lyIxWj0mVzCveQKlpqvp9I55UB1HtNcfUVpNoYEUrZomsbMoh+tJTpcXJ8HrUKCrSdJKTmBkEj3jAO3P34Qr55M3//M4grguWMzuHWVEd++thFvDy3gdYH6pjknU0pQFP/Oi0QUKlOMhwDmHjFl9+Gq5kJQFIV7NldDlyXFC8eToziBcBSzDj+vb2lriY4nXth7QH2CkVRHqR7lBiVe7Vry/TO7AghHaRgTIm3sxpJJQLSNLnjRatTh5hUlyNfI8ezRad4YABiPR6wqclWcI3NqbXviMdz95DHc+uuD+Nrz3fjS0514Kl4LlwibaVCbr4ZCKkZtgQanZl28cU5/GF3TDnxkRQnuv6IOvlAUewaFHSzZv0VdgQZlBiUmbV7BOrm3BxdA00stZiiKQnOxLm292itdJqwo06OlREsibQQC4R8LTdN48cQsVpTp8aNb2lCizxK8qZ6YXMSKlOhMR5keYhHFWcmfmGR2pjKJjZp8DX54cytkEnLr+bBQyyXndD0bS4FWgUduaxesn0xEIRWjLEeJFztnARoZXUvZurZ1VYa014iz/bcyC405B7OAS420ySVitBv1ODJux5TdB3cwgpYSvglNbXyTI9WMhKZpdE07sCK+wVFuUGLG7ufVcdi9IfjDURizs7ho9hu98xlrMgiEfzaePz6DQ2N23PtMJ778107BMX98ZwKRaAz/elE17lxXDrVcIhgVMzn80CgkSfeeylwVr6btzX6mdxsrCGQSEa5qLsAbfeak7+eU3Qea5ht4NRdrYXYFk5pNc+6/CZE2iqJwY3sx3hm1cimd0/Ylu3+WIj0jMlNdnwPhKGYWfajOU0MiFuG21UbsGbRg3smvcx9f8CJPI4daLoExOwvFOkVa0fa9rX3YO7yAr11Vj71fuwRVuSocGOVfzyGzG7lqOWf81FKsRZ+JL9oOjtoQjdG4sDYX6ypzkK2UYnuP8AZVorFLhUEFXyiKBYF0192DFuRp5GgqWro3t5boMGzx8O6hVk8Q/XMuXN1ciLIcFSbt6VMu3wvv5V5NVk4EwnmMJYO5CAD0zbkwaHbj5pVGyCQiXFyfh0NjtqR89jmnH7MOP1alRMeUMglairXcDfvwuA1KmfiMR4gIhNPlhze34qe3tePoty7HJfXpm3azKUdr05iQAECxLgsKqYhzgzRxkTZ+/eG6qhycmnVy35FmgUhbsS4LSpmYZ0YybffD5g1hRRmTBlpmUCIUjXEN6lnYgn3WZfXqlkK44w6Y6TA5/EmpVATC+c7BURsurM3FzStLsLvfIhhtOzG1iI5SPSpymf6OqwTqtgHm+5Nam1qVp8KUzZf02/nmgAWNRdqkDZ1r24rhCUaS3B7Ze4lQpA0AehOiTkNmNzRyCS+yv7k+DzF6qZRhOn5fSEyP1Cqk0MglMDmS7yGTNh9iNLjShttWlSJGA6918zt2Tdi83HFSFIU1lTk4Nsm/RoFwFLsHLLhlpRFfvKQGZQYlNtbk4si4nVcvN2zxcJtXABPFs3qCvFTK/SMLUMnEWFGWDYlYhKuaC/Fmv0VQ9CQau7Ap8ZMpkbFINIa9Qwu4pD4vKW29pUSLaIzGwHzyPXk2fk2r8tQoNyhhdgVPe3PMF4pgzUO78L+7ht7VeCLaCITzlM6pRaz74Zt4/nh6q3B2F3FLvNZsU00uvKEoZzMOLEXQhOqgLqzNw/HJRSy4gzgybseq8mxIBfplEQgfJhuqc3HLKmNGwxJ2XIFWjkvq0/cOFYkoVBhUXP2KyemHSiaGNovvSrqu0oBojMafDk5AKqYEe+OxrqKpZiR9cWtuduFWHm9TkFpQvyTamIVhbT7zHlMZdoF//uYw7nnqOLdrTyCczyy4gxi2eLChOheryrPhD0cxJ7ChOW71cunPALN5M2T28OpNhVp8VOaqEInR3PfR4Qvh+OQiLmtI3iTaUG2AXinF3xOacbNRoVTRJtQQe2DejbpCvvtvc7EOUjHFbdZM232gKKBYnyzuivQKXnok64LIuhtX5KpQnafC3mF+VGzc6kVlQop5bb4aZleQ17x6/7AV/nAUVzUvpa9vqDbAF4qie2ZpfUHTNEbMHtQWLF139l4260gWWfuGrbig2sBl6lzTWgRPMIJ9aY6zIpcxdqkwJJtCsXROO+AORHgbeezGc2pqKrdBp1dwQnDqNOvaBufdcAci+Pmbw1ypSSbI6opAOE95fO8YaJpZoEXSOEFN2/3QZUlhUDM2wxuqc0FRzA2X5fjkIhRSEZqK+ald17cXI0YDTx+ewsC8O61NOoFwLtBUrMXhBy5ftjdgdZ6aS4UyOfwo0mcJplOuLM+GWESh18Q4dqZLC67N54s2tnC+Ir6Q4xYJKbvFM4vMv0viC50inQISEZV2MUHTNLfIeWLfWMbzJBDOB9heYhdUGzhhkmoa4g1GYHYFk4RTYquURExOP1fPxsKKvfF42vSewQVEYzQuSRFtUrEIVzcXYldCiuTYggd5Gjkv1Vstl6AmX41j8egZTdMYMrsFN38UUjGainXcwn9m0Y8CjQJySXJrnWJ9Fkwp6ZHstUg894vq8nB4zJYUSXIFwrB6QqhMSOMsiwui1PvNjt55aBQSrK9aSkdfF///xH51ZlcQ7mAEtQnnxEYxE23/J21eTNp8uLB2aUNtQ7UBGoUEO/v4WQOJEcGS7CyIRRQv0jYwx0QwV6RkEZXos6BXStGbItoSDWjKcoSjd+8VduNMmyXFV547uWzkjog2AuE8ZNLmxeu982gv1WPK7sOrJ/lpDgBjCZxYqKxTStFWokvK4z86YUebUS8YQasv1KCuQI3H3h4BkN5xj0A4n6jKU2HazvR+m3Pyd91Z1HIJt2srZELCUlOgxpwzAHeCZfekzQeDSgZtfCHHirFUx7KZRWbjhR0nEYtQkp2FKbtwn6NJmw+zDj9y1XK80mVaNoWaQDjXOThmY76LxVqubmw0ZZMktbk1ALQZdZBJREk1W75QBA5fmPedZ1/Hpjq+3DWLEn0WVsR7uSVydUshvKEoJ17GrV5elI1lY7UBR8btCEaiWHAH4fCFUV8gbPa1skyP7hkHwtEYY/efw78vFeuzuDpcltEFL4p1CqgSepheVJuHYCSWJFgnBCKCrGHThHXpvhSJxrCr34xLG/KTNqpyVDI0FmnxToJoY50jE9Mj2U2zRNF2OP43YNsOAYwAvrg+H7sHktNdQ5EYpu0+7jilYhGM2VmYSMlSmLT5IJeIkB/vjcdCURRaS3ToMaVG2gJQysTQZUk5QyuhVgKuQBhv9M7jpc4ZeIMR3vOJDJrdUMrE+J+bWzFu9Qqm4yZCRBuBcB7y+/3jkIgoPP7JVWgo1OAXb40I5vBP231JhcoAsKk2N542EIY7EEavyYn1GSJoN7QXIxCOQS4Rob2U1LMRzn+q8lSI0UzUy+TgN9ZOhI0+N2eo9WRTGhOjbZM2L8oSHCwl8YVH6o72TMrGCwCU5SjTRtr2xzdkfnJbG8KxGP50cCLtcREI5wOHxmxYW5kDiViEPLUcGrmEZxrCpSgmRJEUUjE6jPqkhTRbD5Za05atkiFbKcWxCaZcYN+wFTd2FPNafADA+ioDsqRi7B6wwBuMoG/OleQGmcim2jz4w1GcmHRwNVZ1afpsrizLRiAcw5FxO/pNLi4tMJFinQI2bygpojO64ElKCwWYelyZWJRUeyeUxsmmbSemYx+fXMSiL5yUGsmyodqAY5OL3PsPJzhHsuRr5JCKqSTR1jvrhEomTmqLAACXN+bD6gmhKyHlcnqRqdFLOk6DihcVm7QzfTuF/kbNxToMzrsRjCxdJ5PDj+J4VkW2kqkPTL3Pdk07sOr7O3H3n4/j/mdPYv3Db+KvAo3PWQbn3agt0GBdfMO7f45vwJIIEW0EwnnIKydN2NJahAKtAp+7sApjC17erhFrFZ66G7exJhfRGI0DIzYcm1xEjF5KaxDiurZiAMCKMj0vFYNAOB9hFw57h62wekJpI20AcHF9HiiKaZGRDrZNxnCSaPPxFl1lBpVAeqSfJ9pKc5Sce1wqB0asKNFnYXNdHi6oMuDtIWHLbALhfMDiDmBswYsL4r9hFEWhKl/N1XGxjFu9oCjwvnNrK3PQY3JxERO2rik1PRIAPr6uHK/3zuM7r/YgGqPxkRUlgsekkIqxqTYXuwcs2HZqDr5QFNe3FwuOXVeVA7GIwv6RBbx60gSFVCRoaASAMy36+vPd8IQi+PTGSt6YVNt/mqYxJtBfVSmTYHVFNvYOLWXdjC0w16gswdxEp5RClyVN6oPWPcOsNdYLrBsuqDIgFIlxdfMjFjdyVDKuRANg6nyL9VlJ/eR6TC40F+t4AuviunyIRRR29Zm5x9hechVJ4lLJi7RNZ+jb2VqiQzhKY2Buqe7X5PRz14+iqHgrgeT7LGPkRuPPn12Lv91zAeoLNfju1r4kB9BEBufdqC9QI1slQ5FOIeiamQgRbQTCeYYrEIbDF+YsbDfXMTng+1Osixc8QQQjMV79zpqKHOSq5XjhxAwOj9khEVEZ+6pV5Kpw90VVuGsD/weCQDgfYVOsfritH2q5BDd1CC/OAKZO9Og3L0dDIb8mlKU0m2nOy6ZsBSNRmJx+3oKiPEeZlI7DbryU6JPHleUoYfeGktItAabh7jujNmysYVoa1OarMWH1CfYveq/MLPrwSpdw828C4cOCXXS3GpeETnWuiktjZBm3euPOsMkbjyvL9YjGaPTGF9OsXb7QRs0XL6lBiT4L207No6VEm1SnlcqlDfmYdfjx6JvDqDAo027qaBVSdJTqsfXkHF7qnMUda8vSGiqV6LOQr5Fj1uHHRzpKBOvQ2V6rbK85izsITzDCi7QBTF3boNkNczyFesLmRYmef40qDMqkzaTRBQ8MKhly4hb+iaypyAFFAUfj6Y5D5mTnSBZjdhZXrxuN97lsFmiZolNKsbYiB7v6l0QbK84SU12N2VlwByJw+pl7Ik3TmLL7UJYjnJa6spwRwKwbJ8B3DS038DMa+udcKNYpcGFtHtZU5OCR29oRisbwy90jvPeweoKweUOoj/82NBZp0T+X2RyKiDYC4TwjtW9UnkaOhkINr9/MtJ21BE7+8ZGKRbh1lRG7ByzY0TuPNqMOWbLMEbQHtjTi6pbMTY4JhPMFjUKKPI0ckRiNh29uTUpjFCJXLc/4vEQsQlWuiou0Tdv9oGn+rn+5QQlXIAKHj3GzS+zRlgi7E566oOgzueD0h7GxJhcAkz7kCUZg9SS7470ffrt3DPf9tYvn0CbEmRCJBMK7IdUZEWA2XeacgaR6ozGrl9cnDeA7Cc46AqAooFAg0pYlE+PBG5oBALesNGY8LtaxcGbRj1tXGTP2ztxUk4spuw8iCrj7oqq04yiKaVMgE4vwH1fWCY5hRQcbxWI3iqoFRNvGauY+wRq5jC0I196VGZJ7lo1YPKgWEGIAI7LqCzQ4MmGH0x9G94wDHQJ1f0a9kkuPHLd64A9H09YFX95UgCGzh8suGLN6oVdKoVcuiUZ2c5q17V/wBOELRVEmUPcHMOK2RJ/FibZAOAqrJ4SSBDfOshwVZhZ9Sb0z++dcaEzo+VaZq8JHV5fi6SNTvOwH1oSkIZ7u2lSkxUhKBDgVItoIhPOMJVvapZvRpppcHJ1YTMpjZ3exUmvaAOBja0oRjdEYt3ozpkYSCP+s3LLSiHs2V+OGNGlN75XaAg3Xq42NpqWKwVTHslS7/9RxvEVCvOi/3cgsktj0ofF3IbSWoyueEiXU2ymReWcAmx/Zg8f2jC47p80TJOmbZzk0TS9rtvBhMrrggVYhQa56aQFfzTk9Mp97JkXQIyhI8jUKFGjlOBWvmTI5/PGaK+Hl8xVNBXjlixvxyfXlGY+rUKdAS4kWFAXcvIzAu7CWEU+3rirlImXpeGBLI5763Lq0DrgFOjkoamlztzOeplhXyBdZTcVaaOQSHBqzwekLo2/OhTYjXzhVGJSYXfQjFIkxFv4LHkERyLK2MgcnJhexs8+McJTGlQK1byXZWVhwM33QeuJ96oQibQC4Fi3svWJCwNilJDtZrLKRwXKBuj+WVeXZODZpB03TguuqcoMS4ejSc4FwFKML3iTRBgD3XVYLqViELz19Iqn3HNcoPR6RbSzSJglAIYhoIxDOMxJtaVk21uYilOIExS74SrL5PwKVuSqsr2IMFIiNP4HA57+uacB/XdNwxuaryVNjZtEPXyiyZPfPi7TFHcvsqaItRdyl6SE0YfVCLKK47zxbmycUHaNpGrv6zPjEE4fx1qAl47EHI1H0x9PHtp6cSzsuGqPx7892Ysruw0/fGFy2fuPxfWP4l98fSeobKQRN0xixeE670S3hvfP0kSmsfWjXWetCOmLxoCZfnRTJYlMB2SiczRuCOxBJ6+DYWqLjIm1zCXVN6Wgv1UPyLvqV3ndZHb52Vf2y860sy8aD1zfha1fVLztnaY4SazP8ZsslYuSp5VwK4a5+M9qMOuRr+JFDsYjC2socHBqzY8+QBdEYjcsaC3jjynKUiNHM2sPmDcHhC3N1ukKsqciBNxTFL3YPI18jF3TYZDeiTA4/ek1OyCUi1KQRgpW5KpTos7BveAG+UARd0w6uPCR1Pnazmr03ZsqSWF2RDbMriJlFP2dAkyraEucasXgQjdE80VaoU+DR21ege9aJ+/7ayZnCDc67YVDJkBd3r2wsSp9Oy0JEG4FwnmFy+CERUdyNAADWVuRAKqaS6tqm7T7kqmVQyvhNgQHgXzdXo75Aw/WqIRAIHxy1BWrQNJOCNGnzQqOQIFuZXLvCRtBYkZXao41Fq5BCr5TyRNu4zYvS7CwuSlCsV0AqpnhOegDw36/04nNPHsP+ESt++sZgxpTGgTk3QtEY1lflYNDsTtu0+zd7R3FozI5vbmmEXinF1184mbaHJACcjIu1H20fSPv+r5404ZKf7MHlP3sbP9zWn3au98OpGSdXA0PgQ9M0nnxnEt5QFC92np31jKMLXl7Up9ygBEUxzwHpm1uztJToMGb1whOMYMruQ/Ey0a53yxVNBfi3i2uWHScSUbhrY6Vgjdj7YVNtLnb2mTFh9aJr2oHLBYQYy/oqA8atXvzl8BRy1TJ0GPkCK9H+nnXAzSTaWFE5YfPhquZCQffGRNv/nlkXGoq0aYUwRVG4qC4X74zYsKN3Hr5QlDNIYzGoZFBIRVx65KSNaT6emqWQyKpyps7w+OQiF01Lrmljz5u5z7LOjw0C4uuKpgJ8c0sj3ugzY88QswnWPetM6rlXblBBuUwpChFtBMJ5BtPsVwFxwo1QJZdgRVl2Ul3b9KIPJRmaCF9Sn48d91+U1LuFQCB8MLDF+CMWDybizpGpdS5ZMjHKcpRcmuPoggc5KpmgMQFj+5/cq23S5k1KB5KIRSjLUfIibTRNY9upOVzRVIAHr29Cz6yLS6MSojueOvaNaxohooCtafpC/r17DmsrcvC5CyvxrWuZeQ8k9GxKJBaj0TPrgkElw8ExG9cQPJUn9o0hHKWxrjIHzx6bht17+vV5AGB2BXDzYwfw73/tXHbss0eZaJPnLE4TfC8EI1F8++Ue7FkmwnpyxolBsxsyiQjPHZs+62oVnf4wFtxBXn2VQipGQ6EWbw1YQNM053aYaifP0lqiA00Df9g/jmm7HxdUn9slA59cXw5PMIL7n+sCTSOjaGPP9ci4HZc25AsKLLZX26TN965EW4FWwUWphNoCAEsbUVN2H3pMTrQImKokcmFtHtzBCH6yYwiFWgUvQ4iikh0pp+w+FGn5zccTaSjUQi2X4NikHbMOPyiKOXaWQq0CMrGIq+frn3NDIRUJtloAgE9dUIEclQwvHJ9Fr8mJ/jkXrmxeuvZiEYX6NO0cWIhoIxDOMdyBMBYzLExMjoDgTuD6KgP6TC7OUW5m0Y/SDLtMBALhH0e5QQWJiMKwxY0pmzetFXVDWTXmWgAAIABJREFUoQYD8R3dXpMLzWkWM6m2/zRNY8Lq40UTKnNVvJo2s4txNdtUk4vbVpdCI5fgyXcm0h5717QTuWoZ2ow6rC7Pwb4RYYFlcvhRW8CkqrFGDOn6Ek3YmMjGf1xZB2N2Fn67b0xw3OyiHxfV5eL7N7UgEI7hqUOTaY8TYARJatsEIZ4+PIVwlMZbgwvYPWDOOPZP70zC4g5i+6n0qaE0TWNH7zyu+n978fTh9H2bPmxiMRpf+1s3/nxoEj/4e39GIfbcsWkopCL859UNGFvw4sTUYtqxHwZCJiQsH19XhlOzThwet+MPB8bRUaoXbEYNMKINAH6+exi5ahluXZW5Bu1sp6NUj5YSLTqnHCjRZ2VMy2ss0kKjYDZuhVIjAcbsLEsqxoTNi9EFD5QyMYq06XtXAkydfa5ahnVVwpk8BRo5JCIK/7N9AO5ARLB9QCIbqg0QUUyK5g1p+uMZs5fMTVL7YAohFlFYUabHgREbhi1u5GvkSc3CxSIKxpws7n7SP+dCfaE2acM8EZlEhBvai7Gz34zfvD0GmUTEawuRmlqZChFtBMI5xn+9eAoXPfIWemadgs/PptjSsqypyEaMBjqnHIjGmOLZ0pzMNy0CgfCPQSYRoSJXhcf2jGLClr5/UEOhBuNWL9yBMIbNHkFbb4CJtM0s+rj0Q6snBE8wwpu3MleFCZuXq7MAwN1bWkq0UMkluGWVEdtOzcPqCQq+18kZB9qNeqaNQIFasEbOF4pg0RfmdtB1SimKdIq0qZRsDdGq8mysrzJgyMwf5wtFYPOGYMxWoq5Ag4vr8/DkwYmMtW2Pvz2Gy362J6NwC0djeObIFDbV5KIqT4Xvv9af1GQ3kf45F/riwvPFE+lTBH+2cwj/+ufjGLa48as9I0nX+2zisbdH8epJE9ZW5GDE4sHRCWEh5g9FsbXLhC0tRbh9TSmUMjGePTp9Ro7B4g7gqUOTp32NRjNEfW5eWQKNQoIvP9OJmUU/7r2sJq2DY75WgXyNHOEojbs2VPAs7881KIrijFIub8zP6FwpFlFYV5kDmUTEGaIIzddeqsPWkyacmHKgKk8lKJoSeWBLI1778oVpDV0kYhFKc5QIRWL4wU0tuK6tKON8eqUMbfHUzRs7hM2hSpIibX6uMXgmbl1lxKTNi22n5gVrD5k2LEzblP55F5qWqUu7ZaURoUgMr5404drWoiSHS/b9MkFEG4FwDkHTNA6O2uAORPCJ3x3mLXgi0RjmXQHBm8uKsmyIKODYhB1zTj/CUTpjPjeBQPjH8t/XNeHzF1bhCxdX4461ZYJjGoq0iNHA9p55hKIxXsE9S6VBhXCU5hYprCNlRUqkrSJXhWAkhrkEI4kekxMUtbTre/PKEoSiMc76OxF3IIzRBQ/a42YCFQYVnH5+NgBbS5K4odRQqEkbaeuecUIhZcwHKgxKmF3BJOc1ALw6k3/ZUAGrJ4SDaVIuAWD3oAXhKI3H3ub3TWLZ0TsPizuIz2yqwDeuacS41ZvUZDiRlzpnIRFRuGtDBQ6O2bg6Q6E511fl4Gcf7cDMop/XN/N02H5q7l05gL41aMEnnjicsU5vZ58Zq8qz8cfPrIFGIcFfDgtHLvvnXXAHI7i6pRAquQSXNxZgz6Cw0+ekzYvf7h3D97b2vato3KO7hvGtl3vwt+OZRWA0RuPf/9qJNQ/tQut3duBwyudzdMELqZgSzChRyiS4fU0pFtxBNBdruchvOtqMeihlYnxiGVfIc4Ub2ktw84qSd3U+/3l1A379iZVp698B4NvXNWHRF8bJaUdaw5BEVHKJYNuERH5550psu28TPrG+PKOwZPnk+nJc11aU9p5ozM6C3RvCvDMAqye4bKQNAG7sKMHzX9iANqMOF9bwRWu5QYUpuw+jC144fGGuRUQ6Wkq0qCtgrs/ta0p5z2fqiQsQ0UYgnFNM2/2we0O4Z3M1YjEav9mbbJttcQcRjdGCok0tl6CpWIujE4vYfmoewFKhLYFA+PC5qC4P39jSiP+8uiGtZTdb8/DiiRkASJseWZmXbOfPmS0Y+OmRQLKDZM+sC9V5am6R1lCohVRMcdbbifSZXKDppebFrCicsCWLCCFX2/pCLUYXPAgLmJGcmnGiKW4+wNbhpRqrpDrgsmls6QSMK8AsKlUyMZ4/PsMdUyovd86iRJ+FzXX5XE2PUKQvGqPxcucsLmnIx2c3VQIAXuni1/OFozGMW71YWZaNa1oLka2U4pkjmVMkRyxufG9rH3yhzHVyw2Y3vvCXE/j2yz0ZxwUjUXzrpR7sH7Hi/+0cEhxD0zRGLR40FWmhlElw84oSbD81L1gnyFrGs9kabUYdLO6gYDT2u1v78NC2fvz+wDi++rfM5jOeYAQvx01Nfrh9IGON4tOHJ/FyFxMVBAXeNR2xeFBhUKU1sPjUBRXIVcvx1avqlxUF376OsdJPjYycq2TJxPjZxzoyNgBnqS3Q4NKG9HVvANBcrON6yGWqZ3svNBVr/3979x0nWVXmf/xzqnPOOUz35JxhBhyGQRjJICAioCKroquuuurumnbdn6676Jp1xUUEFAPqChIUJDNkmJyY0BM759xdHc/vj6pbU7F7QvdM9/T3/XrNa3pu3bp9q8901X3uec7zMDN39PNz3LCimJ/csjziWDo3qe975RDAca9NXF6awaOfWsPn3hVavbM0M5GuvkH+sNFzg2G04N8Ywz+8cxbXLCkcscpnJAraRCaRLZWeu5TXLCnknLJMdlQFpkge6yUS/g7WymmZbKls5YHXj3BuWSZz80fOnxaRiaUsK4m4aBevH2whPsZFeYTiCeVBPdgONweW+w/e72BA0Ba48D822sWc/BR21YSmZDuBlBMMlmcn+r6fP1/Q5vf95xWkMDBkOdgYuO/QsGVnTbsv3clJ6Qw+ZnCfuqykWFLiokP2c7x+oJlhC99490IA7n4xfK+4oy09LCzyrE1JjoumKD0hbNC2o7qdhs4+rllSSElmIiunZfDEztB1bUeauxkYsszKSyYuOooblhfz9O56GjvDp5sC/OLlw9z7yiE+/uvN9A9GDnLu8r6Glyuawp6j44HXjlDd1suKaRn86rXDYdstNHb20dk36LvovnFlCf1Dwzy/J7QgSW2752df4J0tcdJ0wx13Z3U71y0r4q5bl3OwsTtsYOt4ZGs13f1D3Hn9Irrcg/z33/aE3a++w823n9zLmpnZ/OSWZVy5qICnd9cHzMYebOwaMYAoyUxk41cvGfVCGzwzKqPNgkx1n7l4Fh86v4wrF49N78qx5tww+vXrR5iWlRi21cCJct6bfvfGURYWpY7avgHg6iWF/OjmZcc1exhMQZvIJLLlaBuJsVHMzktmUXEaFY1dAY1Nw93N9ndOWSbugWGOtvTwgfPOjjQPkakkymV8ZaLnjrDo3QlgjgVtPQHl/h35qfEkxUb51v80dvZR1+EOSfNZWJjGzur2kMIUzntOgfdGUUmmp5z6oabAWbHqVk8rEv9+UM6s4Z66wAv9g41d9PQP+WbOnLUnR8IEgv7HNMZQFqawiuPliiYSYqK4cnEB6+bkRiyYUtvuDmhiPCsvmX31XSH7OSmfTmCwoiyDfXVdIUHWfu9zZ3lnDa5dWsTgsA2bbup4/WAzuSlxbNjXyDce3x12n8qWHh7ZWsN1y4qIjXZxf4RiMZ3uAX7yfAUXzs7h3tvOIT0xlm89GRoMOZX/nMId8wpSSYyN8q0v9FfX7iY+xuWrXOqkpO0OSndt7uqjwZuCeNnCfBYUpvKDZ/eFnV211vLr148yryCVm84p4ZolhTy5sy5sMZQfPrufviHPeidjDNcsKaS7f4jnvAFmp3uAQ83do1bjk7ETHxPFv1+zIGLrhDPNyV7o7h/i2iWFJxU0BXOCts6+QdbPC18JcyyNGrQZY+41xjQYY3b6bftvY8weY8x2Y8zDxph0v8e+ZIypMMbsNcZcOl4nLjIZNHf1+Wa/RtLQ6ea9P3uNx7dHvgMJsKWyjUVFaURHuVhc7ClDvMvvzqbTALIgYtDmuVOYkxIXsdSuiExsc70XopFSI8ETwJTnHAtgDjcFlvv3329WXopvfawzmxYctC0oSqO1Z4Ca9sAmytWtveSlxvlKZ8dFR1GYlhASYNW09ZKfFtiKZHp2MjFRhj1Ba3OdWT8nOE1LjCEjMcbXD8n/ewe3N5mWlRiyn+PliiZWTc8kLjqKmbnJHG3uCUnV6+obpNM9GFDae3ZeCgcaPY1z/dV71wHme/ddUJhG/9CwL/hx7G/owphjwdCM3PDpno66djeHmrq5Y+103r20kMe314QNXH7x8iFcBv75sjm8e2khD22uoq0nNJ1wZ3UHbT0D/N2actISY7h0QX7YQMxXbdF7flEuw/yC1LBFr2o7PFWKnQvf9MRYitITQmba3q71jO3c/FSMMXxu/WwqW3p5ZndoRc4Djd28XdvBzeeWYIxhoff/XGOYlMs3D7VwwcxsXzruqulZ5KbE8eg2T2rljup2rPVUShQByE2JIybK8//12qCqjSerOMNzkwoIKN8/Xo5npu1+4LKgbU8DC621i4F9wJcAjDHzgfcBC7zP+akxZnKX2RE5Bf/yp+1c+aOXqAu60An2f5uqePNwC5/67RZ++kL4BfLugSF217SzzJui4VxUOT2SwHNhlJYQQ3KE3mq5qfFcsSifz1w8K6B0rYhMHs7sQaTKkY6yLE/QZq3lSHNouX/H3PwU9tZ3Yq31XaAHH9tJlwy+gK9qDa1WW56dFFJBMlxV29hoFzNykn0tDPyPCQSUYJ+WlRQatLX1UpweWg2zqrUnZLartr2Xg43drPEWEyjPTmJw2Iasa3Peqwv8iiTMyk2mf3A4JBCt73ATG+0iPXHk2ab9DV0UZySQ4G2cmxgbTW5KXNgqmwCvHfTMAK6ensWKskxaewbCrr979UAT75iZTUFaAresmoZ7YJgNYfrZOcVRnH5aZVmJtHT3hxQkOdDYTVJslC8IBc/nzK6ajpCAta7dHVJIYn5hakgKrTOL6pSVXzs7h7hoFxuPhBYkOegNGp20WOf/+f6gWc6uvkEONHb51lGCJ8C8cnEBz+9t9K5d9JzHkjDNoGVqcrkMxRmJLCpKC9sG4mTEx3h+X4ozEnw308bTqFdt1toNQEvQtqestU5O1uuAU6PyWuBBa22ftfYQUAGcO4bnKzJpWGvZfLSN1p4BPvv7LSEfev77PbS5mmWl6VyxKJ9vP7k37Af07toOBoas785hbko8BWnxAXdMK1t7IqZGOn5664qzpgKWyFS0enoWsVGukAaywcqzk6hu62XTkVa6+gYjVjabnZdCS3c/TV39bDrSyqzcZFLjAxt2zyvwpGIGB23Vbb0UBRVNKctO9AWLjpo2d9j3prn5KSFVcKtae0iOiw5oGj4tKzHMmraekDV6ZVlJDFvPe6E/p0rlslLP++f0MGv54FjQ5h+QODN+wSmSdR1u8lLjfLNN5dlJJMREhQQu++s7famR/q/nSISZttcONJOWEMP8glRfimjwz909MMSBxm7f43PzUzCGkFk+wNcY2En59BV2CQqCKxq6mJGbHJA2tqgojd6BIV9A5Xvt4YK2glQONnUHFE/ZXdtBbkocWclxAMR4s0S2hKki6cw8TvMWN3F+7sH/P5ziN4uLA/8/X7W4gP5Bzxq8bZVtTMtKJCPp7CgcImPju+9dwvdvWjKmx/zERTP558vmjkm65WjG4lb73wFPeL8uAvxrtFZ5t4lMOdVtnkqPq8ozef1gC7+MsN5gR3U7FQ1dvHdlCZ9YNxOATWHuQjpFR/zTPRYWpQUUIznQ6PnQFZGz18KiNHZ//dJRK6tNz0nCWvjZiweIdhkumRe+4IL/2rKNR1pZWRYaDMbHRDErNzkgeBgattS294a0DinLSqLDPUhbj2cmx2lFEhxggacyXU27my6/tblVrZ5j+l8ETctKoqat1zeD1j84TENnX0gg6KTLBc+K+WbvvAFmWZiqmRBaYAOOrVnbH1Too67dHTArFeUyzC1ICUgRHBwa5mBjN7OC3pc9M4eRZtqaWVWeictlmJufQrTLhKQz7qnrZGjY+lJk42OiKMlI9KU4Br/2vJR4X3ZFWYRiMQcau0JmIJxAf0fQuNd3uAN+RuCZabM2MMh6u7YzpGHwstIMdtZ0hPS+O9rSQ0pctG/mMjs5lsyk2JACK052SfBNiGUlGeSlxvHEjjq2VrYpNVJCLC/NOKGKlMfjA6uncc2S01N85ZSCNmPMV4BB4DfOpjC7hZ1eMMbcYYzZaIzZ2NgYvreHyGTmBFNfumIeS0vSeXhL+MarD22uJjbaxRWLCpibn0JCTBSbwwRtVa09xMe4yEuN821bXJTGwaZuOtwDuAeGqGrtZUbOxFwELCJjJ1IZc39l3hmVZ95u4LwZWRHLlTszGo9vq6XTPehb+xpsQWEaO/0CkoZONwNDNjRw8n7fQ96goK7DzdBw6H5wrHqlfwATLuWyLCuRYXss1a+2vRdrCRMwegKS4EIoVa29xEa7yPbO+GQlxZISHx1StMRZp+a/pi0pLprijAT2Bc1i1Xe4A/YDzzrD3bUdvlnGoy099A8Nh5RWn5YZvvdcdVsvlS29vnLk8TFRzMpLYUdQuwUneF5QeCxwmZmb7CsoE3DM1t6AgLnUO5Pl/zPv6huktt0dUm1xRk4S8TGugHYPTV19DA5b8tMCf/ZOAOmkh/YPDlPRECZoK0mnf3DYt97NcbSlh9KsRF+wboxhVm4ye4OCtp3V7eSnxgcUtQFP+tulC/J5dk89dR1upUbKWeekgzZjzG3AVcCt9lgORBXg3y2uGAhbWcFae7e1dqW1dmVOTs7JnobIhLW9up2YKMO8ghTfwu9wRUn+sqOWS+blkpYQQ3SUi6Ul6WEbkNa0eZpmB6SueNNDdla1c6CxC2vHrkeKiExu/o20L19YEHG/nJQ4spJiecRbxOGcMDNt4JlJaezs85Wqr24NLePv/32dWSynQFK4cthO9TX/VL2q1p6QYMxJ6XPWtQX3aHNkeoOx0Jm2HorTE3C5jgUE5WEqTda2u8lIjCE+JnA5/uy8lICZNmstdR2BM20A8wvS6HQP+s5vf4NTOTJopi07fDESJ73RPxhbVJQaUrlzV00HaQkxAT+nGd7CM8Gp+MHrCRNjo8lLjeOw38/cSX8MvukXHeUKKUZS66z7C3rtRekJpCXE+Pb19OCzvvVsDmdddnCK5NHmHl9A6ZiTn8L++q6A1769uj1iqu9lC/MZGPLsu0QzbXKWOamgzRhzGfAvwDXWWv93nEeB9xlj4owx5cAs4M1TP02RyWdHVTtz8lOIi45i/XxPVaFn3g6smNXa3U9jZ19A/5cV0zLYVdMR0lQ13EJ+507ilso2Dnh7HSloExGAtIQYspNjcZnRK5vNzkvBPTBMXmpcSMDkmJcfuMbIWXtbHPS+VJqZiMsc6xFX3ea5TAiXHukEY04A0d47QKd7MKS5+DTfDJr3mE6PtqBCJJGCsaqg2SYg7H6etVrh0jiTOdjY7as22eEexD0wHLKuy5ltcta17fP+rILT1qeFme0CqA3Ta3NRURot3f0Ba51317SzoDA14CbejJxk+gaHA24ODg1batpCX3tweqaTVhnu82NRURq7atp9wWCdN4U0+LUbY1hSks6Wo570RWcd4fygmbb8NM96bGc/5zyrWnspzQocz9l5KXT1Dfqqlna6BzjU1B2yns1xblkmmUmxRLvMiNVVRSaj4yn5/zvgNWCOMabKGPNh4CdACvC0MWarMeZnANbaXcAfgN3Ak8AnrbVDEQ4tctay1rKjut23SHxmbjLTs5N4OqjMsZM+VOZXinv5tHSGhi3bwzTOLgy6mMhIimVWbjJvHW6hoqELlwk8lohMbYuK0lg7O8eXFhiJs65tZVlmxAX1wX3VIs12xUa7mJ6T7Et/q2qJ3D8yOS6a7ORYXwDhpD8GB45ZSbFkJMb4AsaDTd1Eu0xI4ACegCSkuXdrb0ggWJblKdTiv7bK06MtzDEzk+gf8qyjg2NplLlBs01z8lO8BVs8P6NdNR2UZyeFVPQtC5o5dNS09eIygemZC4KKkQwMDfN2XWdIUOIEXP7FSBo63QwO27BppIEzbd24DJRmhn5+LChKo7t/yDdGzkxbuJnTZSXp7KvvpKtvkDcOtpASH830MJX6lpWms6Xy2ExbXYeb/qFhX08+h/N/bp+vJYWnCMmiCEFbdJSLD543jcsXFYTMlopMdsdTPfJma22BtTbGWltsrf2FtXamtbbEWrvU++fjfvt/01o7w1o7x1r7xEjHFjlbVbb00t47wKKiY+kZ6+fn8frBZjrcx8osO+lD5X4pKctKPLNu/sVI+gaHaOjsC/shubIsk01HWtlf30lJZqI+qETE56e3ruCuW1eMup+zru2caeHXswFkJceRkxLn66tW1dpLZlIsibGhLUbmFaT6Zlp21rRTnp0U8b3JP8hyAsHgAMsYw9KSYxf6W462sqAwNWzrkvKsRKpbjxUt6ekfpLm7PyRwcQq1+Kdm1nWEVkWEYzNfTqESX5XJoKAtPiaKOXkpbK1s8732cK0Z0hJjSEuI4UhLUD+7dje5KfEBTdDneyt3OjfyDjR6Gnj7p1DCsT5w/sVIfIF1euhMW2NnH93eAjCHmropzkgM+/N0ZsqcILyu3dPqICMxJmTfZaXpDFvYXtnGyxVNnD8jK2wD+KUl6VS29NLs7cHmjEFweuRsb9EIZ13bGwc9xcwXR0iPBPjsJbP58c3LIj4uMlmpUZPIONhe7fnA9k/huGR+HgNDllf8+ugcauomymV8Fc3AM3s2IycpoBhJfbvng80/ZcZxTlkGne5BXtzXOGa9R0Tk7JAQG+XrDzaS82dkUZ6dxDvnjpxGOTc/xTfTFi5l2zGvIIXqNs/Nq22V7RHT2SCwIfaxoC30uEtLMtjf0EVrdz/bqtpYHiHALMn0FC1x0gSrIxzTKYLipEi6B4Zo6e4PWasFx2aVqr3r8+o6wgdt4Elx33K0lZbufqpae1lYGP61l4VpBF7T1hvyPh8fE8X8glRfb7Nd3lm8hUWBwWBGkqfaon/QFum1O+mmzvc/3NwdsAbS38zcZKJdht21nqDRmY0MNyPr3HR8eEs11W29rJkVvmaBsyZtl7ewzVFv8DotKD0yLTGG0sxEXtrfiLWWx7bXcG5Zpq+FgMhUoqBNZBw46Smz8o4FUUuK04mNdrGl8lge/8GmboozEkLubi4vzWBrZZtv8XWVsyYkzAWSUzSgp39I69lE5KSUZSfx/BfWhawpCjbXWxhicGg4bMEQh1MxcMO+xlEr+ZVlJVHb7vZWwO0hKTbKV/bd37LSdKyFB9+qxD0wzIoIQZszW+P0aos0e1cW1KutocNzcywvzEybkzLprDmrb3fSI0ODh+XT0unuH/JVDI60tqo0TBpnbbubggjv89sq2+gbHOLVA82kJ8ZQnh36fj8zJ5kDDf6VOJ3PjtDUUPAES9ZaDjf1UB5h7ONjopjhl+4a3OrAX1piDDNyknjI+9qdZubBFhQEB209RLtM2NTU964s5pWKZv66o46Khi6uXhK5qI7I2UxBm8hJqGgIrGYVrK7dTXZyHHHRx+5wx0a7WFCYGlAx63BTt+9ur78lJek0e+/SwsjV14ozEnwfoDM10yYi42hOfip9g8Psre/0lJKPNNOW7wlUHnzrKDByJT9ndqWypcfboy0x7CyOcwyn56V/ASd/Jd6gzanM6AQuJUEBZmp8DIVp8b7AIVyPNkdKfAwp8dG+2bu6DjfpYapMAqwo9dxI+/XrR4DIQVtZUBqntd6iIWF+pueWZ9A3OMz2qnZe3NfA2lk5YdMOZ+QmUeE/09bWS1ZSbMhsqxOcH27uoamrn66+wYgzbeCZOXXSXWvae8P+jBzLSjN8LR7KIgSCaYmeypdOwZYjzZ5G6eFaWdx0TikxUYZ/+dN2olyGyxcpaJOpSUGbyAnaWd3OJd97kTuf2BNxn5p2d9hUxmUlGWyvamdgaBhrLYciBW3eu9LbvE1EnQuFcGstjDGs9PZVmpGrIiQiMn7megtDfPmhHfQNDvPOCA2781LjyEiM4ZWK5lEr+flXkHQaa4eTluCZxanzNnYOdxPL873jiYkyVHoLoAT3aPO3fFqGLxXdSXmMFJAUpiX4qhjWhyn37yjJTCA7OZZDTd0UpsVHTOUrz05i2B4LLlu6++kbHA77/Z2G5/e/cpimrn7WzQmfdjgjJ5kWb1Vi57WHq9qZGh9DXmocu2s6fLN9IwdtqdS2u9l8tJWq1l7mFkQez2Wlns+vC2ZlRyxqA96edn4zbcHr2Rw5KXFcsaiArr5Bzp+RNWpRHZGzlYI2kRP05iHPQuj/3XCQP26sDLtPbVv4O5HLStM9d6nrOmns7KOnfyhs0DYnP4XYaJdv4XlNWy/ZyXERF/K/c24uyXHRIQ1cRUTG0szcZKJchm1V7Vy2IJ/zZ4RPfzPG+FIk5+SnjFggyZmN2VXTTmVL5JRLONbjK9J6NoAol6E4I5HKlmPpkf492vwtL82guq2X2vZe3/qu4IbZjsL0eN8NtPqOvoj7GWN8s4DzI6xng9Bqj05GRUGYlgPZyXFMz0niLztqMQbWzg4ftC31zkY6GR3VIwTBq8qzeO1gs29NX/kIlYedYipff2w3US7DdcuKIu67qjwLl4GL5428PnJBYRqHmrtp6HRT0dAV9rPQcdv5ZQAjfl+Rs52CNpETtKWyjfzUeNbMzOYrD++kyVv9yp9noXaYcsilxz5QnXUU4T6onFRKpwKZZ8F/5HSU65YV8caXLyY1PnQdiIjIWImPiaI8O4m4aBdfuXLeiPs6QdtoTY7TE2NJS4jhR8/up3dgiEsX5Efc13kPXREhNdJRnJHgt6atJ+xsE+BbF7f5SBsQaZE+AAAgAElEQVRP7a5jcXEaKRHeRwvSE3zl7sM11g533OBiIf6mB1V7rGmP3BoBPD3IwFM5MdJs08KiNGKiDFsq2+juG6Sytcc3kxls9fQsGjv7eO7tBqJdZsRg2RnLrZVtXDQnJ2LACp5g9LUvXezrTxrJgsJUrIU7n9hDT/8Q1y4tjLjv8tIMXvjCOgVtMqUpaBM5QVuOtrJ8WjpfvWoe/UPDPLGjNuDxDvcAXX2DYWfaitITyE6OY0tlm6/cf6S+akuK09lR1c7g0LC3oljkD1RjDElxoWW3RUTG2j9dOofv37TUt3YsEl/QNkLlSIcz2/aDm5ZyfoTiFQAXzs5hbn4KF0dIy3SUZgbNtGWEP9f5hanEx7j40+YqdlZ3cM2SyIFDUXqCr8l1Y2cf07Ijv/7V07OAyOvuwNOjLj81/ljQ5p3FK4hwg+7cck/Qtm5O5NfuVJrccrSVVyqaGBiyXDAr/M/zvBmec3zm7XpKMhPDridzZHvbPYBnjdloRgrqHM7s3UObq5lXkDrizwo86ZsjpVuKnO10lSfitb2qjRf3NmIMXLu0KOwFSWNnH1Wtvdx2Xhlz81OZnZfMY9tq+cB5Zb59ap0UlzBBljGGZaXpbDzcSrTLEBvtihiMLSlJ4/5XD1PR2EVNm3vED2oRkdNlpJkwf2tnZ7NuTg4XzR39vesrV87HPTAUMe3PUZyRyJOfXTvq8UoyE2ntGWBndTvN3f3MyQtfpCkmysXi4nSe29OAMXDl4shFLpwbcQ9vrgKOBWbhLClJ59nPX8j0EVL+wDMrdcCbHlnr7X+WlRQbdt91c3K5YFY21y8febZpWWkGv3+rkqd315McF83KaZlh9yvLSiQ/NZ66DnfEgiH+FhelsaO6nYsirKc7Ufmp8WQmxdLS3c8HVk9TQCYyCs20iXh95eGdfPfpfXznqX38+Ln9Yfdx0hWdFJ2rFxfy5uEW3x1SOJbiUhhhMfvKaRkcbenhDxurmJmTHLYCGBwrRvKb14/SOzA04kybiMhEk5sSz/23n0tuyuizLueWZ44asJ0Ip/elU2lypMDRmeE5pywzbFq7w3kPfmhzNUmxUSwaocEzeIqCjBaIzMhJ4kCjp+x+dVsvhRH6nwFkJsXywIdXRUx3dCwrTad3YIhHttZwwazssA2zwXMT0ZltG6kIieM/rlvI7+5YPeKM3IkwxrCwKI2UuOgRUyNFxEMzbSJAU1cfO6rb+dz62Ww52sqWo21h99ty1DND5jQGvXpJId99eh9/2V7LR9dOB0aeaQPPguoZOckMDlvmFUQuHFKWlUR2chwPeMtGz8hRZUgRkePhVCJ8dFsNM3KSRgx0nPVnI6VGgqd6JHj6uq2bk0PMGAQvM3OT6eobpKGzj9pR0uCPlxOE9g8Nc9EoGRrnTc/i4S3Vo84IQvgCKafqX6+cR1vvgNL7RY6DfktEgJf2NwJw0ZxcDPD83kbaewdISwhckL7laBvzClJ9ldDKspNYXJzG49trfEFbXXsvLgN5KeEXisfHRHHJKAu0AVwuw18+vYbadjfxMS7mqDKkiMhxKcn0BBh9g8O8c5T0zIvm5PDN6xZyw/LiEffLS4vDGLAWzp8ROTXyRMzIOVZBsrqtlzUzT322sTjDs3a6qasvYmsAx0Vzc1lcnMZ5EaqAjjdVPBY5fkqPFAE27GsiKymWBYWpvpLS26sCZ9usteyobmdJSWBKzKUL8tlW1U6dt6pYTbub3JT4MUkhyUuNZ2lJOnPzU5XvLyJynNISPM2wYeTUSIDoKBe3rpo2YlsCgLjoKF/VxvOmj02QM8Nb9v+uFw5Q39HH0tKRK20eD2MMa2dnc255JrmjFATJSYnj0U+t8bUfEJGJS0GbTHnDw5YN+xq5YFY2LpdhcUkaxsDWoBTJxs4+uvoGmZkT+OF26QLPrNnTb9cDUNveG7H6l4iIjD9jDCUZiaTERXNOWfhCHCejMD2B1PhoX+XDU5WbEkdKXDQvVzQxryCVm88pGZPjfvuGxfz6w6vG5FgiMjEoPVKmvN21HTR39/sWwafGxzAzJ5ktlYFB22Fv49XgBdszcpIpz07i6d31fGD1NGrb3L5S1yIicmbcsqoU98DQmKw9c7zvnBK63IMRC0idKGMM03OT2V7Vxn9dv2jMinyM1XFEZOJQ0CZT3qsHmgBY49fLZmlJOs+8XY+11peWeDhCM2xjDOvn53HfK4fodA9Q0957XCWuRURk/Lx/9bQxP+bN547eo+xE/f2F02nq6mfpKE3IRWRq060YmfIqGrrITo4LKEu9rDSD1p4Bjnhn1wAON3cT7TIUhanutX5+HgNDlp88V4F7YDhsY20REZFgly0sGJcAU0TOLgraZMo71NQdUu54+TTPHc+NR1p92w43d1OSmRg27WR5aQbFGQn874aDwLFy0yIiIiIip0rpkTLlHWzsZn1QCf7ZuSlkJMbw2oFm3rPCUwb6UFMPZVnhg7Eol+GZz13I/vou6jrcXDRKmWURERERkeOloE2mtPaeAZq7+0PWqblchtXTs3j9YDPWWgCONHezqjxyFbL4mCgWFaexiLSI+4iIiIiInCilR8pZraHTzfvveYM/b6n2BV/+DjZ1ATA9J7RHzfkzsqhu6+VoSw+NnX309A+FBHciIiIiIuNNQZuc1R7dWsPLFU189vdb+cyDW0MCt0MRKkICnDcjC4DXDjRHLPcvIiIiIjLeRg3ajDH3GmMajDE7/bbdaIzZZYwZNsasDNr/S8aYCmPMXmPMpeNx0iLH6687apmbn8LH1k7n0W01bKtqD3j8YGM3US4TtnDIjJxkclLieO1g87Fy/1kK2kRERETk9Dqembb7gcuCtu0Ergc2+G80xswH3gcs8D7np8aYqFM/TZETV9fuZvPRNq5aXMAn1s0kJsrwxI7agH0ONXVTmplIbHTor4IxhvOmZ/FKRRMvVTQR7TIUpquUv4iIiIicXqMGbdbaDUBL0La3rbV7w+x+LfCgtbbPWnsIqADOHZMzFTlBf9tVB3h64KQlxnD+jGye2FkXkCJ5oLFrxHVq71lRTHvvAI9tq6E0Qrl/EREREZHxNNZXoEVApd+/q7zbQhhj7jDGbDTGbGxsbBzj0xDxpEbOzktmZq6nyMgVi/I52tLD7toOAIaHLYebQ3u0+Vs7O4eNX1nPf79nMf9x3cLTct4iIiIiIv7GOmgzYbaFluwDrLV3W2tXWmtX5uSop5WMrb7BITYeaeXiecf6r62fn0+Uy/DEDs8MXG2HG/fAMOU5I69TS0uM4caVJZw/I3tcz1lEREREJJyxDtqqgBK/fxcDNWP8PURGdbCxm6Fhy7yCVN+2zKRYVpVn8qQ3bXLr0TYA5uanhj2GiIiIiMhEMNZB26PA+4wxccaYcmAW8OYYfw8Rthxt5f5XDvFqRRNDw6GTufvqOwGYnRfYf+3ieXlUNHRR2dLDhn2NpMRHs6RYzbBFREREZOKKHm0HY8zvgHVAtjGmCvgansIkPwZygL8YY7Zaay+11u4yxvwB2A0MAp+01g6N29nLlPT83gY+9qtN9A8NA3DLqlL+87pFAfvsr+8iymVCioy8c24u33h8N8/taeDFfY1cMCtbxUVEREREZEIbNWiz1t4c4aGHI+z/TeCbp3JSIpFsPtrKxx7YxOz8ZH5883J+9sIBHnzzKH/3jnJfwRHwzLSVZSUSFx3YcaI8O4ny7CTufeUQdR1u1s7SekoRERERmdg0xSDjrr13gKd21fGzFw/4mlSfrD9tqiI2ysWvP7yK8uwk/vmyOSTERPGdvwV2oNjf0MXsvJSwx7hoTi5HmnsAT3VIEREREZGJTEGbjKvW7n6u+cnL3PHAJu58Yg9f+fOOUzrepiOtLCtNJz0xFoCs5Dg+unY6T+6qY2d1OwDugSGONHczK0LQ9s65uQDMyk2mMD3hlM5HRERERGS8KWiTcdM/OMzHf72J2nY393xwJf906RxeqWhm05GW0Z8cRqd7gL31nayYlhGw/fbzy4l2Gf6yoxbwVI4ctqFFSBznlmeSnRzLpQvyT+o8REREREROJwVtMm5++eph3jjUwrdvWMwl8/O4/R1lZCbF8qNnK07qeFsr27CWkKAtLTGGc8szeXp3PQD7G5zKkeFn2mKjXTz7uXV85pJZJ3UeIiIiIiKnk4I2GTfP7WlgXkEq715WBEBibDQfuaCcF/c1squm/YSPt/lIG8bA0pL0kMfWz/eU8j/Y2MW++k6iXYayrMhNs9MSY4hR1UgRERERmQR01Srjord/iE1HWlkzMytg+83nlOIy8Ldd9Sd8zE1HW5mTl0JKfEzIY+vn5wHwyNYantvTyPScJGKj9d9bRERERCY/XdXKuHjrcAv9Q8OsCSqpn5EUy/LSDJ7f0xDynPaeAf73xQM0dfWFPDY8bNlypJXlQamRjuKMROYVpPLDZ/ezr76Tz62fPTYvRERERETkDFPQJuPilYomYqNcnFMWGmRdNDeXHdXtNHS4fdsON3Vz3V2v8F9P7OHd//MK++o7A56zt76Tzr5BlpeGD9oArlpcgMvA9967hMsWFozdixEREREROYMUtEmA3v4hevoHR92vqauPP22qoqHTHfbxl/Y3sXxaOomxof3bnZL7z+/1zLZ1uge48X9fo7W7n29et5C+wWFu/Nlr1Lb3+p7znHdmbs3M7Ijn9PELZ/Dyv7yTa5cWjXr+IiIiIiKThYI28XEPDHHdT19h1Tef5QfP7KO3fyjsfne9cIC1336ez/9xG2u//Tx3PrEnYN/mrj5213ZEDLDm5qdQkBbvC8R+vuEgjZ193Hf7udy6ahp/+Nh59A0O8dWHd2KtBeDp3fUsLk4jPy0+4vlHuYz6romIiIjIWUdBm/h8/fHd7KnrZHFJGj94Zj9ffji0EfbR5h6+9eQezi3P5DcfWcXlCwv42YsHuPJHL7G9qg2Ah7dUA/DOuXlhv48xhovm5vLivkb+b1MV97x8iCsXF/iqQpZnJ/GFd83h2T0NPLK1hoYON1sr21g/L/zxRERERETOZgraBIBn367nt28c5WMXTuc3H1nNJy+awcNbqtl4OLAR9hM7PQ2sv3HtQt4xM5vv37SU335kFe6BIW6/7y0aOtzc+/IhVk/PZH5hasTv9/cXzqAsK4kv/HEbfYPDfD6ocMjt7yhneWk6X/3zTu568QAA6xcoaBMRERGRqUdBmwDwf5uqyEuN4wvvmgPAJy+aSUFaPP/2yC6Ghq1vvyd21rGoKI2SzETftvNnZnPf7efS4V2bVtPu5qMXTB/x+5VkJvLIp97B59fP5mtXz2d6TnLA41Euw//cupyE2Cjue+UwJZkJzInQLFtERERE5GymoE0YHBrm5Yom1s3O9TWcToyN5ouXz2V3bQfPvO3pqVbT1svWyjYuW5gfcow5+Sl88qKZHGnuYUZOEhfNyR31+8ZFR/EPF8/ig+eVhX28IC2Bez64kvgYF9csKcQYc/IvUkRERERkkgot7SdTztbKNjrdg6ydHdhT7cpFBXz9sd08uq2GSxfk8+TOOgAuDxO0AXxi3UwqW3q5dmkhLtfYBFhLStJ57YsXk5oQ2lBbRERERGQqUNAmbNjXiMuEltOPjnJxxaIC/ripkg73AL9/q5K5+SkhqYyO2GgX333vkjE/v4yk2DE/poiIiIjIZKGgbZKqaOhkT10nbT0DRLkMly7IJ/Mkg5sX9zWytCSdtMTQ2axrlhbywOtH+PgDm9hb38lPb11+qqcuIiIiIiInQEHbJHTPSwf5j7+8HbDtV68d4f8+fh5JcSc2pC3d/WyvbuezF88O+/iK0gwK0uJ59UAz58/IipgaKSIiIiIi40OFSCYZay2/fO0wy0vT+cun1/Dmly/mfz+wgr11HXzmwa0M+1V6dPQNDvHGwWY63QMhjz23pwFrYd2cnJDHAFwuwzVLC4lyGb529QIVAxEREREROc000zbJbDzSSmVLL/94yWwWFKYBcOmCfL565Xy+/vhunthZx5WLC3z7P7K1mm8/uZfqtl5io11cvbiQO29Y5KsS+eTOWgrT4llcnBbxe/7jJbO5cUUJM3PDr2UTEREREZHxo5m2SeahzVUkxkZx6YLANMXbzi+jMC2eB9866ttW0dDFZx7cSmZSLN+/aQk3rijmT5ur+N7T+wDodA+wYV8Tly0sGHEGLT4mSgGbiIiIiMgZMupMmzHmXuAqoMFau9C7LRP4PVAGHAbea61tNZ4r/x8CVwA9wIestZvH59SnHvfAEI9vr+Wyhfkha9eiXIYbV5bwo+f2U9nSQ0lmIr94+SBx0S7uv/0cspLjuG5ZMcMW7nrhAKvKM2nvHaB/aJgrFmmdmoiIiIjIRHU8M233A5cFbfsi8Ky1dhbwrPffAJcDs7x/7gDuGpvTFPCkOna6B3nP8uKwj9+40rP9j5uqaOzs40+bq7lhRTFZyXG+ff7tqvnMyUvho7/ayHee2ktuShzLSzNOy/mLiIiIiMiJGzVos9ZuAFqCNl8L/NL79S+Bd/tt/5X1eB1IN8YUICfEWsurFU386rXDtPd6iocMDg3zP88fYFFRGufNyAr7vOKMRC6YlcN9rxzi7+5/i4GhYT68pjxgn4TYKB68YzXvWpBPZUsvly/MH7NG2CIiIiIiMvZOthBJnrW2FsBaW2uMyfVuLwIq/far8m6rDT6AMeYOPLNxlJaWnuRpTA4d7gEeeO0IDR1u5uSncs3SQpIjlOY/2tzDP/9pG68f9MTJ3/nbXj56wXTSE2M42tLD3R9YMeL6s69cMY9vPbmHvXWd3LSyhBlhGmFnJMXyP7cs58NrWpmdlzI2L1JERERERMbFWFePDBdNhNagB6y1dwN3A6xcuTLsPmeDVyua+PvfbKa9d4DE2Ch6+od4bk89P//gypDga9ORFj76q00MDVv+/er5LC3N4CfPVfBdb+GQufkprJ+fN+L3m5Ofwr0fOue4zk1pkSIiIiIiE9/JBm31xpgC7yxbAdDg3V4FlPjtVwzUnMoJTnY/fHY/yXHR/OYjq1hQmMrdGw7yX0/s4dFtNVy7tMi3X3NXHx/4xZvkpsRx74fOYbp3huye21ayrbKN+189zM3nlqpPmoiIiIjIFHOyJf8fBW7zfn0b8Ijf9g8aj9VAu5NGORVVtvTwxqEWbllVysKiNIwxfOSC6SwtSeffH91FS3e/b98HXj9CT/8Q99y20hewOZaUpPP9m5Zybnnm6X4JIiIiIiJyho0atBljfge8BswxxlQZYz4M3AmsN8bsB9Z7/w3wV+AgUAH8HPjEuJz1JPHnLdUAXLu00LctymW484ZFtPYM8MtXDwOeUv6/eu0IF8/NZWau1piJiIiIiMgxo6ZHWmtvjvDQxWH2tcAnT/WkzgbWWh7aUs3q6ZkUZyQGPDY3P5WL5+bywOtH+Pt1M3hoczUt3f18dO30M3S2IiIiIiIyUZ1seuRZbVdNO0/tquNIczeeODSUpwR/Bav+8xk+9sBGntxZy/DwsX3fONTCoaZuro/QU+2ja6fT0t3Pv/55J//117dZUpzGKqU/ioiIiIhIkLGuHjmpuQeG+N7T+/j5SwdxYrULZ+fwrRsWk58W79tvaNhyyz1v8OahFlZPz2TL0Tb+tqueOXkp/NvV8zl/RhbffWovOSlxXLU4fJu6VeWZLCpK44+bqpibn8JP3z9yKX8REREREZmaFLT5+f4z+7h7w0FuWVXKDcuLeONQCz96dj+X/mADj//DGkoyPWmOrx5o4s1DLfzrVfP58JpyhoYtf9lRy/ef3seH7nuTD55XxluHW/nGuxeSGBv+R2yM4f9du4DHttXw+XfNidi3TUREREREpjZFCl5Dw5Y/b6nmknl5/Od1iwBYMS2TS+blcekPNvDHjZV87l1zAHhoczWp8dG8f7WnKXiUy3DNkkIunJ3D++95g1+8fIiyrETed05JxO8Hnj5p6pUmIiIiIiIj0Zo2r7cOt1Df0cc1fpUeAWbnpbBmZjYPbalmeNjS1TfIkzvruGpJIXHRUQH7piXE8MCHz+XqJYX853WLiInSj1dERERERE6NZtq8HttWQ0JMFJfMyw157PrlRfzj77fx1uEWKlt76R0Y4oblRWGOAumJsfz45mXjfboiIiIiIjJFKGgDBoaGeWJnHZfMzwu7Bu3SBfkkxu7kv/+2l+q2XqZlJSqtUURERERETgvl7wEv7G2kpbufqyNUekyMjeaKRQVsPNJKWkIM33vvElV6FBERERGR02LKzLTVtPXy0xcq6OkfIjclntvfUUZeqqeM/z0vHaQwLZ6L5oamRjq+euU8rl9WxOrpWbhcCthEREREROT0mBJBW127m5t//jp17W5yUuKoa3dz3yuH+MS6maybk8Mbh1r46pXzRiwckp4Yy/kzs0/jWYuIiIiIiJxFQduhpm4K0+NDKjoODA3z/l+8QVNnH7+7YzXLSzM42tzDt/+2h+8/s49fvHyQlLhobhqlPL+IiIiIiMiZMOnXtPX0D/Kvf97JRd95gSt/9DLbq9oCHn9xbyMVDV18+z1LfMVDSrMS+fHNy/jyFXPp7BvkltWlpMTHnInTFxERERERGdGknmkbHBrmlp+/wbaqNt67spgN+5q4/qev8vin1zA3PxWAh7ZUkZUUy7sW5AU81xjDHWtncPnCAgrS4s/E6YuIiIiIiIxqUs+03fPyIbZWtvH99y7l2+9ZwuOfXoPLZfjtG0cBaO8Z4JndDVyztDDierWSzESi1QRbREREREQmqEkbrRxs7OL7T+/j0gV5XLu0EIDs5DiuWJjPw1uqcQ8M8fiOGvqHhrlhefEZPlsREREREZGTM2mDtrteOEBMlItvXLswoGfaTeeU0uke5GcvHuBnLx5gVm4yCwpTz+CZioiIiIiInLxJGbQNDA3z1O563jU/j9zUwPVoq6dnUpaVyA+e2U+ne5A7b1isRtgiIiIiIjJpTcqg7bUDzbT3DnDZwvyQx4wxfPriWayclsGfP/EOVkzLOANnKCIiIiIiMjYmZfXIJ3bWkRQbxdrZOWEfv355MddrHZuIiIiIiJwFJt1M29Cw5alddVw0N5f4mKjRnyAiIiIiIjKJTbqg7dUDTTR393P5woIzfSoiIiIiIiLj7pSCNmPMZ4wxO40xu4wxn/VuyzTGPG2M2e/9+6QWlVlrqe9wU9nSE7D93pcPkZUUy8Xzck/l1EVERERERCaFk17TZoxZCHwUOBfoB540xvzFu+1Za+2dxpgvAl8E/uVEjv1qRROffnArTV19AMwrSOXjF05nfkEqz+9t5B8vma3USBERERERmRJOpRDJPOB1a20PgDHmReA64FpgnXefXwIvcAJB28HGLj7+603kpMTxqYtmMDhseWhzNZ95cCulmYnERbv4wHnTTuG0RUREREREJo9TCdp2At80xmQBvcAVwEYgz1pbC2CtrTXGhM1jNMbcAdwBUFpaCnj6r33kVxuJjnJx/+3nUpKZCMBt55fxtUd38ds3jnLrqlIyk2JP4bRFREREREQmj5MO2qy1bxtjvgU8DXQB24DBE3j+3cDdACtXrrQAW462cbCxmx/dvMwXsAHERLn45rsXcvXiQpaUpJ3sKYuIiIiIiEw6p1SIxFr7C2vtcmvtWqAF2A/UG2MKALx/Nxzv8V7c10CUy7BuTmj/NWMM583IIjF2UraWExEREREROSmnWj0y1/t3KXA98DvgUeA27y63AY8c7/E27GtiRWkGqfExp3JaIiIiIiIiZ41T7dP2J2PMbuAx4JPW2lbgTmC9MWY/sN7771E1dfWxo7qdtbOzT/GUREREREREzh6nlGtorb0gzLZm4OITPdZL+xsBuHC2+q+JiIiIiIg4TnWmbcw8ubOOrKRYFhSmnulTERERERERmTAmRFWPQ03dNO2q5yNrynG5zJk+HRERERERkQljQgRtPf1D/PDdC7l1VemZPhUREREREZEJZUIEbbNyk3n/6mln+jREREREREQmnAmxpi02ekKchoiIiIiIyISjaElERERERGQCU9AmIiIiIiIygSloExERERERmcAUtImIiIiIiExgCtpEREREREQmMGOtPdPngDGmHdg/xodNA9qn6DGzgaYxPuZkee2T5Zgao4l/TI3RxD+mxmjiHxM0TpPhmBqjiX9MjdHEP+ZYjNE0a21O2EestWf8D3C3jjmmx9w4Sc5zKh9TYzTxj6kxmvjH1BhN8GNqnCbNMTVGE/+YGqOJf8wxHyP/PxMlPfIxHXPCmyyvfbIcczxMltc+WY45HibLa58sxxwPk+W1T5ZjjpfJ8vonyzHHw2R57ZPlmONhsrz2yXLMcTUh0iNlbBljNlprV57p85DINEYTn8Zo4tMYTQ4ap4lPYzTxaYwmvvEeo4ky0yZj6+4zfQIyKo3RxKcxmvg0RpODxmni0xhNfBqjiW9cx0gzbSIiIiIiIhOYZtpEREREREQmMAVtk4Qx5l5jTIMxZqfftiXGmNeMMTuMMY8ZY1K922OMMb/0bn/bGPOloGNFGWO2GGMeP92v42w2VmNkjPmMMWanMWaXMeazZ+K1nK1OcIxijTH3ebdvM8asC3O8R/2PJadurMbIGHOTMWa79/fo22fgpZy1jDElxpjnve9du4wxn/FuzzTGPG2M2e/9O8O73RhjfmSMqfCOyfKg46UaY6qNMT85E6/nbDSWY2SM+Zb3M2mnMeamM/WazjYnMUZzve+DfcaYL4Q5nq7txthYjtFYXNspaJs87gcuC9p2D/BFa+0i4GHgn7zbbwTivNtXAB8zxpT5Pe8zwNvjebJT1P2c4hgZYxYCHwXOBZYAVxljZp2Ok58i7uf4x+ijAN7t64HvGmN875nGmOuBrvE+4Snofk5xjIwxWcB/AxdbaxcAecaYi0/HyU8Rg8DnrbXzgNXAJ40x84EvAs9aa2cBz3r/DXA5MMv7568joFMAAAaiSURBVA7grqDjfQN48XSc+BQyJmNkjLkSWA4sBVYB/+TcNJFTdqJj1AJ8GvhOhOPp2m7sjckYjdW1nYK2ScJauwHPfwZ/c4AN3q+fBm5wdgeSjDHRQALQD3QAGGOKgSvxXATJGBqjMZoHvG6t7bHWDuK5kLluvM99qjjBMZqP580Ya20D0AasBDDGJAOfA/5jnE95yhmjMZoO7LPWNnr3e8bvOXKKrLW11trN3q878VwoFgHXAr/07vZL4N3er68FfmU9XgfSjTEFAMaYFUAe8NRpfAlnvTEco/nAi9baQWttN7CN0JsqchJOdIystQ3W2reAgeBj6dpufIzhGI3JtZ2CtsltJ3CN9+sbgRLv1/8HdAO1wFHgO9Za5yLoB8A/A8On8TynshMdo53AWmNMljEmEbjC7zkyPiKN0TbgWmNMtDGmHM+MqPPYN4DvAj2n80SnsBMdowpgrnf2OhrPB6p+j8aBN4tjGfAGkGetrQXPxQ6Q692tCKj0e1oVUOSduf4ux2ZOZRycyhjh+R273BiTaIzJBi5Cv0tj7jjHaCS6thtnpzhGY3Jtp6Btcvs7PFO1m4AUPLM14Jl+HQIKgXLg88aY6caYq4AGa+2mM3K2U9MJjZG19m3gW3hmE57E84E5eNrPemqJNEb34rlw2YjnA/FVYNAYsxSYaa19+Eyc7BR1QmNkrW0F/h74PfAScBj9Ho0574zzn4DPWms7Rto1zDYLfAL4q7W2MszjMgZOdYystU8Bf8Xzu/U74DX0uzSmTmCMIj1f13bj7FTHaKyu7aJP9AkycVhr9wDvAjDGzMYzNQ5wC/CktXYAaDDGvIInZWgZcI0x5gogHkg1xvzaWvv+03/2U8NJjNFBa+0vgF94n/OfeC5KZZxEGiNvCsM/OvsZY14F9gMXAiuMMYfxvIfmGmNesNauO71nPnWcxBhhrX0MeMy7/Q48N0lkjBhjYvBcxPzGWvuQd3O9MabAWlvrTa1r8G6vIvCucjFQA5wHXGCM+QSQDMQaY7qstV9ETtkYjRHW2m8C3/Qe87d4f8fk1J3gGEXyDnRtN27GaIwYi2s7zbRNYsaYXO/fLuCrwM+8Dx0F3mk8kvAsntxjrf2StbbYWlsGvA94Tr/U4+tExyjoOaXA9Xjubso4iTRG3nSgJO/X6/HM4Oy21t5lrS30/h6twbN2at0ZOfkp4kTHKOg5GXhmdLTWY4wYYwyei4+3rbXf83voUeA279e3AY/4bf+g9/1uNdDuXStyq7W21Pu79AU8a6oUsI2BsRoj46lImOU95mJgMVp/OCZOYozC0rXd+BmrMfIe65Sv7TTTNkkYY34HrAOyjTFVwNeAZGPMJ727PATc5/36f7xf78ST8nCftXb76T3jqWcMx+hP3g/JAeCT3lQvGQMnOEa5wN+MMcNANfCB03y6U9IYjtEPjTFLvF9/3Vq7b9xPfup4B56f9Q5jzFbvti8DdwJ/MMZ8GM+NqRu9j/0VzxqOCjzrQG8/vac7JY3VGMUAL3muXekA3u+d4ZZTd0JjZIzJx5MKngoMG0/Z+Pknk64nx20sx+iUr+2MtfZUX5CIiIiIiIiME6VHioiIiIiITGAK2kRERERERCYwBW0iIiIiIiITmII2ERERERGRCUxBm4iIiIiIyASmoE1ERM46xpghY8xWY8wuY8w2Y8znvH3e/Pf5oTGm2tlujLnd+5ytxph+Y8wO79d3GmM+ZIxp9Ht8qzFm/pl5dSIiMtWo5L+IiJx1jDFd1tpk79e5wG+BV6y1X/NucwGHgRrgi9baF4KefxhYaa1t8v77Q95/f+o0vQQREREfzbSJiMhZzVrbANwBfMp4uwQDF+Fpbn8XcPOZOjcREZHjoaBNRETOetbag3g+83K9m24Gfgc8DFxljIk5jsPcFJQemTBOpysiIhJAQZuIiEwVBsAYEwtcAfzZWtsBvAG86zie/3tr7VK/P73jeK4iIiI+0Wf6BERERMabMWY6MAQ0AFcDacAOb7ZkItAD/OWMnaCIiMgIFLSJiMhZzRiTA/wM+Im11hpjbgY+Yq39nffxJOCQMSbRWttzJs9VREQkHKVHiojI2SjBKfkPPAM8Bfw/Y0wicCl+s2rW2m7gZTwzcCMJXtN2/nidvIiIiD+V/BcREREREZnANNMmIiIiIiIygSloExERERERmcAUtImIiIiIiExgCtpEREREREQmMAVtIiIiIiIiE5iCNhERERERkQlMQZuIiIiIiMgEpqBNRERERERkAvv/0Z+lab5MYOcAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "endog = DataReader('CPIAPPNS', 'fred', start='1980').asfreq('MS')\n", "endog.plot(figsize=(15, 3));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is well known (e.g. Harvey and Jaeger [1993]) that the HP filter output can be generated by an unobserved components model given certain restrictions on the parameters.\n", "\n", "The unobserved components model is:\n", "\n", "$$\n", "\\begin{aligned}\n", "y_t & = \\mu_t + \\varepsilon_t & \\varepsilon_t \\sim N(0, \\sigma_\\varepsilon^2) \\\\\n", "\\mu_t &= \\mu_{t-1} + \\beta_{t-1} + \\eta_t & \\eta_t \\sim N(0, \\sigma_\\eta^2) \\\\\n", "\\beta_t &= \\beta_{t-1} + \\zeta_t & \\zeta_t \\sim N(0, \\sigma_\\zeta^2) \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "For the trend to match the output of the HP filter, the parameters must be set as follows:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\frac{\\sigma_\\varepsilon^2}{\\sigma_\\zeta^2} & = \\lambda \\\\\n", "\\sigma_\\eta^2 & = 0\n", "\\end{aligned}\n", "$$\n", "\n", "where $\\lambda$ is the parameter of the associated HP filter. For the monthly data that we use here, it is usually recommended that $\\lambda = 129600$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['sigma2.irregular', 'sigma2.level', 'sigma2.trend']\n" ] } ], "source": [ "# Run the HP filter with lambda = 129600\n", "hp_cycle, hp_trend = sm.tsa.filters.hpfilter(endog, lamb=129600)\n", "\n", "# The unobserved components model above is the local linear trend, or \"lltrend\", specification\n", "mod = sm.tsa.UnobservedComponents(endog, 'lltrend')\n", "print(mod.param_names)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The parameters of the unobserved components model (UCM) are written as:\n", "\n", "- $\\sigma_\\varepsilon^2 = \\text{sigma2.irregular}$\n", "- $\\sigma_\\eta^2 = \\text{sigma2.level}$\n", "- $\\sigma_\\zeta^2 = \\text{sigma2.trend}$\n", "\n", "To satisfy the above restrictions, we will set $(\\sigma_\\varepsilon^2, \\sigma_\\eta^2, \\sigma_\\zeta^2) = (1, 0, 1 / 129600)$.\n", "\n", "Since we are fixing all parameters here, we do not need to use the `fit` method at all, since that method is used to perform maximum likelihood estimation. Instead, we can directly run the Kalman filter and smoother at our chosen parameters using the `smooth` method." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Unobserved Components Results \n", "==============================================================================\n", "Dep. Variable: CPIAPPNS No. Observations: 479\n", "Model: local linear trend Log Likelihood -2374.899\n", "Date: Tue, 17 Dec 2019 AIC 4755.799\n", "Time: 23:39:46 BIC 4768.301\n", "Sample: 01-01-1980 HQIC 4760.714\n", " - 11-01-2019 \n", "Covariance Type: opg \n", "====================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------------\n", "sigma2.irregular 1.0000 0.010 95.855 0.000 0.980 1.020\n", "sigma2.level 0 0.000 0 1.000 -0.000 0.000\n", "sigma2.trend 7.716e-06 2.3e-07 33.612 0.000 7.27e-06 8.17e-06\n", "===================================================================================\n", "Ljung-Box (Q): 4123.26 Jarque-Bera (JB): 3.56\n", "Prob(Q): 0.00 Prob(JB): 0.17\n", "Heteroskedasticity (H): 2.03 Skew: -0.02\n", "Prob(H) (two-sided): 0.00 Kurtosis: 2.58\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n" ] } ], "source": [ "res = mod.smooth([1., 0, 1. / 129600])\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The estimate that corresponds to the HP filter's trend estimate is given by the smoothed estimate of the `level` (which is $\\mu_t$ in the notation above):" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "ucm_trend = pd.Series(res.level.smoothed, index=endog.index)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is easy to see that the estimate of the smoothed level from the UCM is equal to the output of the HP filter:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(15, 3))\n", "\n", "ax.plot(hp_trend, label='HP estimate')\n", "ax.plot(ucm_trend, label='UCM estimate')\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a seasonal component" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, unobserved components models are more flexible than the HP filter. For example, the data shown above is clearly seasonal, but with time-varying seasonal effects (the seasonality is much weaker at the beginning than at the end). One of the benefits of the unobserved components framework is that we can add a stochastic seasonal component. In this case, we will estimate the variance of the seasonal component by maximum likelihood while still including the restriction on the parameters implied above so that the trend corresponds to the HP filter concept.