{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Putting It All Together\n", "> A Summary of lecture \"Time Series Analysis in Python\", via datacamp\n", "\n", "- toc: true \n", "- badges: true\n", "- comments: true\n", "- author: Chanseok Kang\n", "- categories: [Python, Datacamp, Time_Series_Analysis]\n", "- image: images/tavg_predict.png" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "plt.rcParams['figure.figsize'] = (10, 5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cointegration Models\n", "- What is Cointegration?\n", " - Two series, $P_t$ and $Q_t$ can be random walks\n", " - But the linear combination $P_t - c Q_t$ may not be a random walk!\n", " - If that's true\n", " - $P_t - c Q_t$ is forecastable\n", " - $P_t$ and $Q_t$ are said to be cointegrated\n", "- Analogy: Dog on a Leash\n", " - $P_t =$ Owner\n", " - $Q_t =$ Dog\n", " - Both series look like a random walk\n", " - Difference of distance between them, looks mean reverting\n", " - If dog falls too far behind, it gets pulled forward\n", " - If dog gets too far ahead, it gets pulled back\n", "- What types of series are cointegrated?\n", " - Economic substitutes\n", " - Heating Oil and Natural Gas\n", " - Platinum and Palladium\n", " - Corn and Wheat\n", " - Corn and Sugar\n", " - $\\dots$\n", " - Bitcoin and Ethereum\n", "- Two steps to test for Cointegration\n", " - Regress $P_t$ on$Q_t$ and get slope $c$\n", " - Run Augmented Dickey-Fuller test on $P_t - c Q_t$ to test for random walk\n", " - Alternatively, can use ```coint``` function in statsmodels that combines both steps" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A Dog on a Leash? (Part 1)\n", "The Heating Oil and Natural Gas prices are pre-loaded in DataFrames HO and NG. First, plot both price series, which look like random walks. Then plot the difference between the two series, which should look more like a mean reverting series (to put the two series in the same units, we multiply the heating oil prices, in $/gallon, by 7.25, which converts it to $/millionBTU, which is the same units as Natural Gas).\n", "\n", "The data for continuous futures (each contract has to be spliced together in a continuous series as contracts expire) was obtained from [Quandl](https://blog.quandl.com/api-for-futures-data)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Preprocess" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "HO = pd.read_csv('./dataset/CME_HO1.csv', index_col=0)\n", "NG = pd.read_csv('./dataset/CME_NG1.csv', index_col=0)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "HO.index = pd.to_datetime(HO.index, format='%m/%d/%Y')\n", "NG.index = pd.to_datetime(NG.index, format='%m/%d/%Y')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "HO = HO.sort_index()\n", "NG = NG.sort_index()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot the prices separately\n", "plt.subplot(2, 1, 1)\n", "plt.plot(7.25 * HO, label='Heating Oil');\n", "plt.plot(NG, label='Natural Gas');\n", "plt.legend(loc='best', fontsize='small');\n", "\n", "# Plot the spread\n", "plt.subplot(2, 1, 2)\n", "plt.plot(7.25 * HO - NG, label='Spread');\n", "plt.legend(loc='best', fontsize='small');\n", "plt.axhline(y=0, linestyle='--', color='k');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A Dog on a Leash? (Part 2)\n", "To verify that Heating Oil and Natural Gas prices are cointegrated, First apply the Dickey-Fuller test separately to show they are random walks. Then apply the test to the difference, which should strongly reject the random walk hypothesis. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The p-value for the ADF test on HO is 0.956710878501786\n", "The p-value for the ADF test on NG is 0.9008747444676729\n", "The p-value for the ADF test on the spread is 7.019439302142287e-05\n" ] } ], "source": [ "from statsmodels.tsa.stattools import adfuller\n", "\n", "# Compute the ADF for HO and NG\n", "result_HO = adfuller(HO['Close'])\n", "print(\"The p-value for the ADF test on HO is \", result_HO[1])\n", "result_NG = adfuller(NG['Close'])\n", "print(\"The p-value for the ADF test on NG is \", result_NG[1])\n", "\n", "# Compute the ADF of the spread\n", "result_spread = adfuller(7.25 * HO['Close'] - NG['Close'])\n", "print(\"The p-value for the ADF test on the spread is \", result_spread[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Are Bitcoin and Ethereum Cointegrated?\n", "Cointegration involves two steps: regressing one time series on the other to get the cointegration vector, and then perform an ADF test on the residuals of the regression. In the last example, there was no need to perform the first step since we implicitly assumed the cointegration vector was (1,−1). In other words, we took the difference between the two series (after doing a units conversion). Here, you will do both steps.\n", "\n", "You will regress the value of one cryptocurrency, bitcoin (BTC), on another cryptocurrency, ethereum (ETH). If we call the regression coefficient b, then the cointegration vector is simply (1,−b). Then perform the ADF test on BTC −b ETH. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Preprocess" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "BTC = pd.read_csv('./dataset/BTC.csv', index_col=0)\n", "ETH = pd.read_csv('./dataset/ETH.csv', index_col=0)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "BTC.index = pd.to_datetime(BTC.index, format='%Y-%m-%d')\n", "ETH.index = pd.to_datetime(ETH.index, format='%Y-%m-%d')" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The p-value for the ADF test is 0.02336900232347285\n" ] } ], "source": [ "import statsmodels.api as sm\n", "\n", "# Regress BTC on ETH\n", "ETH = sm.add_constant(ETH)\n", "result = sm.OLS(BTC, ETH).fit()\n", "\n", "# Compare ADF\n", "b = result.params[1]\n", "adf_stats = adfuller(BTC['Price'] - b * ETH['Price'])\n", "print(\"The p-value for the ADF test is \", adf_stats[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Case Study: Climate Change\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Is Temperature a Random Walk (with Drift)?\n", "An ARMA model is a simplistic approach to forecasting climate changes, but it illustrates many of the topics covered in this class.\n", "\n", "The DataFrame ```temp_NY``` contains the average annual temperature in Central Park, NY from 1870-2016 (the data was downloaded from the NOAA [here](https://www.ncdc.noaa.gov/cdo-web/search)). Plot the data and test whether it follows a random walk (with drift)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Preprocess" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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1874-01-0151.3
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" ], "text/plain": [ " TAVG\n", "DATE \n", "1870-01-01 53.8\n", "1871-01-01 51.3\n", "1872-01-01 51.3\n", "1873-01-01 50.9\n", "1874-01-01 51.3" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "temp_NY = pd.read_csv('./dataset/NOAA_TAVG.csv', index_col=0)\n", "temp_NY.index = pd.to_datetime(temp_NY.index, format='%Y')\n", "temp_NY.head()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The p-value for the ADF test is 0.583293898787112\n" ] }, { "data": { "image/png": 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WnPbJUrGOiVwKQOODm7fxOGGwClPrFJ7VwuuhgKoqWpP/CTAN5ZUIFw7/4XtP262xKPd3cqFg5qUNWxcXm9V461zcAaAAMDWYsvOsGCxdPEhAldqoQHEBxeFwOB40tfBinBiWijVM5pMAgHyEK18OB3BUoOTWIE0gXhU0LhVFbxFQLH9KDzCv//zkCr53fBFvvmbSPMaYIu/8ZhW7h1JISQJkUWi7hZeVg0UPq0gFtvAsEchN5BwOh9MhVUW3WwNxK1CTeVaBMq98eQWKEwarMKUS3hWoeg9N5F4CKpsMbh3WVB3/x3eexL6xLO5640HzvnErUMUapgbTIIRgMCOh0KGJ3I+8/T4MaOFZAirHW3gcDofTGRVFx8iA2VqIauBVdQNr5Tom8ryFx4mHPYXnUQkCgKrSSxO51tL2Yp6oiuL92v3yA6dxdq2CT7/rGgxaJu04FSgWorl70HyvDKaljk3kfjRaeP7vQ9bC4xUoDofD6ZCKqmPE8mZEvbJeLdVBKewWXi7ClS+HAzim8FoqUGwKr9cmclcFyvq7l5G8UFHxhfufx9sP7cKrXzKOjJSwf05UWIjmlCWghtoSUM0mcj8G7AuZAA8UjzHgcDic7lBTdAxnrQpUxPbJUtHMgJriFShOTBoeKO8WXi+n8KpqawsvI/uLogvFGhTNwNuu3WUeoxxf5LEMqF2DZmL4YFpqOwfK/Zy5EQWCgWQi0APFBRSHw+F0iYqqYchqTUQ1kbMMqEmXgOLrXDhhNKbwmk/L6T5M4Xl5oNjfvVp4Jdtwbd5HFgWIAonlgWoIqPZbeOW6hoRAIIvhUiYfsg+vVNOQlkSIAvG9j5tIAooQcpYQcoIQ8jgh5Jjj9t8nhDxLCHmKEPKZyI/K4XA4O5yqoiOTTJjLXLVo/pNltgfPauElEyJkUeBTeJxQmPhw50AlWQsv4muw3cd2e6CYOCp7iCJ3ajchBGlJjNXCu2CFaNoCKhNtX50T1np0BoD6kU8Hr1UqK/EWCQPxgjRfRyldZX8hhLwOwLsAHKKU1gkhE7EemcPhcHYwLJ05JYmRr6yXinWIAsFoNmnfxte5cKLA2sQtq1xYBapHMQaUUpQ9cqDSlq+p6lGBKnuM/KekeEuPz1shmmMD5ntlMC1hq65B0w0kIlSUALM6FhZhwMilglt4cRcJA5218H4PwP9DKa0DAKV0uYOfxeFwODsGSqntC0lLYuT2yVKxhvGBZFMbgAsoThRYC8+5jw7ofZBmXTNAaauPyK5AeZjIvfxCGVn0FFt+sBBNwXqvsEm+oEk5N16tRz/yKSk4ibyuxZrAA6ILKArgR4SQRwkhH7JuOwjg1YSQI4SQBwghL4/1yBwOh7NDaZxUErGurJe26vYEHiOXCm4dcEwUzcAnvnUC5zer230oLfyXn5zEgydXw+/YATVVR0oSWtpRkiggIZCemcjtLCWfFTIVj8f1qkCl41agrBBNxlDGFFCblehp5BVFRyYZUUClpcALmVJdi2UgB6ILqFdSSm8E8FYAHyGEvAZm+28YwC0A/jcA3yAejUhCyIcIIccIIcdWVlZiHRyHw+FsB/Z0jyQgJYmRc6CWizU7A4rBK1DROLNaxj1H5/DTZ3ZWM4NSij/96Ul89Rdne/o4NVVv8T8x4rwG42JnKbk9UGwKz2MAgvmisg7xkpZjeqCsEE0Gq0DFMZJ75Vf5kQszkdf13lSgKKXnrf8vA/g2gJsBzAP4FjU5CsAAMObxvV+hlN5EKb1pfHw81sFxOBzOduA8qaQkIVYLr7UCleAVqAiU6uZztLJV3+YjaWajokLVKU4sbPb0caqK3uJ/YsT1F8V9XKC1hcfEnJeJvFTXIIkESUdmVZxWtztEEwAG02ZkSDwBFa+Ft1XTQKn3appSXY2VQg5EEFCEkCwhJMf+DOBNAJ4E8B0Ar7duPwhABtDbGieHw+H0AedJJeqJoabq2KiomMy5K1DBrQOOCfO+rJR2loBi0RRLxbr9515Q04yACpRgB212G69qEgAIgjlZ52cid1drMjEqUO4QTaC9ClS5Hs9ErhvU9xhLtfgtvCj3ngTwbas7lwDwNUrpPxBCZAB/SQh5EoAC4IPUT9pxOBzORQS72s/I5hRelA91VjmZ5C28tmCrNHZaBcopmk7MFzB5dSrg3u1TVXQkfQRUXH9RHFi1lU3dOckmRd8KlFu4pOTox+jOgALaE1BVjwR1P/K2SV31bNWV22jhhd6bUnoawPUetysAPhDr0TgcDucioNJGBWrJlQHFyKUklOoadIPGCum71GCTXTtNQC0XG8dzfKGAN1w92ZPHqWs60pJ3UygVoz0WF1Zt9WqFpWXvCI+yh+E6LYmRoxbcKeSAQ0DFSCMvOxZ+h2Hvw6tq2DXY/LW6pkPRje638DgczqXB88tbePTc+nYfxo7AGWqYlIRIBl62xsVdgcpbH8rlGCPelyI7tQJ1wRLG+8ayODHfOx9UkAeqtxUofwGVlRP2xJ0Ts1rTmlzuNbHnhTtEEwDkhICMLGIzZgUqbJEwIxewD49FNUQVYwwuoDgcDgDgP/7wWfz+1/5luw9jR9A4qSQiV6AWrZPClEtAsSt13sYLZqve8EDtJDfIUrGGkayMl80O48RCoWfHVtP8p/Ciivh28DORA1a2k8drv+ThgUrHCJx1h2gy4qxzUTQDim60xC/44WzhuWHifcCqUkWFCygOhwMAuFCs43yhFquE/mKlMYUnRm6fnFurIJdK2Hk2jJz1ocwn8YJhz4+iGbHCFHvNUrGOiVwSh6YHsVpScL7QGyN5WAWqVy08vxgDdpt3BcqjhSeLqGsGdCNcYLpDNBlxFgrbrceIFah8wGLvLWsCtFc5UBwO50XOqtU6eW55a5uPZPthJyvmgaqqemjlYW69gtnRTEsQYi7gg5vToOR4fnrRxjt2dr2t6tHylnmyPzQ9BAA9a+PVVCMwxqBXAqoc0MLzm6zzq0AB0RLTFwvNIZqMwXT0fXgVtXGRE4Wc7YHyb+FxAcXhcGJDKbVPWs9c4AKq4vBApSQBBgVUPVxAzYxkWm4P8l5wGpTqvRNQT58v4te/9M+4/9n4Yc4s2+vKqRwSAsHx+UJXj43Bksi96KUHqqroEEjrChkgWEC5xQYTMlGiDFgFys1QJnoLj4me6ALKPF6v6ibLIIu7TJgLKA6Hg2JVg6KbHotnLxS3+Wi2n2YBZX5AB53AdINifqOCmZFsy9caLTxegQqiVNfsk1y3s6DWy+Z6kLgXB7phXlhM5lNISSKumMrhxELvBFRQDlTvksh1ZORES+UUMNtjFdfwA6XUyoFqPtaoO/sopVgq1lu8goDVwqtGW+XCWnhRc6BSkohkQvD2QNkVKG4i53A4MVkpNXwdz10obeOR7AyqVjVAEIh9YggKMjy/WYWqU8yOtlag8gFXvpwGWzUN+8cHAHS/AsVEwKmVeK/ttVIdBoW9nufQ9CCOz3ffSM6WV/u28GJkLMWlqmq+WUpZjwpUTTVgUHgEaSasnxd8nFt1DVVV96xAxTGRl5V4LTzAvJgpVj0qUMxEnuQmcg6HE5Nl64R1YDyLZy4Ud9QU1Hbg3LGVjlCBemG9AgCY9WzhcRN5FLZqKvYMpSCLApa3umvUZr+70zEFlB1NkTOnxa7bM4RCVcUL691deKzqFAaFbwsvlRChaAaMCAbtuAStQ0nLCVQUvelxWau11UQu2D8viGWfvDQAGMrIqKlGJB+VbX6P4VvKp7334fEWHofDaRt2xf+qy8dQrGl29s2lSlVprNVotCb8WyjnLAF1mYeASkkCEgLhLbwQSnUNuaSE8VyyBxUoS0CtlmN9HwtHnXRUoADgeJf34jGBF2QiB8yog25TUfxbhywXyXnxwKbyWpLI2YVGiIC6UPDOSwMcUQMRqlBB+VV+5H3WKrEWXtRIBAYXUBwOpyGgXmIu/H72EjeSO9sa7Mo6qAJ1bq0CSSTYPZRu+RohhC8UjkCppmEglcBYDwXUZkW1/VBRWNpqFlAHJ3OQRaHFSK7pnfmT6iECiiWUu0U8pbTjx64orRN1DC9jOKtA+bfwgi8U3KLUSZx1LpWYJnLANJJ7iTO2B88dqxAGF1AcDgcrpTrkhICX7x0GwAWUs62RSoSbY+fWy5gezviuasmlpKYxfU4zukFRVnTkUgmMD3RfQDkX4sZp4y0V6xAIMDYgAzDTsq/ancdxK8rAMCg+8w/P4NpP/RBPdmAuZ+Lc30Tu3Ub+xLdO4AN/caTtxwWCW3hMFDmN5GW/Fp5dgQoWdA1R6tHCiyOgAvKr/MinJc8WnpcpPgpcQHE4HKxs1TE+kMRQRsZkPskFlKOtkfJoY7jxizBgDCT5QuEgnL6a8VwSq12ewnMuxD29Er2Nt1ysYWwgiYTYOFUe2jOIJxeKKFRV/Kv/fgxfvP8UFM3AV39xtu3jY5Ul3wqU7C3in1vawsOn121B1w7VoBZesrUCxczbXqtczPsGv86Xi3XkUglP4cMqUFHCNIPyq/zwb+G1xjJEgQsoDodjCijLKHvFVB7PLl3aAqrqUYHym8KjlOLcWsVzAo9htvC4gPKDCahcyhRQa2Wl49aUk6qiYyCZgCQSnFqNU4FqzSu6bnoQpbqGt33u57j/uRV8+l3X4PabZ/B3T5zHZiV6e7Dp+OzgVu9TcjLh7S/asITG3Q/PtfW4QLiJ3LxP47Vb8gmdjBpj4PWcMliKf9QKlCgQz/wqP/I+LbytuhZ7jQvABRSHw0GzgLpyKoeTy6WunsAuNqqq3pjCC6lAbVZUbNW0wApULuXdOvDj9EoJr//s/b6trD//2Wn84dcfj/zzdjrOMfLxXBKUIpZXKYyKYlYYZkezsSpQS8V6S6uJGcnLioa//p2b8Vuv2IsPHJ5FXTPwzccW2jo+JjqYWHfDXoN1zS2gzOfob584H3n8301F0W2h5Cbr4YGyW3gp7yDNsBgDFkzqhV2Bimgiz0iiZ36VH/m0hLpmtDyP5moa3sLjcDhtsFpyVKAmc1A0A2fXKtt8VNuHcy9ZysfAy5izJvCCBFQ+ZgXqyfNFnF4p44zP1NgjZ9fxwHPxU7V3Ks4x8nFrwexyF31QrMpyYDwbywO1vFWzM6AYV0zm8NnfuB5/99FX4dbLxwAAV+/O48aZIdx95FxbESD2FJ5PJSiVaH0NarqBQlXF66+cQFXV8Z1/aU+8VRUtoAJl3s5Sv80/e5vI2fslLMZgqVjHZM67AsUiP6KayDMxRY/fWiVmIo8LF1AcziWOphtYKyv2ieuKqRwA019xqVJxnFTSIePZLMJgdrQ1hZwRdwqPnUD8/CRVVcd6pbttru2EndBYCw/obhp5VdGRlkXsHx/A3Hol0vOmaAZWS0rLyZ4Qgve8bLolsuLOw7M4vVLGw6fXYx9fPWIFyvkaLFRVUAq85iVjODQ92JZ4o5Sioup2pclN1rOF5x1jIAoEckIIrEBRSj1FqfNn+LXZ3FQcVeKo5H324ZkeKN7C43A4MVkvK6AU9onr8okBCOTFuRPv7GoZv/1XRz03zDtpmsILyeCZWzOrRGEtvFJdi3yCYx/wfqKtouigtOGBudixBVQygQkmoHpQgdo/loWqU7ywER6EyQScX7vJzdsP7cJgWsL/OHIu9vGxypJfIrjXa5D97oezMu48PIPnlkp45OyG/fVTKyX85l8cwSNn/QVdTTVAKXxbeF4xBuW6hrQkek6cZmQxMAdqo6JC1WngczqYkZq8ZCfmC/jgXx5t8VZV6v6VMz/yae+tACXewuNwOO3AWiVMQKUkEXvHsi/KnXgPnVrF/c+u4OSyfxvHMCjqmmGfzJhJteZXgVqrYCKX9D35AWZlxaDN02BB2ALK52qenaTWyt2dVtsuSg5fzXhPBJSZLM9WxURp4wXlFXmRkkT8+sum8cMnL8Q+9kaQpv8yYaBZUDP/03BGxjuu341cKoG7LfH2T88u491feAg/P7mKh0+t+T5uJWQdCkv5dpvI/XKj0lKwgIrynA6l5aYW3uf/6SQeeG6lpZ1dUfTIe/AYE1Y18UKhIaAppaaAiplCDnABxeFc8qy4BBRg+jxejFEGbDXHRoBB2Z3JQwgxl7lq/h6ooOoTEH+dCzOc+/lJ2MgeoJAAACAASURBVDGubnXPaL2dNEzkCaQkEblUoicVqAPjZps1yk68oJUjfrz/8Aw0g+Ibx16IdXy1kByoJPPhOV6D7DU8kpWRkRN4z43T+PsTF/An//gc/uevPoLp4QxSkoD1gMlAe2m2nwfKw9cUZLhOyyIqAS28hoAKqEA59uFdKNTw418uA2gV1BXFf4efHzPWpOw5h7+zrhnQDeorCoPgAorDucSxBdSAQ0BN5XBuvRK6lqFd/uz+U3jo+dWe/Owg2ElxI8JJxXlVnpJE3/HsufWK/cHsh5951Y9CaAvP/DkXWwXqG8dewA9OLLbcvlXXQEjDVzOeS3bVA1WxPFBDGRkjWbllEu/Bk6v4zz9+ruk2ew9exAoUABwYH8CtB0bxtSNzsaYIw1a5MCFT86hAsdH/9x+egaIb+NOfnMRbrp3CN3/vFRjPJSNdLPhVoETBvHhwC6igCpRfpRZoCKgJHxM5YAooNoX39UdegG7t4XMPFZQVPXb4ZT4lYTgj2b5FoLl9HBcuoDicSxx2onJWoK6cyoFS4ORy96tQqm7gsz96Fn/54Jmu/+ww2Ad40Mmtal+VNz5Q/VoTNVXHhWINsyP+BnIgvoBiG+P9KlDs9tXSxVWB+rP7T3kGTpZqGgbkxiqNbqeRm7EU5sl2/1hzlAGlFP/n95/Gf/7xSSw6WjtLxRoSAsFIRo71WB99/eVYKdXxri88iGcitsGZB8ov08grY4l5oEay5vEdnMzhw7cdwCffdiW+8P4bkZETGM7IgT455gUM8hJl5USTZ7AUIKAyshg4hcdEaVBVbzAjoVhVoekG7n1kDjfNmtsR3K8HMwA0vuiZGcnYy78B/1iGKHABxeFc4qxsmcnAzqvfg5PmJF4vjOQvrFegGRTHFwptjXx3gt3CC6pAqa0nlZQkerbw5jcqoBSBIZqAU0DFa+GFeaC6ndjdSwyDYmGz6nnMWzW16QQ2nktitQceKMCsEp12hGk+Nrdhv85ZuwgwXysTuWTs/Wi3HhjDN/71K1BXDfzaF3+BHz51IfR7aqqOlCT4ZhpJormQ2vl62CgrkBNCU9vv42+9Eh96zQH755gCKvxiIWiaLe0yhpcV/5H/lCQGTuEtFWsYzkh2MKgXg2kJmxUVP31mGYuFGv7Va/YjK4stAqqstLd+ZWY029TC85sqjEIkAUUIOUsIOUEIeZwQcsy67VOEkAXrtscJIW+L/eicHckDz63gyGl/4yHnxYUzRJMxO5pFShLwXA8EFLv6X9mq24KmXyxvsRaev5CpevhCUj4VKJYB5R5pd9PwQMVt4bXeX9UNaFZbY+0iElCrpToUzcCaR9XMvUpjvIsLhXWDoqYattDYP57Fakmxn+O7H57DQDKB6eE0/vHpJfv7gsbtw7jhsiH83e+/Ci+ZzOFf//Wj+POfnQ68f031X6fCMNvIDg9URcFIRg4MkhzOSLHb1W6ycsJe3wKYmVCBLbxAAVUPbYkOpiVoBsV//fkZTOVT+JUrJzxbuqavLb7omR3JYGGzCtWKsmDvyV5XoF5HKb2BUnqT47b/ZN12A6X0B7EfnbMj+b9/8Ev8yT8+F35HzouCla26PTrOEAWC/WMDeD5G6GBUnFf/nezwiouqG3bLK9AXorQaelOS0JJeDDTMqNErUFFbeP4mcudtXmJkpzK/abbHClUViqua556CGs8lsVXXuuLBYxURVq1wTuJtlBV878QifvWle/DWa6fwz6dW7SrhUrGGqTYFFGB6p77+oVvwhqsm8ZkfPhNYLXQGt/rhru6sl1Xb/+THcFbGRtn/YqES4oECgEyyuS0XNPIf1sJb3vJf48JgC4WPnl3H7TdfhoQoWIK6Zt9H1Q0omhE7xgAwjeS6QXHeej36LUeOAm/hcVpYKytdTQHm7GxWSnWMe5g6Z0czdoWlm5xeKSOXSkAUCE50sME+Ls6KRtyrcj8P1Lm1CrKyiNFssE8mzhQepdTOqfGaaHIex8XUwltwZC+5PWhbNc1+joDGQEM3/n3McM88bfutSbzTK2V887F5KJqBO2+ZwRuvnoKqU/z8pDnc4LXGJS4pScTH33olVJ3ib47N+96vphkRKlBC0z7GzYpi+5/8GMnIKNW1FsHKqLqeGy/coqhc13zbXWk5vIUX9pyydS6iQHD7y2cAtFYko1TO/GATs+yzrdQHAUUB/IgQ8igh5EOO2z9KCDlOCPlLQshw7Efn7DgopdgoK1gq1vruT6GU4nvHz/umBC8Wqry12ANWtupNE3iMmdEM5ter9hRMtzi9UsYVkzm8ZGIAx+f7J6CYgTyZEGJflZseKO8W3sxoNnQfV1YWIZBoFaiyotvPuZdoY4JAEomvifxnz610rb33yNn1JtNtu8w7BJRbGG3V1KYpKNZS7saFnO3zsQTKzEgGCYHg1EoJdx8xTcpXTpmrWIYzEn789BJqqo5CVW27hefk8okB3LJ/BF87eg6Gz3upquhIhgiotLsCVVEwHGJwH7IElt+S44rrufEi4zCRGwY185d8W3gJ36qhblCsbEVo4VlVtV+5cgJTg+Z93UMFUbxbfsy6ogxKfTCRv5JSeiOAtwL4CCHkNQD+DMABADcAWATwWa9vJIR8iBByjBBybGXlxbO76cVKsapBs94kpZC05m7z+Aub+OjX/sW+AnTz5QdO43f/27G+HtOLnYqioVTXWjxQADA7koWiG7hQrHl8Z/ucXi3hwPgADk0P4vj8Zt+EOvNbHZzMhRhrW6/K/SpQc+sVzIb4nwAzS2ogGW2dizNE0Osx2Ul091Aaa+V6y/NXVXT89l8dxV8/HD8R2w2lFL/7347hi/c/3/HPWthsiDC3gPLyQAFoatu0i7taIYkCZkYy+OZj8zizWsadt5hVjoQo4HVXTuCnzy7b7Z04EQZB3Hl4Fi+sV/Gzk97nwLqmI+0ToslwR2lsVlQMZ4NbeGyC0M/zZz83AWbsjKOqxLxQftWatGyucvF6T6+V6jAoQkXp/rEBDKYl/O6r99u3jeeSKNY0+9/PjqMdE/lkLgU5IfSvAkUpPW/9fxnAtwHcTCldopTqlFIDwJ8DuNnne79CKb2JUnrT+Ph47APk9Bdnrky/Db62P8Xn5LZRUbBV10LXcHCiw4IYPQWUfaUWfXt9GIWqitWSgv3jWRyaHsJGRW2qTPQSZiC/YsoUUH7CzcsDlZSElmXChkEjZUAxcikpUgXKuacrqIU3M5JBTTVa0s0XNiswaHfaXyulOgpVNbBiF5WFjapdZXJ7t0q1Vg8U0J00cq+wyP3jWSwV6xjOSHjrtbvs29941SQ2K6qdVdVpC4/x5mumMDYg4+4jc55fj+aBauyZ0w2KzQgVqGGrmuMX21FRNHOHnegvBcwKlCVc6sxP5hdjkIBuUCgeXQQ7V8vjs8bJ1GAKj//bN+LmfSP2bez1wF7TXu/RqAgCwcxIxv5cK9U0CKTNnxV2B0JIlhCSY38G8CYATxJCdjnu9qsAnoz96Jwdh1O8LHW58hD62Nab3K/yxdKKu/GhWlP1yBktL2ZWSubv2EtAMa9AN9o3DLZCY79VgQIQ6oOqqTp+udj572qpWIMoEFw+MQBVp75rVbxaeF7TRUtbNSiaEZpCzsilEi07uLxgFahcKuE5hccEwfSw+bjuVh3b89YN0cMmJrtRjV7YrOLQZebv3Hmhphvm78JZARjNJiEQuHwvGp46H7/l69XuOWAZyX/jpsuahMtrDo5DFgXcc9RMEu9WBUpOCHjvTZfhJ79csqtbTmpavCm8YlWFQREuoLKsAuXfwstIYmALOiuL9uvQHvn3qfzYeVWKl4CKvhrHfTxuQV22jyN+1QiAJaAaFahsMhHahvciSgVqEsCDhJAnABwF8H1K6T8A+IwVbXAcwOsA3BX70Tk7DueVYb8FFFs54HeVzm7vRkLxvUfn8M7PPxQ4cnsp4JVCztg1mEJCIE2ZKZ3CTsj7x7O4YioHSSShPqj7Hp3HO/7Lg74+jqhcKJjThsx46zeJV1V0ENIcauiVRM4qZ2ERBozxXBKnV0uhLUtWgZrKpwKn8KaH0wBawzSZWTtOErYf7PcVNb/KD0op5jeqODiZQzIhNB0za8fkHBUoUSAYyTaPrt/19cfxa1/8ha9H0o+yx763Q9NDkBMC3n/zTNN9s8kEbr18FAushReQmB2XO26eAQVw7yOta16iTuGx16C9By+khTecCRZQVSuhPYiMtZ6FUho6sWbv7PP4XF3airdb0Mn4gPk97POqExM50AjTZHvw2kkhByIIKErpaUrp9dZ/11BK/y/r9t+klF5HKT1EKX0npbQ1n59z0eH80O13C4+9yYs+H9bs9m5UoJa3zEyafvu8dhpee/AYCVHA9HC6ae1Bp5xeLSFhldCTCRFXTuVxYiE4ymC9rEAzKM52KORYrs9IyEnF66qcGXid4mfZXvURrc3zjkO7cXqljKNn1gPvx6pUU4MpT4FftYI+WeXL3apjJ/8gn1dUWMUwavyCH5sVFRVFx56hNMYGkk3HbK/ScJl4nZNXP31mCT98agl1zbDXfESl6nGyfdt1U3jkk2/A3rHWBPk3XDUJwBTQ+XR7J1YvLhvJ4LaD47j36JydQcSoqUaogEp7CagwE7nVwvO7WGA7AoPIJBOg1DzGsMoP+1kVj8rpUrEOQoCxgXjJ7oCjAlVyC6j2fj+zoxmUFR1rZcXc7deGgRzgMQYcF2vWG01OCNvWwgutQHVBQDHh1Ktdb0EUa+qOqXytbNUhEPiOQ8+MZjHX5QrUzEgGkuW5uG56EMfngxPJ2Ydlp14sM9cnaV+1+1VoqqreMtadkgQYFFD1xnEyg7NX9c6Ld1y/G7lUwtcHwyiEVKCqVnuEVb7cfiJWGeuKgFo1n/MorUfAbMd5ea+YqJseTmNsQG465sYi4eZqChNQVUXHv/vbp8ACweNWIr1OtoQQe9rLDRNQk/lUW22dID5weBbLW3X85JdLTbezJPIgnB4o1p4NizFISSKyshhoIg+KMAAaoqhsDZwA/hWoVFAFqlDD2EASiQC/lR+jAzKIo6XrVVWMA7v4OLdWCVxNEwYXUJwm1ssK0pKIy4bTtum2X7A3ub+AMr/ejeNiH9pBmSW94vYvP4z/74fP9v1xvVgp1TE6kITos65iZiTdVRP56ZWyncMDAIf2DGKrpgVWl5jY7NSLxVKQo7U1mj8avU4MK6U6EgIJrQIw0rKI99w4jb9/cjHQ4M1aeJP5lOdEE7u6Zy08twdqYcN8njYqascTjo0KVLSqzzcfncer/t+ftlQ8mKibHs5g1FWBKtXNn+2uArDR9S/e/zxeWK/i9157AIAZIBmHRg5UtJPt1GAKL50ZCg1HbYfXXTmBqXwK3338fNPtUZLI0w4P1HrEChQADGXkgAqUhmxoC8/8vVTqumP6LbgC5XVhurQVngHlhyQKGMnItoDyqirGgf1u59bL2Kr5r6YJgwsoThPrZTOcbTKf6n8Lz65AtX5Asl410J0K1FY9eFlrL1nYrOJUDxK+28EvA4oxO5JFsaahELD6JCq6QXFmrWwnQQNmBQoITiRnJ8BOvFgs16dJQPmciCuKhozkrkCZH9TOIMOVrTrGBuLtSrvz8AxUneK+R/1DFQtVFblUAllH68QJO3kMpiXkUwnfFp6iGR29vhXNwAsbVcgJAXXN8A1jdPLE/CZqqoHjrsGAeUvU7RlKYzTbXIEKauEtbdXx5QdOW0nh5txSXG9XOyfbL//my/DZ914f63GiIAoE1+7Jtywzrqrxksg3bQ9UuIAayfrvw6tE9EAB5o7Ikj2F5/097Gd5VqCK9Y48Zc6WbpiQC2N6OANCzM+Ucp0LKE6XWCsrGB1gAqrfFSj/Fl5Z0cEy6LrSwqttXwuvomhdMcJ3A689eE7YiP659c6rUOc3q1A0A/sdvhNmKj4RYCSvWgKiEy8W8ytN5JLIpyUIJNgD5T6peJljw547L14ymcPN+0bwtSNzvqGKxZqKfEqyc4HcfpKKqiMhEEiigLFcEqsOQVHXdCxv1bFnyKxOddLGm1svQzcortmdBxCtCsWEwQmXIF7YrCIjixjKSBjLJZvyq9iFkdvIO55LQjcokpKAT77tKlssxG7hqTpkUbDbxlGYyKUw0UUDuZOZkSzmLAMzYLaFDRpeIUtJIhTNgGFQrJdVSCIJrR4Bpg9q3ecCqBrFA8VaeHU9soncS7gvF2uYHOxQQDliDATXoEccUpKIqXwKc+uVlgyyOHABxWliw6pATeSTWC62hvT19LHtFl7rm915WzfEx5bVNui3F0nRDKg67dqi1E4JEwHu1N5OeN4RYcCQRAFX7863VCycMJHbiRfLOQEkCgSDaf8lq14nFXs821ENMlfgxG9JfOCWWcytV/Dz570DY4tVFYNpyW6duK/mnZNTY9lkUwtvcbMGSoFr95iip5Mog1OWGLp+eghANCM523Ponqxc2KhiejgNQghGszJUnaJY1Zp+rruFt8s62f7Rm6/AeC5pm//X4wqouha5fdcPZkczqKp6QwxYv98wMWC/BjXdzoCK4tEaycr+SeSqFmrEZlWeqmIKqKDMJPY8uz9XFc3AWlnprALlSCMv181Fwp141C4byWDO8kBxEzmnK9gtvFwKim5gswutmygYVjAc0KgOOWEfsllZ7GoFqt8tPFZNWC0pvhWIfkEpDRUBlw03743qBGeEgZNDewbx1ELBd2UMmzq7UKy1LXjdGTRBS1araquAYp6omrsCFdFA7uTN10xiNCvjbp+k8GJVQz6daLRDlFYBxY5vdEBuigRg7bvr9pit0U4qUOz3xfK6wgRUqa7ZbX93ttf8RtWuio2xPXdWFlTDRN58EvuVqybw5d98Ge48PAvAPDknE0Lsz6Qok2b9hFV12QUBawuHT+Gx16CB9XJ4iCZjOCP7D0xEaOExscRM5NkA4WJXal2vWSYWOwkmZS08SqnZZu/wdzo7ksFZ3sLjdJO1ch2jlgcKaFy595pizQyGEwXi+UHNKlD7xrNdER/2FF6fK1DscXWDdmVKqhMKVRWqTgNFQDaZwNhAsiuTeKdXShhMSy2Ld6+bHkJZ0XFm1dsX5vwwZl6auCy5IgdGMv6+EK9MnlSiuYVnGBSrJaWtClQyIeI3broMP3lmGYuF1lDFQtVs4TVGwptfoxVVt6sGYwPNFSiWAXVNVwRUCeO5JHYNmsInrIV3xhJcL987jMVCrWnYY2Gzij3DLgFlXQht1TUQgpYFtcmEiDdfM9XkMRvJ+osBPypquEjoJ84JMKDxmooSpAmYIj7KGhfGcEbGVk1riU4ArEpOyOOyClRFMbdABPmO/F6zcUI0/RjPJVHXDBRrWldE8exoBqvWehkuoDgdU1E01FQDw1nZPtH0y0jOPhT3DKVRUrQWgcRE1f6xga6Ijy3bA9XfHCjnB0s3FqV2wnJABpST2dFMVzxQbALPffUalkheUXT7pBvWSqSU4o6vPIzvPr7QdPtysQY5Idib3ocCrsq9PpxTrtbERkWBbtC2BBQAvP/mGRiU4luPLbR8rVgzW3hpn5NRVdHsk+3ogIyNimqHS85vVCAQ4JpdrIXX/vvk1EoJB8aztrk7LMqAte/e/dI9AGD72kp1DYWqij1DGfuYgUZkSqmmYUBORDLjD2X821F+RPH59BOzldmo6rK2cGgFymHQjrJImMGElrtyZximeT0TIh6coqhc1wP3z/nFGCxbAmqiwwoUYFZ+zQpUZxldM6ONSjhv4XE6hk3GNFWg+mQkZ/6n2dEMKAVKLmFjCyir/dOJD0rRDNStiaJ+V6Cce/y22wcVFKLpZNbyCnTK6dUS9o8NtNzOXmvuPCNGTdVx5VQOQLiAWisr+OfTay3CZKlojlAz8TaSlXxbQV4fzqwCxQQUe/21K6BmRjOYHk7juaWtlq8VqiryackWSe62pdPkPmoJSyYG5zermMqnMDqQBCHwNQ9H4fSqOTGZT5kn4LDQ2VMrZQgEePt1uyCQhg9qYaORAWUesyWgrOdwq6ZGPoGNZKX4FSiPqcrtJJkQsXswbQsouwIlB5+OkwlnBUqJNIEH+KeR17Ro04m2gKrr2AppdyUTAgTS2sJrVIA780ABTEB1LoqdK5h4BYrTMeyDaSSbtE8My/0SUNZjs3BAdxuP/X2fNcHVifhwngiqHjubeomzmnCxCKjLRjJYLNZQ19oXm8wf4/Y/Af5lf0ZF0TE9nEZGFkO9WOzrj57baFr54R6hHs7IWPdZKFz1aPk0zLHmz4z63AWxK5/GYqH5/aXqZvSA00Te0sJznDzGLTHCfFALG2arzDbKt1mBWi8r2Kyo2D/WqECFtfBOr5QwPZzBUEbG5RMDdkXRjjCwBNRIxgpFLDV2X0Y9gZkVqPhJ5JmAqsl24FxmywQyE+l+OD1xGxXVXhQcht/qoqjrUJyvw7AWHiHETu13slSsISEQexCgHZxp5GUlvHIWxiwXUJxu0hBQMlKSOXLcrxYeuzqatQVU84ck+ztbAtqRgHKIs4ra3xZeUwVqm6MMmEclSguP0kYYYjswf8wBDwEliQJkUfAVUEzQzIxkwgWUY0Ho044FxGaIn0NAZWUomtHyQa/q5pSk24/CUqLZ/VksQjsmcsauoVSLB4pdKORTCd+1GM7QRVaBYllQC5sNs/ZwgM/LyT89s4x/8zdPNIlJFqB5YHzArg6FmcidIanX7RmyE+btFHLruBKigOGMbFeg4kxBjVjCNw7lHdbCA9D0WrYFVFiMgTWlt7xVh27QyC08e52L63ljVaIw75UoECQTgu2BChMbaTnR8l6+UKxhIhcvM81NUwuvHh4AGsZQRrIvDngSOadjmIBiJt/JXP+yoNibeyagAiUQ2LurOhFQLMIAAGp9n8LbORWoo2fWMT2cDl2kOeuaGmoH5o9xRhg4ySRFz/1ZgHmCycii6cUKSUV3tvicO+eWi/Um/wW7ene3g5hAavFAdbmFB5iJ10uFepPfj61xGcxIvqGEzgoUe6+ulevQdAOLhZpd6RnO+Ec1OPn+iUXc9+g8Hj7deL6cE5OSKCAtiYEVKMOgTS3aQ9ODWC3VcaFYw4IVxjnmEJvOMM2tmoZcKqIhOiujUFV9Jza9qCo60juohQeYLdzVkoJSXYtdgTpvCdKwNS4MuwLlqtzF2SeXTSbsKbxwASW0tJ2XOsyAAszgWEkkdguv08EAQoj92cYrUJyOsStQVltgIm8mAfeDjYoZDDdlvcm8KlADyQQGkuaVedcqUH0WUCxBNyUJ2yqgqoqOn59cxRuumgzNUpkZMUVrJytdmD/Gbz1GVk6gXG/9XTgrQrOjWbywUQ2cwJxbr2Aqn8Le0YwtCEp184O/qQLlk0ZuX5X7tPCYmFnZqiMji21fuQLA7sE0FN2wzdRAY41L4BSeMwfKEnBrJQVLVmVi2oqeGM74RzU4YR6l/3GkEatwarUEWRTsn5VLJQIrUIvFGmqq0ahA2QnzBcxbVTFn9cG5ULhU10JFPGM4I4HShtCMQjdG3rsNex+8sF6x28JRgjQB2G3fODEGQOvFQpx9cmlJjNTCa9y3+bWyuFnDbmuas10IIXYWlLmCpnNRzC7Y3Sn4UeECimOzVlYgicT+MJvMp/rqgRrOyPaVqFcFin3NmUjbDk0eqD6byCuWSNg7mt1WAfXg86uoawbeePVk6H3HBmRkZLGjJHDmj0n6XGWnZdHOe3LCfj8pyWzhKZoRGK0xt24uKz68bxSPnF2HYVD7NezMoBnOehtr/XwhLOTQ6YHqpPoEwL5YuODwQdkVqLTUiE7wnMIz36O5ZAKyKGClVLeFkN3CC1jh4YS12H745AX7NXl6pYzZ0Yy9IzFMQJ22Q1JNAXX1rjwSAsHx+c2mDCjG6IBsC0d2cRQFVk2JYyTfaTlQgLkiCTArpo3XePDpOG0LKPP3FdVEnpJEpCWxxQMVZ8VNNimau/DqeriAkhP29gDAnIxdLNTs13snsM/+bv1O2cUhb+FxOma9XG9Kt53MJ+1+e+8f2xRQeR+/RbGm2VcJzkTadmA/Oy2JfV/lwq76ZkYy2+qB+vHTS8ilErh530jofQkhpmejgxbe3HolcDlrVhY9K1BVR5vBnZ/jxbm1CmZGMzi8fwSFqopnl7YaE0A5jwqUry+k+QOVEIKU1GhNtBui6YRdkZ93+KCKVuU1n5YgCOZjOkU+pdTKgRLt4xodMNthLWbtCAJKNygWC1W86epJaAbFN469AMAURE7D/0BKso/Ni9O2x81s4aUkEQcnczg+XzCN7S4B1VSBqkX3QA1l4q1z0Q2KumbsqBwowBGmuV62X1NhXqSkJbDOb7IKVLS2J7tvJy28jJxAoapC0Q0MhBjy05LQZI0oVjVUVd1Olu+E8VwSFwpV1DWj4xgDAHjbdVP4tZfuiVzNc8MFFMeGpZAzJvMp6AbFWrn3J3oWDOdfgVLtcWrnUsl2YIuEJ/LJ/legFB0pScCuwdS2VaAMg+InzyzhtVdMRN4PFsXAHYS5ysNfQKVlbzHbaKkJoV6sqmLugZsdydjC8MjpNdssP9HUwrOMtS0eKM0+HjcpSWzyQPW6AgWYJy5nO6SuGaCuvWksTNNdgRrKSKipRuBFwvJWDapO8ZqD43jF/lF87cgc6pqOufVKk18tH6EClZVFTDiek0PTg3j8hU2slup2hEHjmM1wx6qio6zo0StQPu0oP9j7uxvtnm4ymJYwmJZcFaioLbx4FSh239Zqq/9r3U1GFu0LvrBqTUZONA3nsAuEXR228ADzs599DgXlUUXl0PQQ/uR9N9iV1rhwAcWxYYuEGcwzstyHSbz1imJN/wlICMTDA+WoQHXawrNOBBO5/guosrUKYTyXRKGqdhQN0C7/8sImVktKpPYdY3bUFFDtJMBXFR1rZaXlJOokKyfs6pyTiqMitHvIHM/3C/V8warAmBlLlqKnqQAAIABJREFUGewZSuPo2XV7EMLZQhhMS545SUGj3c6KZTdaeKNZGZJImitQVTaFJ9mP6fRAebVd2DqXhc0qxgaS9ol2xKfK5sQWXcNpfOCWWSxsVnH3w3NQdWpXkwDWwguoQFmZUU4/3XXTg7bo2jPsbuGZzx07GUb1oLCJMq8og5/8cglPusJYK/XoIqHfsPcUawuH7cJjFarlrToSAonsGwO8q5FxWngZOWG3wqN4oJyinV0gdKWFN5CM7BnrB1xAcWzMRcKNk0I/wzQ3KwqGrPbhgMfV7lZdbWrhbVbaFx+luoqEQDCUkfvewqtYmTTs5LvqEx7ZS378yyUkBILbDo5H/p6ZkQzqmtFWevrCpnmSDBJQmWTr6DPgDBkUIYkC9gylMbfuHafAWnuzVsLw4X0jOHpmHYuFGrKy2FTlSIhmKrm7FdQQbD4VKM1AXdNRqKpN1ZZ2EARzaMJdgZJFwfbDZGSxaaKp4tHuGbUWCjvXpQCNdldQtcYZMfDGqycxNpDE535yEkDzzsJcUgqpQJVbIioO7Rmy/9zigbKqJ2dWTTEcVUDZHigPUfiJb53AF/7p+abbomYdbQesqltTzap02DCHJAoQBQJKYX9WRmUoI7dUWxcLNRDSEKVBZGTRTqIPn8JrFlDsAmH3UBcElKOKvBOqilxAcWzWykrTnrJ+rXOhlGKjotpXzF5XuyWXiRzwT64OY8vyXGTk1sC3XuOsQAHbE2Xw46eXcHj/iN0migJbe9DOJN68q7XkRcZjcgdoxAawE+DsaAZzPsfAjo15pQ7vH8FqScE/n1rzTED2WrIadFWesq6smejttAIFtIZpFmsq8unGsta07K5AtVZUxnIyVssK5jeqdtYS0BAbQcGT844KlJwQ8L6XT9ttxANjzRUovyTyqqJjYbPaElFxcGoAstUinh5pbt+y6cGz1u9sIBnttZiRRcii0JqqrZrt21VXZXonC6jZ0QwWNqoo1bVQ/xOD3S+O/wkARjw8UCcWCrh8fCBijIHo+HOECpTaXIESSGeZaQznz+AVKM6OQdEMbNW0Jg/UmLUOwlmBopTiR09d6GrlpljToBvUvhJyX+1SSm3RAzROXO3ukivVzCwTd3ukH7DpkfEB84TebwF1drWMk8slvOGq6O07oBFw2o4PilU53G0cJxlryseNuyJ02UjGdxpwbr2CXDJhn1xu3jcKAHjmwpbnDq7hTOs6l0YOVOtJIiUJqGt6V1LIGe4wzaK1xoXhfo16GX/HskkomoFza+Wm59jOugpo4c1vVDGSle2fd/vLZ0CIWSEadJykcykJFUVvSndnsCqSO2U+mRBx5a4cRIFg0vVcjWXZbkNLQEWsQBFCMJxtTVhnItR9UdXwtG1/tcLNzEgGmkFxeqUU6n9isMpkHP8TYFagCtXGzkRKKY7PF+y4iTCcQxWhJnKX6F8smCG2iYh+yyCc7zlegeLsGNgVnfONKYkCRrPJpq3qDzy3gg/99aP44VMXuvfYjgR0oHVkuqYa0Aza5IEC2hcfW3WzmpWWxb4HaZYVM0dluypQP/7lEgDEFlB7rAWo7aSRz29UkRAIJnL+JfyMLKKi6i2rVdwG29mRDDYrqmcO0Ny6OYHHqjd7RzN2my1qBSqohce8HbaAGui8JeEO0yxUG8MSgPm8VCN4oADAoM1t0mGfFR5OnMnlgClQ/6dDu1umM9l7z6sKZYekeuw5fO0VE7jhsqGWkyc75rgtPIAlrDf//pmX62KqQLER+mcvbEWuQKXarUBZrwX2vrlQrGG1VMehPdEEVNwKVF0z7Nf0YqHaFf8TgKa2+U5Yz8MFFAdA8yJhJ5P5ZFML7+4jc+b9O9jy7sYWb3YLr3lkmrXz3C28dsVHqWYG96Ul75N2L6nUzQoUO4H0W0D949NLuHIqZ+8cjIokChjJyG2Z9xc2qrYB3I+MnLBHzp1UXWF/zgBCN3NrzVEJhBAc3m9WoTwFVFZu8UB5tcgYpgdKj7wCJwruMM1iTWuqQLmn8CoOTxjDmfDtFENDae8VHk4WNiotrdU/vf0G/NkHXtZ0Wy5gncupZVMEsT2VTv7wjQfxzd+7teX2rPX+Y761OIboYQ8/D4twKNa0Jm/kThZQ7LW6UVGRjCmgoqaQM9zrXNii50OXDfl+jxNnxTOs8mPvjbR+D4uFWlciDIDm1/pO+J1yAXWRUKpr9tVaL1h3VYEYk/nGOpfFQhU/sSoYhZj7qIJwV7/yLr8FMy+yjKjRbIcCqt7wQOkGhar3T0CVrQRdSRQwkpWbqnu9ZqOs4Ni5jVjTd07ajY9wVzm8YHutWkMjmytCM44AQie6QfHCRsX+OoNVUrwM38MZqaW9VVF0JAQC2WMiKi2JqKmG/Rw4J1bbxR1lUKyqTd60lPWYDK/9Zc7jcLbwEqKAfCrhW4Fie+rc5n4vczK7ePHKgjq9WsKeoXRsT8rogGy33qK28ADzM8r9e2NtYqDZNF+xBfj2t3vcTOVTtkcsHRKiyWh4oOK99hoBpObv78R8AaJAcPWufKTvd4qVMBO5M0GfUorFzVpXIgwAU5wxsX3RtPAIIWcJIScIIY8TQo65vvZvCCGUEDLWm0PkAMCX7j+FX/viQz37+SzrKagCdc/RF0AByKIQa5VCGOxNzcrS7hZeowJlvmHkhIDhjISVUnvigyUfs6u5fhrJ2RQe0HkgaFx+cWoNukHxuisn2vr+tgXURjXQ/wQ0TnDuKAN3xYUFELqjDBYLVag6tQ3kjFdfPoaEQHD5RGt7aTgrt+QkBe3YSkqC3cIbycqRM7SCcIdpFquqfaEAWK1NZwXKo6LiV4EC2Pi693t1raygphqhvxsguALlXCIch1HHccfZRTbk4V1bcLSWnT6onVyBEgSC6RHzuY/tgYopoNzBsccXCjg4mYv8uM7nL6yFZ3+uKnpXQzQZrPJ7sZnIX0cpvYFSehO7gRByGYA3Apjr+pFxmjizWsZGB6P7Ybh9SIyJXApr5Tpqqo57j87htoPjmBpMdVVAbboqULmUhFJds1tr7EPbuXC0kzDNRgXK/CDoZ5QBm8IDOs+zisvx+U3IooBrd0fzPbhpR/Cx1StBEQZAw8/gNvXXFB2ENDJyBpIJjA3ILWGazNzuTjvfO5bFw5/8Fc/IBq808pqq+/pRTG+H3pUUcoazAkUpRcFVgcq4p/A8WnjsPTuYllqW8g5l/NPI3cGbQfgJKEpNE/R+j/ZdGONW5YyQeNWEEav16swkm9+o2uLC+Z7y2224U2DDGbE9UDFbeE4/HKUUJ+Y3I/ufgMYFjiwKntXZ5vs2LkwXi90L0WSwCc6LpgIVwH8C8EcA+tcDuURpXKH6Z7F0wnpZsTJBWlt4lAL3Hp3D8lYddx6eNfNzulqBUpqC4XIp0w/DThwNAdV4w3QioFgoZ1o2X/79qkBputG0gqDTRPW4PDG/iat25UI/AP1ggi+OZ2yxUAWl4SfpwMW5ktjUVrrMIxWdCSp3BQpg06StbSmvJatBO7ZYjEE3UsgZzjDNqqpDM2jzFJ5sGnLZOqWqR0tKEgUMZSTP5zhonUuU6UhGY0NA8/t+eauOsqK3RBhEgbXiB+RE06LhMIYyMgza3E5c2KzaFwaeFaiIAqXfsMyy6BWodmMM2MWCivmNKjYqauQJPKBxgRMl/TvtqEAtbnYvRJMxnjOnw8N2B/aDqEdAAfyIEPIoIeRDAEAIeSeABUrpEz07Oo4N80h0s/LjZM3aRec2+rIsqC/cfwq7B1N4/ZUTGMpIXT2OjYraFAznXufiNpEDVjWkjeqNopkihpnIAXjmD/UC1o5iH0JMQPXDxG4YFE8uFGN9aLoZz5nj8sWAQEU3zqTrIJggqLimvKpqq6DZN5rFsxe2oDpG6s+tV5AQCHZHqKYwhj1SrS8Uay1VHEbaCtJcLnZPQDnDNN1rXICGsGR5WH5TgtPDac822lBGwkbZ+73KjNdBK3YYfhUo5sv0MpCHMZYzT+px/E8AMJK14hks4avpBi4Uazg0bRqi1xyfCxVFh5wQujJC3wuY4I8qoNJtVqDSsohkwszPOmGltV8/Hc1ADjSqPVGW7jY+V3Xb49aNEE3GzEgGo1nvi6J+E/VV9UpK6Y0A3grgI4SQ1wD43wH827BvJIR8iBByjBBybGVlpYNDvXTRdMM2cgct9OwEc5lv64mDTS+tbNVx+80zEAWCfFpCISCcLy5mArozc4Z9WKvW//0rUHHFR7neSNNl2TC1PlWgWM6RXYEaSKKuGfZuvl5yZq2MUl2zTzLt0M70I4s9mB4KPkmzD2h3Baqq6i0nl7detwtrZQU/+eWyfdvcWgXTw8GTfm7cqdZnV8s4embd12SfkgToBsXyVq1rAgqwwjQ3ay1rXIDmkxFgXtXLCaHl3/mlD7wM//6d17T87JGQFl4umYgUqOp+TzLOsyTzCFUsN3YFKob/CWhUyZm360KxBt2gODg5gJQkNEUZVBVtR/qfGA0BFe1U3K4HCrCqkWUFx+cLkEUBB6eiVw3Zcxjld5V2iP7FQrVrIZqM/+W1B/A3H35F135eJ0T6rVFKz1v/XwbwbQC3AdgH4AlCyFkA0wAeI4RMeXzvVyilN1FKbxofj746gtNgpVQHa/f3sgI1mm19kbMAQlEgeN/LLwNgXiF3twKlNLUO2RUpq3QwgTEgNwuommr4piP7wcTYQEpylJpbwwF7ATNIOytQQH+iDE6wseVOKlADLMA0unl/ftP8AA0r4bMPXbeJvOrRUnvdFePYNZjC3UfO2beZGVDxqiDsNcc8ePccnWt6nbthQk7VaVdPCLuGUlgsVu2Lo8GmFl6zT8+vxTg9nGkyZTOGszIqiu55keBe/RJEMiFCTggtFShWYWjH48KmB2NXoDINPw/gEOnDGWutTUMwlhV9x7bvgIZnL24S+UgbAor54Y7Pb+LKXTkkE9GfF/aai1SBcnqgCjVM5LoTosnIpaS2Kp69IPRfRQjJEkJy7M8A3gTgEUrpBKV0L6V0L4B5ADdSSruXrsixaVr10CMBtV5WPLNFRrNJyKKAN141aVejhiwB1a3W00ZFafpAyLdUoMypOadPgoUyxhUfW3XzZw4kEw7fTZ9aeO4KVB8F1PH5AlKSgMvb8Kow2jnehY0qJvOpUN9V1sdEXvUwdSdEAbe/fAY/P7mKs1YL6dxa2TbkRoVl46yXFdQ1Hd849kLT69yNsxLWzQoUC9NkrcR8unkKD4C93b6qxhMEw7ZIbP3cmN9ojTAIIp9KtFRLFwtVDGWktkzaTIT6tUz9cJv/nW3iMddgRjVgqnIncNlIBqJAIovIXEqCnBBiBY8yRrIS1spmC++6GAZyoPGZFUVAZaRGNflCoYZdXWzf7TSiyMJJAA8SQp4AcBTA9yml/9Dbw+I4YUY8oMcCyiPXRhQI/vK3X45Pv6vRHhhMS9AMinKXptc2KiqGs81rIwCnB0pr+cBoV3yUHJlS/Y4xsCtQ8jZUoBY2cc3uwY6uBNsRrfMeQY1eOD90nfjFCtx+82UQBYJ7js5hs6KgWNNaJvDCkKycpM2Kir8/cQEbFRUfuGXW9/7pHgkoFqZ5xkr0HnSZyIHmFl4cQeD2CzlZ2AjP53KSS7UuFL5QqGHKR3CGwSpmcUI0AdifFbaA2mSTXimMZWWXiVzbkRlQjJQk4q9/5+bA152TD966F//9d26OZbpnDGVk/HKxiK2aFrsSzUzkYWtcACDlGM45X6h2NcJgpxH6yqKUngZwfch99nbrgDitNO3KimHgjYpuUGxWlJYMKMarXtIc8cU+4AtVNbZ/wQ2lFBuWgZ3hXhuxVVP9BVRMIzn7mSxIE+hfjIEd6pdseKCA3gso3TKQ+7WmopJPJyCLQqznfGGziptmh0PvZwsFV4Wjpuqer8vJfApvvGrSrBpZniWvCbwwhrPmOpe7j5zD3tEMbj0w6nvfXlagAHNnH9DsgWLVpprdwosnCNxtSkahqmKrrkVu4QHeS77Pb9ZiGfed2C28mJ8hA8kEJJHY+XHzGxVM5JJISWbC/5PnC/Z9g3K9dgq3Xh49QnE8l2z7tTeSke1Q1uv2xPNCstdhlOiARjyMhguFGl53RXu5cxcDfR1NaGcRKcds4aUkASmpuwGWjEJVhUGjrwdgrY9uGMm36ho0g7oEVPPItFmBai7ztys+Sk4TeY8qUN8/vojf+eojLbeXrRYeq0ANZSRIIul5FtSplRKqqt6R/wkwE6rjRC/oBsWFQi3SSVpOCJBEYk8qMoJOgHfeMoONioovPXAaQCNkMw7DGRmPntvAI2c38P7DM4FX9iz2AuiuKZaFaT5rCSjnxYK7AsViHaLiNsozFhy+oagMJBOtFahire0RdTb1G7cdRQjBUKaxhsfp5RobMD1QLCOqqur2++1Sh03uJRMCDk7Ga+UnRPP8E6XVmLLa9RcKdVSU7oZo7jT6KqB0g8dFtcOFQg27B9MYTEs9aeGtWynkUQUUy6nZrHa+zmWTpZA7HjsrixBIcAtvMG2Jj5gCqlhrVKDcJ6du8YMnF/HTZ5ZbjLvuChQhpC9p5Me7YCBnjMUQUEvFGjSDYk/IBB4jIydaYwwUvWkTvJNXHhjD7GjGXpDcVgUqI2Fhswo5IeDXXxZcoUtZpltJJPZFRDdgAuTkcgkDyURTm7XhgbJaeGq8ioq9A81nd1y8Fl5zBaqm6lgvK9jd5glSFAj+5L3X486I7SsnI45F0M5W5OhAEppBbUO+abrfuS28fsKmrK/ZnW+rlf+ZX78+UqsxIQqQRcFeMt3NEM2dBhdQFwHnC1XsGkohn+ru9BuDeQYiV6DS5v26IebW7UXCjRMSIaTpatds4TWfsASBYKwN8dHwQElIJgQQ0v0Yg+esSoLbuOuuQAH9CdM8Mb+JrCxi/1j7BnJGHME3HzEDipGVxRZfXU3Vmyo/TgSB4M7DM+Zx5ZJtnSiZcH/7dbtCX/8p5l3zCeZsl9GsDFkUoGhGS6RA2tEOMf/vH/TpxbBr5J8RJ0ST4fZAsWy6qQ5OkO+6YU9bE1VsnYthUJzfrDkqUOa/d9X6TKvUtR3fwusX7PXdbpTJO6/fjQMRh1DSsojTK+aARzdDNHcafRVQRh+33r+YMI2aaeTTUk9yoPwWCfsx6BFA2C7uRcKMXKrxb/WqQAHmSdO5RDQKpbqKhEAs8USQttKlu0Vd03Hamgxz5+94LTbth4A6vlDAtXsG2zKeuhnPJZtydoJY2GRBjdFOsGm59XcRVkH49ZddBlkUYk/gMZjAYEIsCFaB6qb/CTCF4OQgm0hr/rdmpGafXlxPjySaE1tuE/mCtfrEz/fohXtHZSPCoP8nSLZQeKVUh6IbdiuS7QVkr9GKRxDrpQrzw8WdwGuHtCTaVU7ewusSvAAVHxaiuXso1fX8Jcaa9eHqlQPlhdNE3in2Dr6MW0AlAlt4APDKy8fwi1NrePTcRuTHK9XMPXisgpCRxRbfTSecWi7blVZ326Ss6C27pMZzSSz3UECpuoGnzxe70r4DzONdKyvQ9PDsrDi71gBzRNqZA0X///bOPFySszrv7+mu3pd7b9+5y+zSaDQzGq3AWBLISAgkQDZIgIMdwAEvsWyQnMSJ40CIjQmOs5DEwXFiIjtgOw8QHNvyEtkgCQyYRYhREBpJo5mRRrNr7p2791rd1f3lj6qvurq7eu+qrrpzfs8zz9zbS3XV13W7Tr/nnPcIYWukaSWTCOPX3n4QP/vDV/b0Gs3ce+M2PHjnXrymj0L3UQdQgG6mCaBhjIv1Na0pvH4DgilLvZDk/Jqe9upHSZMzKuX5LZtbxnGBlDVQdaNWmcLTP0ekqu6HInK3eM3uKfzkrbtw1zX2RrGjJB4OoiaAAAGzDvy9eAV3AyiOoPpGmmjOT0SRjiqOzMKT306tVgKdSISDUAI0mgDKULGanXXT0RCypQpKlSrK1VpDZ5LkwTv3YutEFP/qz5/t6YIO6MGYtesnGgqaHU6j4PhC1vy5OW1SUDWzHVgyk4xgJa86lt4+vpCFqtVw/RAO5FZmUhEIYd8W38y51SK2JMN9jamw1qPJjqFuRdM/eetu3HP91p5eo5kbd07il9+yv6dAQrpAOxJAGV45zSk8mWYuWrrw+ikiB4xOw6Zz8dxqEdv7KCAH6v5sshFjGBPNYckkQsZcN6OWy1A55ZfAZeNvqqzVTIuMy51kRMFvvON6M4PgJPJvftQmml7D9RSeG3O/rBTLVfzG/32+pf3WL1hl8lEpUC8uZvGLX/g+PvS5p/Chzz2FP//+eaQiSs/OtEQ0soHCq/mybSdO0lCg5Ie1nQKViCj42NsP4ugrG/jD75xuud+OrNoYQDVPux8W2YoOtHY+5cvVljbgmVQENaF/4DuB6UA+Itm+7kbefX+lytEriYjSYGoquyO9koIxU3gj7MCTyDqR5i8KRIS4EVjWagKlSs2si+qVqXiorQLVD83jXIYx0RyWqXgY1ZrA0Vf0vzd5LJlEGETAUlY1z6VeBuAyo0X+zW5mE03A5QBKACj3qBSMim+9uITf/+bL+PZLy66+7qiQJppbJ/QaqGypMrSS9ydPnccjz1zAiYUcTizkEAwQ7nvVtr62MapgbrVQxmQs1FKfI1N45uiVNl4xb7l2Hm/YP4P//Ogxs6i1E7mS1jJrbJQ2BscubphDXdfyrTVQzcGA02aaz5xfRyqq9G0y2Y5+/LfOrxb7apOPh4OmWztQrxnrV3FxiolYCPfeuA1vODB6XxtpZWA3ly4WVvRxLNpgAaW1Yw3Q13UlX+57fp1s5JBfaoYx0RwWqVg/d2EdU/GQ6ZAdDBAy8TCW8mVTteMUnvvINd/M9U9AD0aaoyavVvuawTMsspWyl5SDF7HWGUzEQqgJIFfWbFNavSJdqf/qF3944G1MxEdjqbBaKNtOFk9FFeRUzfy2227cAxHhX997He7+ra/jE488j//23ld3fL2cqjWkYKIjLiI/vpDDoSumsLihtipQatW0MJA4HUAdObeOG3ZMjKxrbLbH/RVC4PxaEXe1GcxrR7MaKLsjvXIBDAQIv/2eVzmybVOBirV+JMfDQZQqVXNt+g2g9Hqh+t9q3QNqUAVKD6CGMdEcFtnwcuT8estxTCfDWMqqZkenVxTMywn5pWc+vXktDACXFSgAyLswed6KbKX0bwBVQiwUxEQsZAZNwwQutZrAM+fWcf2QRcUTsdBIuvBW8uUGCwNJyqiBkh/Wncz2dk3H8cCde/HIM6/g8ecXOr5eziaFNyoFaqNUwfm1IvbNpTCVaF2fQllrMfWbSQ42068X8qqGFy5uDNy2bMeWHg1ML+VUqFqtrzRRPNxYRC6HPHtFgXKSTgqUHlhqdUWlz/XIJPTi77Kmr+fp5f49oIC6Ciy/1Axjojksk5ZO4Obj2JLUGx3qCibXQLmN/NKzjVN4o6V52rrTyADKOh/JT1xcL2HrRBREZHboDJM6O71SQLak4cYhA6jJEaXw1gqVlgJyQA+YKlVhtiN3cyv++Tv24MB8Ch/83FP4wpNn2j4uW6o0uOnGRhhASf+nA/MpTDWlTQBDgWqqX5lNR0AEnF3tz46hG+fXinj3p78DrSbwhn0zI9tuLBxEKqJ0DaAGUTniho2BrJOs2z5s/gBqz0wCB7emcePO1mA3atRAFQZMSUmFd61QxndPLuNX/vQZTMRCuHou1dd2rDMqhzXRHBar5Upzmng6GcFyTjUDzsvh/PEapgK1yVN4Y1Cg3Jk7JpEpvGZPHr8gTTSBurw/TCfeM+fWAPQ/C6kZXYEafk1XmubgSeSHtfR56payjChBfPH+1+K1V23BR/7sCD72F8+iYlNvly1pDcNLYyFlZCm8Y0YH3n4jgGpen3xZaylojYaCuGI6YQZfo+B7p1Zw73/9Js6uFPCZD/wQbtnTfr7bIMw0Tby3YxCjxkREgVYTZp2kDGyjl8EFMBFR8Nf/+PV49a5WOwUZWA4aUMq/r9/9+kt43+9/F5PxEP7sQ6+zVbs6IbvwNkraSEw0h2HS8pnRrEBNJ8JYypUHTnkyw1OvgeIU3khxM4W3XqyYjrTLPk3hSRNNoC7vD2OmeeTcOiJKAFf3OQupmYlYCFlVG6qgXQihK1A2NVDyw/qCcSHuZV7WRDyEz3zgEH7u9VfiD79zGu//n082dF+WtRpUrdY0ayxgq0Adu5jFmeX+Zjceu5hFMqJg+2TMNPqzYqdAAcD+uZQZfHVjYaNkBsF2/MlT5/De33sC6VgIDz9wG+50oOB5SyqCSxudA6hzfXpAAZaxJcaXrEFTVpsNmWaW52m/KSkZQH32W6dw294tePhDt/XsKG3FOqNynCaagP75EDQaT5qD9JlUBDlVM7808ygX95F/s5u9iNz1AKrgYgrv5CVdfdIndzvr9uwEVhNNoK7CDJM6e+b8Og5uSyM0pDfHRDwMIdAyXLQfiobHk91csZQZQOkf1L1ObFeCAXz0Rw/ik3/vBnzn5DL+5Klz5n15tbWjLx5WbM/Jf/LFp/GJR57v/WCgWxjsm0saw05DWM13r4ECdMXq1HK+p5Eyn/rKCfzcHx1ue/+v/+VzuGHHJP78Q7dh7+zwo1vs6EWBOvrKBrYkw22L/+2wm/tmvf1yJRbWVdJBU1K7p+MIKwHcf/sefOanfqhv5UkSDQWgBAjZkjZWE01Abx6RtZMtReTGFzIZxF/u5884uGomia0T0U1togmMIYDKuZjCe8mof7p++wRWfFgDZTXRBOojVAYtIq/WBJ47vz4ST6CJEQwUlu3QCZvgSF54L6wVEQ8H+zZje/ehnZhOhHH0lY2W10taLurRUBClSq1FSVvcKJl1PL0ghMDxhSz2z6cB6K3j1sLdWk3oY0lsjnX/fApCACcWcl1fZ3Gj1BKYScpaDTlVwxv2zThqltdtHl6lWsPfvrCIO/b1p35JpUAOFC6wAgUApg8PjfpuAAAgAElEQVTUoDVQ2yZjePbX34J/+SPXmKrNIBCROVB4nCaaEqms7ZhsrYECYCrIHEC5z4+9Zge+/eE3bmoTTeAyUKCUAOHGnZNYzpddN/EcFvkhJTt0kmEFRIMHUC8v5ZAvV0fiSj2KcS4yVZO0MbqTCtT5tWJP6Ts79s+ncMwSlMjUZ7KhBkp/bemxA+jBzmqhjMVsd18pyWJWxVqhggPzemHupKVwF6irKe0UKAB44eJGy33NLOfLKFdrULXWLyKmwjbgevXKbFpPkbT7Wz58ahUbJQ13H+w3gDIUKCNQ8JqNwbiIDdmFB6BhfNAwyIHC4zTRlEzFw0hGlBbrBzlQ+MyKHkBd7ufPuBjlwG2vMgYFys0AKo9d03HMpqJQtdpIHafdQJpoSgUqECCkIgo2Bkyb/eCs4Uo9grloMu02TAAlzwW7GoV6y7TWVxrIyv75FE4sZE11KWesWzraaGMAoKGQfK1YQU3oE93tCtHtkA7k+4zOJjnbT45zkd2ndgrUFdMJhJUAjvVQSC47+3I250DOJkXpBNKJeylrrz4+fnQBYSWA11/dX/efPA/kWnENlE6sqQZqnIqKNLgdp4mmZPd0HAfmUy0Xamm1cXZVKlBcA8U4g+tnVsHFFN7JpRz2bEmaOfGVfNk2XeRV7OoMJuKD2wccOb+OeDg4UAFpM2YKbwgvKBnQ2l3wrUHToAHB/rkUCuUqzq4WsHs6YUnhtSpQ1kJya73cpazak1mg1cIAgFmfIQMeed7bKVDBAOHq2WRPheQyFZ1TNTNVIenFM2sU1N3IS9jV5HAuhMBjzy/gtqum+/5baw5mCxV9+PJmTwN0Ix4KolIVZkPEOAMCmcIrlKtjM9GUfPy+a6HZNLHIgcKvrJcQUQJDpS0ZphOufjIFiFxToKo1gVPLBVw1kzA9Q/xmpmk10ZSko4M7gD9zbg3XbZsYyQfK5AhSeHm1fVu2NWgaJoUH1NUhO4UmZqNAWT3DFjZ6S+O9cDGL2VTE7CicakrhmQpUm4vf/vlUVwVK1arIGsdgV7zfzbV9VHRyTz+xmMOZlUJfDuQSafEgHaSL5ao5wPdyRp6jspN4nGuSjMgU3vhMNCXxsGJrbxIPK4iHg6jWBNc/MY7i6l9ikMi1Gqjzq0WUtRr2zCSQSfozgLKaaEoGnUGnVWt47sLG0A7kklGYesqgwk5hCgbIvH3QsTUynSbVIXOuXlcFyhpA9da9eWxhwwzYgHqBq7QykGpbu8GmB+ZTWMyqWO1wjlqLx+0CKNdSeB0CqMcMJ/g3Heg/gGouIi+Wq1y/AksAlSsjFgqOtbYkHVWwlCtjJV/G1jGn8DohVShO3zFO4q4CFXDPSPMlw0Bzz0w9hec3LyiriaYkHQ0N5AN1YjEHVauNpP4J0LvXIkpgNApUmwu+VJ4GVaASEQU7MzG8sNAYQKUi9YCsuXAZaDxPeikkr9YETizksN/i7GwdNQFY1bZ2CpTevdcpjWcN7OyUXLsUpRNMJyIIkH0A9fjRBdywY2IgdaL5vShW7H2zLjfipgKljl1RSUUVczrA1jGn8Doh66A4AGecxPUUnlujXOQIlz1bEmY6xW9eUFYTTcmgCtSRc3oB+fUjsDCQTMZDWB+iBkoG08k2F8lhAygA2D+XNlNjObUCJUANKRDpcm1VoKQKFAxQTym808t5qFqtQYGKhoKIh4P1GqguCpQMvjql8RoDqNZ1rweIzgYdwQAhk2j1glrMlvD02TXcdU3/6hNgUaDKdRuD6GVeQA7UjTOXc+WxBwTW9LCXTRKnE3oANe6Ak9nc9PRJS0SnAGQBVAFoQohDRPQJAPcBqAFYBPBTQogLnbYTIHLNifzkpRwm4yGz/ikUJF8pUM0mmpJ0TBlolMsz59eQiii4Yjoxql3Ux7kM4QNVV6DsP+Tkh/UwNT0H5lP422OLULUqciUNyajSkAIxbQyaFKhUREEyqvSUwjtuWCVYAyhAT+NJN2R5rIk2weJcOoKJWMis17Jj2fIFwK4Lzy5F6RQzqVYvqK8eXYQQwN0D1D8Bequ9EqAGGwO+ANaDgJV82dZ01k2sX2a8HEBJK4PLvYOTcZZ+FKg7hRA3CSEOGb9/UghxgxDiJgD/F8CvddtA0M0U3qUc9mxJgIhARPpoDR+ZaTabaEomYiHdwVvrrb1e8sy5dVy3fQKBEXakDKqGSfLlKsJKoK0r+igUqH3zKVRrAi8t5pFVtZb6ILsU3kq+jEwyjNl0tCcFSgZJW5q64qYSIVPN6jaXi4iwfz6F4z2m8OysLHJqBcEAuXLRsAugHj+6gO2TMbMTcRDi4WBDCo8vgI0BVGzMKc1GBcr7KTw/dV0z/mPgFJ4Qwur6lwDQ1aXS7RTeHku7fiYR8dVA4WYTTUl6gHl4qlbF0Vc2Rlb/JJmIhbE+xGDjvGo/2kQyKgUK0Iu8s6XWAKpdEflUPIy5VASLPShQ+TaO6roC1egD1ekDff9cCscvZtsavq7kyyAClIB9N2vOOD43ioyb3ciL5Sr+7sQS7j44N9TrJyKKuZ6cwtORa6DVBGJj7kqUX2bGbaLZDVlE7uV9ZPxPr+G5APAoEQkA/0MI8RAAENG/AfB+AOsA7uy2kUCAXFGgsqUKFrMq9szU01XTibCvUniyhstOgQL07rdmxaMdf33kFVSqYmQdeNZ9ef7CesNtX3r2FXzsL5+D1Z7lLdfO4TfecX3L8/NlrWNAMQoF6sotCYSChBcuZpEraS3bsrUxyJexbSKKuXQUT55a6foa5kiapg/rTCJsuiEX1CoCBEQ6OELvn08hq2o4v1bEjql4y/3LRmAnhLBP4dkobE4h5+EJIUBE+INvn4Kq1Qauf5LEwkFzFh6n8HSsazDuonr59zNuE81uSI+0OAfgjIP0+nXmNiHEqwHcA+ABIrodAIQQHxVC7ATwOQAP2j2RiO4nosNEdFgtFV2pgXp5SRaQWxWosG9sDEqVKn77KyewZybRMhBWtvT34gVVqwl86vET+KUv/gA37pzEnfv7G63RjUkbU8+/PnIRpYp+Ib3rmjkkIwr+7sSS7fN1BcrZACoUDOCqmSSOX8wip7a6mkfbGGlmEmHMpSNYK1S6DvnNq5o+aLUpFTkVr59z+bJ+rJ3UGVMta1MHtZovI5MIIxlV2ipQTptoSmZSEVSqApdyKj768BH8+y+9gDcdmMWtezJDbTcRViyz8DRO4aExaBq3oiL/fsZtotmNLaaNAZ8/jHP0FEDJ4nAhxCKAhwHc3PSQzwP4sTbPfUgIcUgIcSgRj6NYqaJq4x47SqR6c5VFgfJTDdR//9pLOLNSwG/cd11LfVCv/kuFsoYHPv//8FuPH8e7XrUdX7z/1pHXA0zEQsiXqw3jTo6cX8etezL4t++6Hv/2Xdfjtr3Ttp5F+j5W23alAfVuMqvtwCBIk8qcjUITCgYQCtYLl4UQDTVQgH27vpWcWrVVfqbiYWRLGirVGgpqtW2xvORq2YnXpg5q2QigUoaZYTNZlwMoAHjv730Xn/vuGfzCHVfhofcfGto1PGatgWIfKACNQdO4FRVTgfJwATlgtTHgGijGObp+2hFRgohS8mcAbwbwLBFdbXnYvQBe6LYt6YDttJnmyUs5BAgNYyamE2FkVa1lCOvfvrCI//ClrrvuGicv5fDpr72E+27ahtft3dJy/4QxOLPTPLxqTeA9Dz2BLz93ER/9kWvwn378RkdqSZoHCq8XK3h5KY8bLMOK9eGjFdu6npzaLYUna6CG+xDcP5/ChfUSFjZKth1qsVDQVJlyqoZKVWA6ETbTFBe7FJLn2xzHVKLuBSUVqE5MxELYNhFtq0Ct5MvIxHUFKmtTA2cXIDqFnId3dqWAT/39m/Dhew6MxOE+0VxEzgFUUwrPGwGUl000AZjef+NeL2Zz08un7RyAh43UgwLg80KILxHRnxLRfug2BqcB/EK3DQWIUIOuPDg5buKlpTx2ZuKIKPU/HukFtZqvYH6ifvsfHz6LLz93Ef/oTVePvWBVCIFf+4vnEFEC+OiPXmP7mF4UqMVsCT84t45feet+/NztexzZV6BxoPCWZATPnm8dVpyKKqhUBVSt1rK+BbWKuVT7D+I3HpjFyUs57My01gP1g/RYKpSrth5JsXDQrIGSKbdMIoI54yLRrROvXSpSupGvFcoolLsrUEDnkS4r+TIyV4ZRqdZsg7qcquGKLaOzqejEq3ZN4h/cuhvvPrSjIWAelnhEQX6lgEq1hkpVjF1x8QKhoG7voNWE6Vs2LuZSUfzMbVfinuu3jnU/upFJhPHzd+wZ2FKDYXqhawAlhDgJ4Eab221Tdp2QAVRO1eDkaX3yUh57mi4kdTdytUF+Pnkpj5oAXlzM4boRmkwOwiNHXsE3X1zCx++9FrNtAoteaqBkgfFOm0LkUZJuGij8jI1ZpwyUN0qVlgAqp2odg4qdmTg+ft91Q++n1Z/JTs2KhxWzcFk2GkwbNVBA93Eu7ZQfc5xLvoy8qvVUALxvPoVvvriESrXWkL6t1gRWC2VMJ8LIqxpyl+xTeG4pUNFQEJ94x/DvTTPxkB7MSkWQFSidWDiIbElDPDTelFQgQPi1tx8c6z70AhHhI/fYfwllmFHh+igXoD6Z3glqNYGXl3INFgYATENN6zyxak3g5WW9XqrbIFenKZQ1/Ou/eh7XbU/jJ2/d3fZx0VAQYSXQMYDKujTSQ6bw5L4cOb+GXZk4Jo3AAdBnZwH2s9sKZXcu+NsnY+br2L1eNGRRoIw6ualEGBOxEMJKAIvdFKiyZlvLJVN4qwV9en0nywbJgfkUKlVhNkJI1gplCKGfx6mo0sZIs+JaDZRTSBsD+X6MWxX2CjIVxSkphvEOro9yAezneI2KhWwJpUoNVzYrUMm6AiW5sFY0DSk7zSBzg5cW81jMqvjgHXu71pJMxDrPw8u5NNJjsimd+My59RarhFSHACqvujPrjIiwb04PqJO209uDKFb0/VuxKFBEhLl0pIcUXtW+BsoIJFcLZeTLWtuZf1auntXVspcWcw23Sw+zTCKMZCRkBsmSslaDqtUcf8+dJhYOolipml2RHDDoyL8TVuQYxju4GkAFyfki8tPLuu/O7unG9FXGmI1ktTJ46ZJ+kZI+QeNEXjCkqtOJdLTzOBe3RnpMmCk8fTr7udUibtjeHECFjH1qDPjKWg3lag3JHuqCRoEc1munQMUsCtRyvh6oAHrNx7ApvNVCGQW1NwVKNj5I/yjJck4GdhGkoooRMNWV3LxLqqPTJMJBVKrCDMrZxkBHrgMHlAzjHVxO4TmvQJ2RAVSmUYGajIUQoOYASk+T3LZ3C45d3MA4kTUf0R6chruNUJGDZp0s1Jf7AQDrRQ1HjALyXhUoGUS7ZQwoPZbsUlzRUL3za7VQRkQJmBequXQUC9nBuvBi4SCioQBW84YC1cOxpqMhTMZDON0UQK3krQqUvh1rGk/+TblVA+UUsu1cBoysuOjIdeCAkmG8g8spPP1/69yxUXN6JY9ggLC1aQhvIECYije6kZ+8lMNELITX7pnGwoaKtTGOeqkHUN0/INNdUnimAuXwxVQJBpCMKFgrlvHM2TUAjQXkQHsFyu0L/m17t2BXJt5iTAro3+rl+i/nymb6DgBm053HudRqAoWyvQ8UAGTiYazkK109r6zszsTNLwKSZbsAyvJFRL7nvq+BMgKFpZy+5hww6MiAngNKhvEOY1GgnHQjP7NSxPbJmO2A2mYzTX1eXsLs0hpnIXmxjwCquwLlXnAi9+WZ8+vYM5NoUb3kPrQqUEaNi0spvL2zSXzjV+40rQmsxEJBc/1X8ioyyXoR/Fw6ipyqtVVN5Yy7dms9GQ9jYaOEak30rLbtmk7g9EpjEblUoKYSIVtVTwaoTquOTiPrxGTAOO7RJV6hnsLj9WAYrzCWInIn5+GdWc631D9JpprGuZxcymHPliQOGPUx4ywkVyt6MXsvKbx0NNTVxiAeDo7E2LAbEzF9X46cW2+pfwLaB1Dm/DgPpJys7tdykLBEWhm068ST53K748gkwji3qqtJvdRAAboCdWGt1ODwvpIvIxVREFGCZp2TNajbLCk86fu0LBWo8HiH53oF7sJjGO/h6qcTQQ8Q8k4Wka8UsKuN8eJ0IowVI02XUzUsbOgDh+fSEaSjylgLyUtafwrURkmzdfcG3B3pMREL4cRiDhc3SrjexlAxGCAkI0qrAiUDDw98o45ZU3j5sukZBsA0+mxXSF4PBO3ft6lEGBfW9OCrly48ANiViaNaE7iwVjRvk+NlgPpom6xdDZTPU3hSkZQ1UGxjoBPjLjyG8Ryuf71LhBXHUnjrxQrWCpW2AZR1oPDLlnl5RIQD82kcH2cA1VcNlIJqTSDfppbMzZEeE7GQ2fl4ww57I9KUzeiRboGHm8RDeudXpVrTAxWjYxOAOQ9vsU0heb6L8jMVD6FsKEm9BouyE++0pQ5qxZiDB8CiQNXXNOuSdYXTyBTVEqfwGpApPK4JYxjv4H4AFXEugDrTxsJAMp0IY7VQRrUmcHJJtzCQhpv751M4tpBtq+o4TUmm8JTeuvCA9uNcsqpm63fkBHKcS4CAg1vTto/RAyj7LjyvKFCAYTdQrpqeYQAsbuSdA6h2KTxrOrDXei95/lo78azKmFQXc6XWInK/K1AyzbnMReQNcAqPYbyH6wFUPBxsq5wMi/TO2ZWxnweWSYQhhO5b9NKlPAJUv1jtm08hW9JwYb1zy7pTFCtVhILU0zT7buNccqWKa0qEDOb2zibbBhGpaAhZtXFfuwUebiJVP5lqy1hSeMmIgng42DWF10mBkvQaLM6loggrAZxZrheSr+TVugIl68oaaqAqCAbI9wGHWURupvC4BgoA5ieiSEUUVuQYxkO4/teYdFCBkp1Lu9ooUJlk3UzzpUs57JiqDxyWPkHHL2axfTLmyP51olSpIqr0dvHrqkCVtLaz9EbNhBEgdBoom4oqDcX7AMwg2hMpPONb/flVvebIGkAREebT0fYKVLmLAmXZVq/qQSBA2JWJm18IhBB6cbuxrYgSQChIjTVQxhw8ab/gV2QR+Uq+jFgo6PvjGRU/8UM78eaDcwj3oFAzDOMO7itQEcU5BWq5gGmLT04z9YHCZdPCQLJvTg+gxlVIXqrUEOlRPUjHuihQqrtF5ED7+ifAUKCaUnh5VQORN1I0ch9kt5y1iBzo7AWVUzsHgtYUXj9q265M3KyByqoaKlVh7heRXpjfkMJzse7NSWSas1ytccG0hVAwYNbjMQzjDVwPoJKRoHMK1HKhrfoE1JWF5VxZHzi8pW6qOBELYdtEdGyO5Gql2nO6opsClStprtXCSKXrpp3tFSi9C685hVdFIuwNxUReqM8bXW9TTQFUJzfybkXkVjWrH7VNKlBCCKyaJpr14vZkVGkx0vS7iSYAhIMB037DC8E1wzBMO8ZQA6Wg4FQR+UoBu9t04AH1i9nzr6yjVKnhqtnGWql986nxKVBateeWbbMGymZAb60mkCtrrtVAvfHALP7451/bMYWXjiot+6qPP/HGBbKuQOkBVLMCNWek8OwaDPKqhkAHJW1ygBooQK/NK5SrWMqVTVNJ636lIqGWFN5mCKCIiF23GYbxBWNQoBRHZuGVtRpeWS9i17R9ATlQT6d879QqADQoUIDeiXfyUr7BwNAtiuVqz9+4pbpkp0AVKlUI4V43VjBAuPnKTMfH2A6/LdvPjxsHsjD3/GoRwQCZAapkNhVBqVKzDVizJa2jkmZVoPpRVHZbhgpL9/yG4vao0mBj4KZ1hdPIQJM7zhiG8TJj6cIrlKsjtws4t1pATaCjAhVWAkhFFTxtzG27aqYx2Down0K5WsOppbzd0x2lVKn1nMILBgipqGJbA+XFkR71eXj1ACSvap6wMADqbtfnVguYiofNkUMSOf7FrpC83SBhc9uhIMLGcOLm7XZCepmdWck3DBKWpJrMSXMuWlc4jQyc2ESTYRgvMxYfKK0moGqjVXmkZ06nGihAT4OUtRqSEQUzqUjDfeMsJO8nhQe0H+eSc2mQcD/Y+Rbl+xiu6zRy3fPlakv6DugSQJU7pyKJCJl4uO/28x1TcRDpdX1mCi/ZrEA11kB56T0fBllIzgoUwzBeZgxO5PqHYmHEnXhnjQCqkwIF1L/F7zEcyK3snU0iGKCxDBUuVWqmpUIv6ONcbBQoD4708LoCZQ1uMrYBlDTTbO3Ey6nVroHLZDzUd7AYDQUxn47izHIBK3kV0VCgYT9T0aYuvFJlU9RAAUA8ZIwtYQWKYRgPMxYFCsDIO/FOLxcQCwVbVKVmZCfTni2ttVIRJYgrtyR6VqDOrRbw45/+jtklNQz9dOEB+jgXuxqonAdHesgLu7UTr1CueqYGynqhziRbA6jZ1OApPEAPygYxQJSdeCv5CjLxxv1KRkJmsKzXl9U89Z4Pg1SgOIBiGMbLjC+AGvFA4dPL+hDhbm3x06YClbS9/4YdE/j+mdWearSePruGJ0+t4OgIrA+Kld6LyAG9IH61YFcD5UUFSt+XjaaaHe+k8Op/Bs2BCqB3gyUjCpZyrQpULwHUg3fuxT+7e1/f+7UrE8fpFV2Bag7srIX5eQ+qjsPAXXgMw/iBTaNAnVnJY2eX9B1QVxj2zNh369165TSWDafybmwU9WNYzdv7MfVDqdJfDZR1MLIV2ZnlpSLytJnCsyhQHkrhEdVHoNil8OTtdkpjL91vr9u7BXcdnOt7v3ZPx3Epq+L8WrHBAwqo17jlSlrXcTJ+Q6p1rEAxDONlegqgiOgUER0hoqeJ6LBx2yeJ6AUieoaIHiai9kZAFmQNVF4dXQ2UEEL3gOpSQA7UFYZmCwOJbMl/4uRK123JGqTVwvApvH668IDGwchWsh4sIjdntxn7VqsJ5MtVc+6ZF5Cqx7RNCg/QzTWXbQIoJ/2spCXHicVcS3G7GUCpmnkebpYaqAQPzmUYxgf0o0DdKYS4SQhxyPj9MQDXCSFuAHAcwEd62YgTCtSlrIpSpdZTAPWma2bx3lt24eo5+wBq93Qcc+kIvvty9wBKKirD1kAJIfruwrMORrbiRTUiGW0MoIoVPXhOeiSFB9Q78dopUNNtFL+86lwtl2yIEKJ1v1KWNTXr3jykOg5DzFCgohxAMQzjYQZO4QkhHhVCyCjoCQA7enmeTNuMch6eaWHQQwpvz0wSv/nO6xEK2h86EeHmK6fx5MvLXeugzBSeTS1SP5SrNQjRn++NHDfSfFHPlTTEw0FzHIYXCAUDiIWCZsApg2cvTZaX9TadUnjNa13WaihXa0g6dBzW87l5v2RQmlM3XwpPKlCcwmMYxsv0GkAJAI8S0VNEdL/N/T8D4G962ZBMd4xSgZJDV3sJoHrhliszWNhQze22IzuiFF6prHti9RNATRs1Mc0Xda/OREtF68aPMnj20gXfTOEl7Ls4p40UnjWoluewUwrUZDxkvpfNKbxURFebGmqgPPi+D0KMU3gMw/iAXgOo24QQrwZwD4AHiOh2eQcRfRSABuBzdk8kovuJ6DARHb506ZIjXXhnlvMIkG4+OApuMeqgnuySxpNdZXapnX4oGSNO+qmByrRToDw60iMVVZBVmxUo71wgZfA6lbBPg2UMA1arcuq08kNEZlq6ecCxmRZVK2ZgullsDORnBDuRMwzjZXq6YgshLhj/LwJ4GMDNAEBEHwDwNgDvE23yXUKIh4QQh4QQh2ZmZhBR9Gnro1SgzqwUsHUihrAymqbCvbNJZBJhPPHycsfHSSfw5jqkfikZNUHRPow0ZbFzc2Fz1qMjPVLR+vDbvAdTTjKYm7KxMQAsAWuuvt7yS4CTfla7M3oheYsCZXF396J1xTDETQVqcxwPwzCbk64RBxEliCglfwbwZgDPEtFbAfwLAPcKITrnuhq3h0Q4ONIuvNM9duD1ChHh5isy+G6XTjx54VoZOoDqP4UnL/StNVAVTyoRjSk8Q4Hy0H7GQkFMxEJta+NkwGp9r+spPOeUEjmaqKUGSnY2qhpyagXBAG2amiG2MWAYxg/0ItnMAfgmEf0AwJMAHhFCfAnA7wBIAXjMsDf4dK8vmogoI1WgFtZL2DoRG9n2AOCWPRmcXyvi3Gr72FC2j68N6QNlKlB9pPDkYGS/pPDS0ZCliNx7XXg37pzE666abnt/PWCtm2nmVOdruV67Zxp7ZhLYNtl4fkeUAEJB0mugjDl43Uxk/cK+uSS2T8baerUxDMN4ga6f/EKIkwButLl976AvmogoI52Fl1NHXzh9s6UOql1tlUzhZVUNZa02cApRtvX3+4172sabyKtF5MmI0pLC81KK5hfuuKrj/bK4fDlnp0A5dxy375vBV//ZG1puJyIkI4rZhefFoHlQdk8n8K0Pv3Hcu8EwDNMR153IAb1NOTciBUoI3ZRx1GmUA/NppKNK20JyraoXFG9J6hfWteLgaTypQEX6DKCmbNyxcyXNk7Uwdl14XpmF1wvSwd6q+I3bPiBprKlXg2aGYZjNzHgCqIiCwoi68FSthmpNjFzNCAYIN1+ZaWuoKS+esvZqmHEu9Rqo/t6OZgWqVhPIlTWP1kCFUKxUUanW6sqNh7rwupEIBxFWAg0B1LiL4VORkGmkyQEUwzCMu4wlgIqHFbN+ZFicvIjdfGUGLy/lsbhRarlPmmhKt+hhvKBU08agv4BCN3es1+QUKlUI4c1uLGvXWL6sIaIEoLQp2PYiRNQSsLqRwutEMqogp1Y2XQqPYRjGD4zlCpaMBEemQMlaKic8hW65Ui8qtlOhZAH5bmNe2TDjXOpF5P0GUBGsWMwdsyXvDRKWWEeP6PPj/HfBbx4onFOrCAcDI7PP6JeUtQbKg+85wzDMZmY8CtQIu/CcrEO5dlsa0VAAT59da7mvHkDpCtQwVgbF8uBF5JWqQNZYg5wHBwlLZFC3UaqgoI6+Zs0NMjYK1DiPI6fW6jAAABprSURBVBlVTB8oL77nDMMwm5kxKVDKyHygCg56CinBAGZTUSzl1Jb7ZEG09OlZG2IeXkkbrAaq2dwx6+GRHmnr8FtVM2ci+onmeXjjVtJSZhF5hWugGIZhXGZMNVBBFCtVVGudh/X2Qs5hTyG7IbJA3cJgJhlBPBwcapzLIE7kct+AuvqV8/BID6lAZUsVFMpV36bwmrvwxqn8JCMhrBcrULWaJ99zhmGYzczYFCgAI6mDKjjsKTSdCDd4/0jkHLx0NISpeHioIvJSpYZwMIBAoD8jxGYFystDZVNNCpSX5uD1ynQijJyqmUX/+fL4FSjN+BLixfecYRhmMzO2LjwAI0njOe3F006BkgXbyaiCqURo6CLySJ/pO7lvQN2byMtF5Obw21IFhbI/a3YyhpmmXO+cOl4lzbqGflxPhmEYPzMmHyhdfciPQoFysAsP0A0UVwr1TjfJRlEPAoIBMhSoYXygqgPN/WoeKJz1dBG5YWOgasirVU+5kPeKDFilIplXtbGOo7G+z1wDxTAM4y5jciKXCtTwAVTOYS+eTDyMslYz3bMlG6WKWRg9fAqv2reFAaAredFQwPSCGrczdiciim5EmTV8oLw0B69XZMAq3+v8mIvhrUGTF1VHhmGYzczYnMiB0aTwCmUNwQAh4pAXT3OdkUTvfAqZjxkuhVfruwNPMp2ImApUrqTXFgX7rKVyi3RUwYbhA+VE16TT1AcK12vOxprCi3IKj2EYZlyMN4U3AgUqr1aRCAcdm0RfT5M1WhlsFDWkY3UFaqOkoVKtDfQaJW0wBQpAQ/2V12eipaIhrORVVKrClxf8aUsKTwhhpPDGqEBF6qoTF5EzDMO4y3gVqBHUQDntxdNcOCzRU3j6BWwqof8/qBdUqVLt28LAun9WRcTLgUkqquDihh6I+rELbyIWQjBAWMmXUaxUURPjHYhsDZrYxoBhGMZdxlwDNXwKz+lWclN1yDen8Opqj0ztrA1YB1Ws1BAdMKCwzmfLenykRyqq4OJ6EcB4A49BCQQIU/EQlvNlS73Z+AJBq9rIChTDMIy7jDWFNwofKJnCc4pmqwDJRqmCdMxQoOL2j+kVtVJFdMAaLqvNQq5U8bQSkYqEcCmrK1B+dCIH6gOcZfDvBRuDYIAG6uJkGIZhBmcsn/6yhf1/PXEaXzt2CQAQChJ+/d5rzeG8Vp46vYLHnl/Eh+850HKf0ym8eDiIiBJoKBIXQjQqUEYKr9nK4MvPXcTp5Tzuv/2qjq8xaBceoF/QC+UqSpUqcqqG2VR0oO24QTKqQJrP+3EWHlAPWPMOd3/2QkQJIBQkxMOKYzWADMMwjD1jUaCCAcJ7b9mFLckIipUqipUqvnFiCV/83lnbx//u117Cp7/+km2Rdr7srKcQEbUMkS2U9TE0Zg1UvLG9XfLZb72MT375mGlw2Y7huvDqKUbvF5HX982PKTxA73pcaUjhje84iAjJiOLpujeGYZjNytg+eX/zndc3/P7e33sCjx9dwK+8tVFlKpQ1/N2JJQD6/LnpZKThfjfMDJvdyDeMgKg5hWcNoIQQOHYxi0pV4OvHL+FtN2xru/2SNpiRptw3AFjNl5EraZ6uhbF6Ffk1hTeVCHlGgQJ0Vc+va8kwDONnxqJA2XHXNXM4vpDD6eV8w+3fPLEEVdOVJzl/zkqh7LynULMCJR2/paISCwcRDTWm+S5lVTOl9/jzCx23XywPl8IDgKWcilxZ83QNVLpBgfJrCi+CtWLFDKLHbQiaioQ8rToyDMNsVjwVQAHAY03BxuNH67+vF1tTYW607k8bhcOSDWM/0hZFJRMPYyVf379jC1kAwK5MHF99YbGtR5QQAqpWQ2TIAOrsahFCeLsba3Ok8MIQAji/6o1uwrsPzuGNB+bGug8MwzCXI54JoHZNx7F/LtUQMFVrAl85uojtkzEA9cDFen+pUnPcUyiTiDQ4kTen8ABgKhFusDE4dlEPoH7hjquwUdJw+NSq7balujaMEzkAnDGUOy+P9NgMKTwZsJ5ZKQAYfwD1S3fvwwff0LlJgWEYhhk9ngmgAOCug7P43qlVMxB5+uwqlvNlvOvV2wG0KlDSiNNxBSoZRt7odANaU3iAXge1YgmgXriYxZZkBPfdtA1hJdCirEnkNgc10kzHFCgBwqll/YLu5YJiuV4BGjxgHDfTzQGUTwNBhmEYZjh6uooR0SkiOkJETxPRYeO2dxPRc0RUI6JDo9iZuw/Oo1oTprXBY88vQgkQ7rtJL8DeaOpmKxhePE524QGWQm0jQLJL4ekKVH3/ji9kcWA+hUREwQ/v3YLHjl6EEKJl20UjgIoNqKIREaYSYZyRAZSnU3j6eiV83HafMUb7nF0pIhby7txBhmEYxln6kQHuFELcJISQwdKzAN4F4Buj2pkbtk9gJhXBY0Ya7/GjC7hlTwY7puIAWhWonNkJ5WwKT3bZLRtpvA1bBSpkdupVawLHF7LYP58CoNd3nV0p4sRirmXbpcpwKTxAV0WkIuLlInK5XuNOew1DxjgXLqwXfX0cDMMwzHAMfNUWQhwVQhwb6c4ECHddM4uvH7uEEwtZvLiYw13XzCEaCiKsBLBRbOzCk07mTqdR5EBhGSBtlCoIK4GGzjl9oHAFWrWGMysFlCo17J/TA6g3XTMLoLVAHhg+hSdfWypZnlagjIAj7tMOPEBXGgHoBfs+Pg6GYRhmOHoNoASAR4noKSK6v58XIKL7iegwER2+dOlS18ffdc0ccqqGTzxy1Pwd0NNl7RUod1J4ZgBV1BrSd4CuQAmhq2SygFwqUHPpKG7cMdE5gBpiFIdMKwH+KCL3cp1WN0LBgGnHwAoUwzDM5UuvAdRtQohXA7gHwANEdHuvLyCEeEgIcUgIcWhmZqb7C+3dglgoiG8cv4QD8ynszOjpu3RMaamBqs8jc1YJaB4ovFGqNHgaAXVlYrWgB1BEwNVzSfP+u66Zw9Nn17CYLTU8T6bwIkOm8CReDk6ioQCUADneNek00syVAyiGYZjLl56u2kKIC8b/iwAeBnCzUzsUDQXx+qu3ANA9biQTsVCLjYGZwnP4QpaOhhAMkOkFlS1pSMUalR5rofmxhQ3sysQbitvvvlY/lq8eXWx4nlSghhkGm/FJAEVESEX9P3pErreX680YhmEYZ+kaQBFRgohS8mcAb4ZeQO4Yb71uHgDwlmvnzdvS0dYAykzhOVwDFQiQblOQr3fhtShQ8Xqa74WLWbP+SbJ/LoVtE1F888WlhttHkcKTClQ87P2usK0TMcx4eOBxL8gAihUohmGYy5dergBzAB422s4VAJ8XQnyJiN4J4L8CmAHwCBE9LYR4yyh26p2v2o7rtk9gnyUImYiFWsa8FFxK4QHSjVwPoLKlimnuKZEpvIWNEk4t5fG267c23E9E2JGJYzGrNtxe0kZQA2WYafphpMcf/PQPIer3FB4HUAzDMJc9Xa8AQoiTAG60uf1h6Om8kUNEDcETIGugGrvwpALltA8UUB8iC+g2BulYswKlp/S+d2oVNQHsm0+1bGM6EW6xMhiFjcFUwj/F2bNpf6tPQD1Y5i48hmGYyxff2EFPxPQuPKsZZaGsuWZmOJ2I1IvIi5WWLrxYKIiIEsATJ5cBAAdsAqiMRcWSjMLGQI5zSXq4A28zwQoUwzAM45sAKh0NoVoTKJSr5m05tepK+g6oBz+qVoWq1VrSZUR6ndSlrIpwMIArphMt25hOhLFaKKNaqweBwzqRy30DuKjZLTKmAsXrzTAMc7nimwBqwuh6s1oZFMqaaypAxhjVIse1pGOtao9M7Vw1m4QSbF3aTCIMIdAwdNi0MVCGSOHF/ZPC2wxwETnDMAzjmwBKBixWM828qrlS/wTU3cjlyJTmFB5QD2Ts0ncAkDH8g6xpPLVSRUQJDDUbTgkGkEmEW+qyGGfYkvRP0T7DMAzjDL65ApgKlGWcS16tulbIK1WHl5f0TkC7i6dUoPa3C6DijY7mgF4DNUwHnuQ/vftG7MzEuj+QGZprt6Xxb955Hd50YK77gxmGYZhNiW8CKKn4NChQZc30X3IaGfycMgIouxSefEyzB5R5f8IugKoN1YEnufPA7NDbYHqDiPC+W3aPezcYhmGYMeKbFF5dgWpM4blV9yPnzZ1e1lN4tgqUkcJrp0DJNOCyJYAqVqpDuZAzDMMwDOM+/lGgjPqexhood7vwAOCUYeZpVwN1703bEVYC2Dph73U05WAKj2EYhmEY9/BNAJWKtnbh5cvuFZHL4EcqUHYpvL2zSTz4xqvbbiOsBJCKKo0BlFZDhAMohmEYhvEVvknhBQOEVEQxFSghhKspvFAwgIlYCDlVQ4CAxIC+TdOJcEMKr1SpIjqEhQHDMAzDMO7jqyt3OhYyu/BUrYaaAOIujtOQDtSpaGhg24GpRBirTTYGnMJjGIZhGH/huwBKKlByDp6b5pGyDmoYv6VmBYqLyBmGYRjGf/grgIoqZg1UQdVHoLhVAwXUfZ5SkcFnzukjYVTz91HZGDAMwzAM4x6+unJPxEKmjUFdgXI/hTeMApVJRLCSL5tDkbkLj2EYhmH8h68CqLQlgCqU9QDKTQXKTOHZWBj0ynQijEpVIGsEgBxAMQzDMIz/8FUANWFTA+XmQNeMpYh82G2s5PQ6KN3GwFdvA8MwDMNc9vjqyp2OhpAvV6FVayiU9Root4w0gbqT+HApPCOAKpRRrQmUtRoXkTMMwzCMz/BVADVhBC4bJa2uQLmawosAGC6FZ1WgVE0PAjmFxzAMwzD+wlcBVNoyD68whhRe3QdqBApUvoxSpQYAbKTJMAzDMD7DV1duc6BwqYL8GFJ42yZjiCgBXDGdGHgb1oHCpQorUAzDMAzjR3wzCw+oK1DrxQryqgYlQAgH3YsBM4kwnvzoXUgPoUDFwwqioQBW8ioHUAzDMAzjU3wVQJkKVFFDXtWQiCgDj1QZdh+GYToRwXK+jCIHUAzDMAzjS3oKoIjoFIAsgCoATQhxiIgyAL4I4AoApwD8uBBi1Znd1JHF2+tFPYU36EDfcTOVCGHVWgPFNgYMwzAM4yv6uXLfKYS4SQhxyPj9wwC+IoS4GsBXjN8dpaEGylCg/Ih0I1dZgWIYhmEYXzKM9HEfgD80fv5DAO8Yfnc6Ew0FEAqSqUDFfRpAyYHCJbYxYBiGYRhf0msAJQA8SkRPEdH9xm1zQohXAMD4f9aJHbRCROY8vLyquToHb5ToA4U5hccwDMMwfqVXCec2IcQFIpoF8BgRvdDrCxgB1/0AsGvXrgF2sZF0NGR24WUS8aG3Nw4yiTAK5SpWC/o4F3YiZxiGYRh/0ZP0IYS4YPy/COBhADcDWCCirQBg/L/Y5rkPCSEOCSEOzczMDL3DqVgIGyUN+bKGpI9TeADwyloJAKfwGIZhGMZvdA2giChBRCn5M4A3A3gWwF8C+IDxsA8A+AundtKKHChcUKuI+7YLTw+gLqwVAQBRxZ/HwTAMwzCXK71IOHMAHjb8lhQAnxdCfImIvgfgj4noZwGcAfBu53azTjqq4NxKATnV/wrUhXU9gIpwDRTDMAzD+IquEYgQ4iSAG21uXwbwJid2qhMTsRBWCmWoWg1xFwcJjxI5D+/8WhFEQIRn4TEMwzCMr/DdlTsdC2GtUAHg7hy8UTKdiAAALq6XEFWCrrupMwzDMAwzHL4LoKyjVPxqpJmOKVAChEpVsIUBwzAMw/gQ31295TgXwL8BFBGZheTcgccwDMMw/sN3AVSDAuXTLjygXkjOARTDMAzD+A/fBVDpWF118qsCBQBTcQ6gGIZhGMav+C6AalSg/BtAZZIygPLdW8AwDMMwlz2+u3o31kD5V70xU3hsoskwDMMwvsN3AdRm6MID6l5QrEAxDMMwjP/w3dU7Fd0cNVBcRM4wDMMw/sV3AZQSDJgjXOI+Dj4yhplmzMfHwDAMwzCXK76UcNJRBTUhEAj418F7KqGnIiMcQDEMwzCM7/BnABULoVwV496NoZDjXLgGimEYhmH8h28DqFKlOu7dGIoM10AxDMMwjG/xZQC1OxNHOOhv5WYqHsJUPIRtE9Fx7wrDMAzDMH1CQriXCjt06JA4fPjw0NspVaqo1oSvu/AAYL1QQSIShOLzYJBhGIZhNiNE9JQQ4pDdfb6MQDZL2msiHur+IIZhGIZhPAdLHwzDMAzDMH3CARTDMAzDMEyfcADFMAzDMAzTJxxAMQzDMAzD9AkHUAzDMAzDMH3CARTDMAzDMEyfcADFMAzDMAzTJxxAMQzDMAzD9AkHUAzDMAzDMH3CARTDMAzDMEyfuDoLj4iyAI6NaHMTANZ5Wz2zBcDSiLYFePc4vbqtUa6/V4/Rq9sCeP3HuS1e+/Fuj9d/uG3tFkLM2D5SCOHaPwCHR7ith3hb41l7jx+nV7fF5/6YtsXrP/Zt8drz+m/Kbfk5hfdXvK2x4tXj9Oq2RolXj9Gr2xo1Xj1Or25rlHj1GEe9Xrz+PtiW2ym8w0KIQ669IGPCaz9eeP3HC6//+OC1Hy+8/s7htgL1kMuvx9ThtR8vvP7jhdd/fPDajxdef4dwVYFiGIZhGIbZDPi5BophGIZhGGYsDBVAEdFniGiRiJ613HYTET1BRE8T0WEiutm4/Z8btz1NRM8SUZWIMsZ9byWiY0T0IhF9eLhDunzoc/2niOhhInqGiJ4kousszzlFREfkc8ZxLH6jzdrfSETfMdbyr4gobdx+NxE9Zdz+FBG90fKc1xi3v0hEv01ENI7j8Rv9rL/l/l1ElCOiX7bcxuf+APR5/r/P8tn/NBHViOgm4z4+//ukz7UPE9Fnjdt/QERvsDzna8Z1V74vs2M4HH8zZLvf7QBeDeBZy22PArjH+PlHAHzN5nlvB/BV4+cggJcA7AEQBvADAAdH1ZK4mf/1s/4APgngY8bPBwB8xfKcUwC2jPt4/PSvzdp/D8Adxs8/A+ATxs+vArDN+Pk6AOctz3kSwGsBEIC/ke8d/xvd+lvu/1MA/wfAL1tu43PfpfU3br8ewEnL73z+O7j2AB4A8Fnj51kATwEIGL9/DcChcR+Pn/8NpUAJIb4BYKX5ZgDym98EgAs2T30PgC8YP98M4EUhxEkhRBnA/wZw3zD7dbnQ5/ofBPAV43kvALiCiObc2M/NSJu13w/gG8bPjwH4MeOx3xdCyPfhOQBRIooQ0VYAaSHEd4T+ifZHAN7h/N77n37WHwCI6B0ATkJff2ZI+l1/C+ZnP5//g9Hn2ls/9xcBrAHgjrwR4UQN1D8B8EkiOgvgPwL4iPVOIooDeCv0b4MAsB3AWctDzhm3MYPRbv1/AOBdAGCk9XYD2GHcJwA8aqSX7nd5fzcTzwK41/j53QB22jzmxwB8XwihQj/Pz1nu43N/OGzXn4gSAP4FgI/bPIfP/dHRy/n/E6h/eebzf3S0W/sfALiPiBQiuhLAa9D4vnzWSN/9KqdP+8eJAOqDAH5JCLETwC8B+J9N978dwLeEEDKCtnvTuDVwcNqt/78DMEVETwP4RQDfB6AZ990mhHg1gHsAPEBEt7u8z5uFn4G+fk8BSAEoW+8komsB/HsAPy9vstkGn/uD0279Pw7gt4QQOZvn8Lk/Orqd/7cAKAghZO0On/+jo93afwZ6YHoYwH8B8G3UP/ffJ4S4HsDrjX//wNU93gQoDmzzAwD+sfHz/wHw+033/33Uv4EA+ptrjYh3wD7tx/SG7foLITYA/DQAGN80Xjb+QaaXhBCLRPQw9LTqN8D0hZEafTMAENE+AD8q7yOiHQAeBvB+IcRLxs3nUFcBAT73h6LD+t8C4O8R0X8AMAmgRkQlIcTv8Lk/Ojqd/wZ2n/18/o+AdmsvhNCgf5GGcd+3AZww7jtv/J8los9DP/f/yN099zdOKFAXANxh/PxGGG8WABDRhHHfX1ge/z0AVxPRlUQUhv5H9pcO7Nflgu36E9Gksb4A8A8BfEMIsUFECSJKGY9JQP8jfBZM38guFiIKAPhXAD5t/D4J4BEAHxFCfEs+XgjxCoAsEd1qBLXvR+PfBtMH7dZfCPF6IcQVQogroH8L/00hxO/wuT9a2q2/5bZ3Q69xBcDn/yjp8NkTN85tENHdADQhxPNGSm+LcXsIwNvA537fDKVAEdEXALwBwBYiOgfgYwB+DsCniEgBUAJgrSt4J4BHhRB5eYMQQiOiBwF8GXpH3meEEFzo2QN9rv81AP6IiKoAngfws8btcwAeNtLfCoDPCyG+5NpB+JQ2a58kogeMh/wZgM8aPz8IYC+AXyWiXzVue7NR1PlBAH8AIAa9C+lvXDkAn9Pn+reDz/0BGWD9bwdwTghxsmlTfP73SZ9rPwvgy0RUA3Ae9TRdxLg9BP26+ziA33PnCDYP7ETOMAzDMAzTJ+xEzjAMwzAM0yccQDEMwzAMw/QJB1AMwzAMwzB9wgEUwzAMwzBMn3AAxTAMwzAM0yccQDEM4zmIqGqMmHjOmCL/Tw2PG+tjPkVE5+XtRPTTlsnyZWMC/dNE9O+I6KeI6JLl/qeJ6OB4jo5hmM0A2xgwDOM5iCgnhEgaP88C+Dz0EVAfM24LADgF3Tj2w0KIrzU9/xT0SfNLxu8/Zfz+oEuHwDDMJocVKIZhPI1hOHo/gActA0/vhO6c/LsA3jOufWMY5vKFAyiGYTyP4WAdgO6sDOhB0xegzxd8m+Go3I2faErhxRzaXYZhLgM4gGIYxi8QABgzHX8EwJ8bQ7K/C2OQahe+KIS4yfKv6OC+MgyzyRlqFh7DMIwbENEeAFUAiwDeDmACwBEjoxcHUIA+sJlhGMYVOIBiGMbTENEM9OnyvyOEEET0HgD/UAjxBeP+BICXiSguhCiMc18Zhrl84BQewzBeJCZtDKBPin8UwMeJKA7gLbCoTUKIPIBvQlemOtFcA/U6p3aeYZjND9sYMAzDMAzD9AkrUAzDMAzDMH3CARTDMAzDMEyfcADFMAzDMAzTJxxAMQzDMAzD9AkHUAzDMAzDMH3CARTDMAzDMEyfcADFMAzDMAzTJxxAMQzDMAzD9Mn/B2qTRCRxhufiAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot average temperatures\n", "temp_NY.plot();\n", "\n", "# Compute and print ADF p-value\n", "result = adfuller(temp_NY['TAVG'])\n", "print(\"The p-value for the ADF test is \", result[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Getting \"Warmed\" Up: Look at Autocorrelations\n", "Since the temperature series, ```temp_NY```, is a random walk with drift, take first differences to make it stationary. Then compute the sample ACF and PACF. This will provide some guidance on the order of the model." ] }, { "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": [ "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf\n", "\n", "# Take first difference of the temperature Series\n", "chg_temp = temp_NY.diff()\n", "chg_temp = chg_temp.dropna()\n", "\n", "# Plot the ACF and PACF on the same page\n", "fig, axes = plt.subplots(2, 1)\n", "\n", "# Plot the ACF\n", "plot_acf(chg_temp, lags=20, ax=axes[0]);\n", "\n", "# Plot the PACF\n", "plot_pacf(chg_temp, lags=20, ax=axes[1]);\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Which ARMA Model is Best?\n", "Recall from Chapter 3 that the Akaike Information Criterion (AIC) can be used to compare models with different numbers of parameters. It measures goodness-of-fit, but places a penalty on models with more parameters to discourage overfitting. Lower AIC scores are better.\n", "\n", "Fit the temperature data to an AR(1), AR(2), and ARMA(1,1) and see which model is the best fit, using the AIC criterion. The AR(2) and ARMA(1,1) models have one more parameter than the AR(1) has." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/chanseok/anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:162: ValueWarning: No frequency information was provided, so inferred frequency AS-JAN will be used.\n", " % freq, ValueWarning)\n", "/home/chanseok/anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:162: ValueWarning: No frequency information was provided, so inferred frequency AS-JAN will be used.\n", " % freq, ValueWarning)\n", "/home/chanseok/anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:162: ValueWarning: No frequency information was provided, so inferred frequency AS-JAN will be used.\n", " % freq, ValueWarning)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "The AIC for an AR(1) is: 510.5346898313909\n", "The AIC for an AR(2) is: 501.9274123160227\n", "The AIC for an ARMA(1,1) is: 469.0729133043228\n" ] } ], "source": [ "from statsmodels.tsa.arima_model import ARMA\n", "\n", "# Fit the data to an AR(1) model and print AIC:\n", "mod_ar1 = ARMA(chg_temp, order=(1, 0))\n", "res_ar1 = mod_ar1.fit()\n", "print(\"The AIC for an AR(1) is: \", res_ar1.aic)\n", "\n", "# Fit the data to an AR(2) model and print AIC\n", "mod_ar2 = ARMA(chg_temp, order=(2, 0))\n", "res_ar2 = mod_ar2.fit()\n", "print(\"The AIC for an AR(2) is: \", res_ar2.aic)\n", "\n", "# fit the data to an ARMA(1, 1) model and print AIC\n", "mod_arma11 = ARMA(chg_temp, order=(1, 1))\n", "res_arma11 = mod_arma11.fit()\n", "print(\"The AIC for an ARMA(1,1) is: \", res_arma11.aic)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Don't Throw Out That Winter Coat Yet\n", "Finally, you will forecast the temperature over the next 30 years using an ARMA(1,1) model, including confidence bands around that estimate. Keep in mind that the estimate of the drift will have a much bigger impact on long range forecasts than the ARMA parameters.\n", "\n", "Earlier, you determined that the temperature data follows a random walk and you looked at first differencing the data. In this exercise, you will use the ARIMA module on the temperature data (before differencing), which is identical to using the ARMA module on changes in temperature, followed by taking cumulative sums of these changes to get the temperature forecast." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/chanseok/anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:162: ValueWarning: No frequency information was provided, so inferred frequency AS-JAN will be used.\n", " % freq, ValueWarning)\n", "/home/chanseok/anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:162: ValueWarning: No frequency information was provided, so inferred frequency AS-JAN will be used.\n", " % freq, ValueWarning)\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from statsmodels.tsa.arima_model import ARIMA\n", "\n", "# Forecast temperatures using an ARIMA(1,1,1) model\n", "mod = ARIMA(temp_NY, order=(1,1,1))\n", "res = mod.fit()\n", "\n", "# Plot the original series and the forecasted series\n", "res.plot_predict(start='1872-01-01', end='2046-01-01');\n", "plt.savefig('../images/tavg_predict.png')" ] } ], "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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 4 }