\n", "\n", "Adding the stochastic seasonal component adds one new parameter, `sigma2.seasonal`." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['sigma2.irregular', 'sigma2.level', 'sigma2.trend', 'sigma2.seasonal']\n" ] } ], "source": [ "# Construct a local linear trend model with a stochastic seasonal component of period 1 year\n", "mod = sm.tsa.UnobservedComponents(endog, 'lltrend', seasonal=12, stochastic_seasonal=True)\n", "print(mod.param_names)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, we will continue to restrict the first three parameters as described above, but we want to estimate the value of `sigma2.seasonal` by maximum likelihood. Therefore, we will use the `fit` method along with the `fix_params` context manager.\n", "\n", "The `fix_params` method takes a dictionary of parameters names and associated values. Within the generated context, those parameters will be used in all cases. In the case of the `fit` method, only the parameters that were not fixed will be estimated." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# Here we restrict the first three parameters to specific values\n", "with mod.fix_params({'sigma2.irregular': 1, 'sigma2.level': 0, 'sigma2.trend': 1. / 129600}):\n", " # Now we fit any remaining parameters, which in this case\n", " # is just `sigma2.seasonal`\n", " res_restricted = mod.fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alternatively, we could have simply used the `fit_constrained` method, which also accepts a dictionary of constraints:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "res_restricted = mod.fit_constrained({'sigma2.irregular': 1, 'sigma2.level': 0, 'sigma2.trend': 1. / 129600})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The summary output includes all parameters, but indicates that the first three were fixed (and so were not estimated)." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Unobserved Components Results \n", "=====================================================================================\n", "Dep. Variable: CPIAPPNS No. Observations: 479\n", "Model: local linear trend Log Likelihood -1204.605\n", " + stochastic seasonal(12) AIC 2411.209\n", "Date: Tue, 17 Dec 2019 BIC 2415.353\n", "Time: 23:39:47 HQIC 2412.840\n", "Sample: 01-01-1980 \n", " - 11-01-2019 \n", "Covariance Type: opg \n", "============================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "--------------------------------------------------------------------------------------------\n", "sigma2.irregular (fixed) 1.0000 nan nan nan nan nan\n", "sigma2.level (fixed) 0 nan nan nan nan nan\n", "sigma2.trend (fixed) 7.716e-06 nan nan nan nan nan\n", "sigma2.seasonal 0.0643 0.010 6.548 0.000 0.045 0.084\n", "===================================================================================\n", "Ljung-Box (Q): 3518.19 Jarque-Bera (JB): 0.57\n", "Prob(Q): 0.00 Prob(JB): 0.75\n", "Heteroskedasticity (H): 1.44 Skew: -0.00\n", "Prob(H) (two-sided): 0.03 Kurtosis: 2.83\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n" ] } ], "source": [ "print(res_restricted.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For comparison, we construct the unrestricted maximum likelihood estimates (MLE). In this case, the estimate of the level will no longer correspond to the HP filter concept." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "res_unrestricted = mod.fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can retrieve the smoothed estimates of the trend and seasonal components." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# Construct the smoothed level estimates\n", "unrestricted_trend = pd.Series(res_unrestricted.level.smoothed, index=endog.index)\n", "restricted_trend = pd.Series(res_restricted.level.smoothed, index=endog.index)\n", "\n", "# Construct the smoothed estimates of the seasonal pattern\n", "unrestricted_seasonal = pd.Series(res_unrestricted.seasonal.smoothed, index=endog.index)\n", "restricted_seasonal = pd.Series(res_restricted.seasonal.smoothed, index=endog.index)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Comparing the estimated level, it is clear that the seasonal UCM with fixed parameters still produces a trend that corresponds very closely (although no longer exactly) to the HP filter output.\n", "\n", "Meanwhile, the estimated level from the model with no parameter restrictions (the MLE model) is much less smooth than these." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(15, 3))\n", "\n", "ax.plot(unrestricted_trend, label='MLE, with seasonal')\n", "ax.plot(restricted_trend, label='Fixed parameters, with seasonal')\n", "ax.plot(hp_trend, label='HP filter, no seasonal')\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, the UCM with the parameter restrictions is still able to pick up the time-varying seasonal component quite well." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(15, 3))\n", "\n", "ax.plot(unrestricted_seasonal, label='MLE')\n", "ax.plot(restricted_seasonal, label='Fixed parameters')\n", "ax.legend();" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 2 }