{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Moving Average (MA) and ARMA Models\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/arma_acf.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": [ "## Describe Model\n", "- Mathemetical Description of MA(1) Model\n", "$$ R_t = \\mu + \\epsilon_t + \\theta \\epsilon_{t-1} $$\n", " - Since only one lagged error on right hand side, this is called MA model of order 1, or MA(1) model\n", "- Interpretation of MA(1) Parameter\n", " - Negative $\\theta$: One-Period Mean Reversion\n", " - Positive $\\theta$: One-Period Momentum\n", " - Note: One-Period autocorrelation is $\\frac{\\theta}{1+ \\theta^2}$, note $\\theta$\n", "- High Order MA Models\n", " - MA(1)\n", "$$ R_t = \\mu + \\epsilon_t - \\theta_1 \\epsilon_{t-1}$$\n", " - MA(2)\n", "$$ R_t = \\mu + \\epsilon_t - \\theta_1 \\epsilon_{t-1} - \\theta_2 \\epsilon_{t-2} $$\n", " - MA(3)\n", "$$ R_t = \\mu + \\epsilon_t - \\theta_1 \\epsilon_{t-1} - \\theta_2 \\epsilon_{t-2} - \\theta_3 \\epsilon_{t-3}$$\n", " - $\\cdots$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulate MA(1) Time Series\n", "You will simulate and plot a few MA(1) time series, each with a different parameter, θ, using the ```arima_process``` module in statsmodels, just as you did in the last chapter for AR(1) models. You will look at an MA(1) model with a large positive θ and a large negative θ.\n", "\n", "As in the last chapter, when inputting the coefficients, you must include the zero-lag coefficient of 1, but unlike the last chapter on AR models, the sign of the MA coefficients is what we would expect. For example, for an MA(1) process with $\\theta = -0.9$, the array representing the MA parameters would be ```ma = np.array([1, -0.9])```." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlIAAAEvCAYAAACOiy/xAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nOydd7gU1fnHv2d3b6H3ppRLFRRFEQUFBDuKJclPE41GY40l0cRYMEbsUROjxpiiscXeY8OGgoIKwgUBkSpNeocLl9t29/z+mDmzZ86cKbs7u3tZ3s/z8HB3dvbMmZlT3vO2wzjnIAiCIAiCINInUugKEARBEARB7K2QIEUQBEEQBJEhJEgRBEEQBEFkCAlSBEEQBEEQGUKCFEEQBEEQRIaQIEUQBEEQBJEhsUJctH379ryioqIQlyYIgiAIgkiLWbNmbeGcd9B9VxBBqqKiApWVlYW4NEEQBEEQRFowxla5fUemPYIgCIIgiAwhQYogCIIgCCJDSJAiCIIgiCImmeSojycLXY2ihQQpgiAIgihibn/3O/T74wegvXVzAwlSBEEQBFHEPDvN8JMmOSo3kCBFEARBEEUMY8b/SZKkcgIJUgRBEASxD0BiVG4gQYogCIIg9gFII5UbSJAiCIIgiH0AkqNyAwlSBEEQBFHEmC5SJEjliNAEKcZYlDH2DWPsvbDKJAiCIAgiHDh5SeWEMDVS1wJYGGJ5BEEQBEFkCTPD9pIkR+WEUAQpxlhXAGMBPBFGeYVk0YYqSlpGEARBFB00t+WGsDRSDwO4EcBenYN+8uJNGPPwVLw2a02hq0IQBFG0bN5Vhye/WEETe54hjVRuyFqQYoydBmAT53yWz3mXM8YqGWOVmzdvzvayOWHZpt0AgEXrdxW4JgRBEMXLr1+cjbveW4Cl5phL5AkSpHJCGBqp4QDOYIytBPAygOMYY8+rJ3HOH+ecD+GcD+nQoUMIl80dIgssQRAEET47axoAAA2JvdqIsdcgpjTKI5UbshakOOc3c867cs4rAJwDYBLn/Pysa0YQBEEUJYxWqwWBxKjcQHmkCIIgiIJACpL8QHvt5ZZYmIVxzj8D8FmYZRIEQRDFBemjCgPJUbmBNFKNlHU7aiiihSCIvDJlyWZUjJuApRsp4KYYoTklN5Ag1QiZtWobjr5vEt6YvTYv11u4vgoV4yZg+WaKoCGIfZn3v10PAKhctT2n12nMLlKvz1qDSYs2FroaOYHEqNxAgpREWMJ6MslRVduQ8e+XbDQEmsqV28KpkA9vzjbyZk1cUFyDx9tz1qL/rR+gLp4odFUIYq8i14oLIUg1RgXJ9a/NxcXPVBa6GqHCIDKbN8IHXgSQICUh9iHKdrF07wcLccjtH2N3XTyj3xdqsdaYV4mZ8Kf3F6K2IYnt1ZkLtQSxL5GvMUBM7LT3W34hOSo3kCClIdvB5O056wAA1YogNXXpZizeENz3IF+Nvtg7Fw3WBJEe+eozxT72hMG6HTXYsLM2u0Ioai+nhBq1ty/SkEhiT10CrZqWWMfcmuovnpwBAFh531jPMgulGWJFFktTbPdDELknP32m2LTfueTo+yYB8J83gkByVG4gjVSW/ObFbzDozo9tx0RjzXSwyLfau1j7VmP2wyAIonjHnsYKjYW5gQSpLPnwuw0AgFVbq1HbIJyaha9VxpKUUUqeTXvFtkoUt0NjR4qKcRPwu1fmWJ8H3fExLnhqRgFr5M6e+sx8DIuJZJLj1crViOd5K5WcO5vntvh9lqtfmI2KcRNcvyc3h9xAglRIjPrLZ/jVc8a+zWENQntLk39u+ioc+8Bnha6GK7rcKUs37sIpf5tq7fm1N/HO3HUO/7t0+N83qbQaO2saMGVJ49tEfPryrThw/EeYurTx1S2fvFq5Gje+Pg9PfbkiL9fL92KK8hqFywQzfYVKaq+9/NVlX4IEqRD53JyQRFvNVPrP92ot21XKrW/Nx4ot1SHVJjy89vN6+JOlWLi+qlEKEV7MWb0D17z0Dca//V2hq5JTZq4wUn9MX761wDUpLNv3GIL+1t31oZRXXRfHV99vCaWsrMhAYtu8qw7rd9bkoDL7DukIrhuravHLp2dklconl5z3xHQMN/3HCg0JUhKhaZJEQVmWp6sP5xzJHC0rinUjUd1zLI0ZTT+Xu89PXrQJa3eEO/BXmRq0jVVZRvE0ciIR009wH19Bu3XJNdv3YP7anWmX97tX5uDnT3zdaNpPOq/3iHs+wVH3No6J04uF66saXe661F57wX/zyKdL8dnizVYUemPjy++3hj6+Zso+L0glkxwffLveJqlnK1CIkjKVd8T1dZqiy56tRK8/vJ9hzQxBbM32PcqxjIuz8d688DtcTX32A5Iu5LckajzjhkQSnHN8ty79ScmPi56ZibGPTA2lrJr6BC7970ys3Gpo/oSgUeyQKULPiPsn47S/f5H27xasrwIA1DUEW0As2bgLFeMmZCS0eWH5LxbZ+92yuw6n/G0qbn7z20JXxYUMHnixvaQcsM8LUk9/tRJXvjAbb80JbzsW0e5ykbPjk4Wbsvr9E1NXYMT9k7X5rLKdmn/94jdZlmBn4foqDBj/ISbM09v9g5LQzMYlUaPp1yc4XpzxA8Y+8kVOzHw79oSjFv98yWZ8snAT7npvAQCg2OWoiMdiYl8krKcgtNkRn5FfXO+ThcZuB+/mYJEEFN5Hqroujvp4eFrp3bWG72LlytxusZMptDDJDfucILVqazU27UqptX8wV/g79jSENliJwSHT8qw5MgeN/qtlhn/E6m17fM60s3NPA9YFUKOGOTB+u8ZYBX+2ODvhUTd4WIJUPIkF64xV+qo0n0k+iUWEBs24mWiRmmEF4vZ2VDfgp/+e5tCi7iukNDfh9KuEWU7URRJXj4p2l0iEOxhlYmrKBQfd9hHOeXxaaOVZKVca6QKAlEu5YZ8TpEb95TMcec+n1uc6czVSFotax7KdoizTXoajRC7nSFEj+RpikJaP3f7Od7jCjEIEgJF/nmQlhvNCp/3JFGvLnkyzSFhpJJx1KpN8pESVw3zsYa+0Y1F77fYmf7Ynv1iBinETHGbaH7buwbZqvRO1mOffnbcOM1Zuwz8/W5braroyd/WOvGtOvt9kmNSCCvcfzl+PRRuqfNMkBHYJtAQuo5/EcyTxZKO1X7pxly0YYebKbXhaiW68/8NFnukAAGD2DzsyroOKlQMwg9vaVl2fVTSuF5nstbcXDTEFJ2tBijHWjTE2mTG2kDH2HWPs2jAqli+EIFVeon8UiSTH/R8uwpbddcELFb7mGftI2YoJFVGniKaXyEee+WqllSMLAKpqg3XwRBYD4y+e/NqW0yjbuUvcoq5OQiPVEE9CPGndM8mUMAVKAIgptphoDpZA1XVx3P/hotAdZf8zZTkAYPseQ2h6YupyTFmyGcf8ZTKOuvdT7W/EwC/ek+zTU1OfwNn//goLTX+fdFi1tRp3vrsg8CLnkwUbceY/vsQrM1enfa0NO2vxvhSOvm5HDR6fsiyQUPb6LMPV4H2XcHaZFVuqccXzszHm4am4e8JCz3PFRKq7/XMfn44Xvv7Bdkz4EsaT4QZlpMLxM+8nJz40Bec8Pt36fPa/p+GOdxfYzvmXKYDnKkBHJZskwIPvmogTH/zc97wgAUdu3+8NGqktu+tw+zvf5TQQKGzCGI7jAH7POR8AYBiAqxljB4ZQbl4Qk4askZL5atkW/OuzZfhDGs6DKWfzzFqtbsyqbUgEXhU3JJKuUTlWnWSNlEdZFeMmpBUunc14O3XpFpufkqhXpgKOtQrT1MkSpBJJ6/sw5Kgde+pRuXJbVgKlDlUjFabQJ/j7pO/xr8+WZSQ0eKFW9e4JCy2BuU7jnzJr1Tbc874hEFiClCTcVa7ahpkrt+MeH6FBx1UvzMZTX67A4o3B9rwUaT2Wbtqd9rXOfuwrXPXCbEuo/tVzs/Cn9xdh9bYAJvI0hHs5cennPn5+oi66iXaapN259e3vsKc+bpkAw14YCPI1sedKo5YJ5zw+Da+69LF1AfbUO+mhKRgw/kPPc9TxJ2VKbTzPwY3b3/kOz3y1Ep+a/nl7A1kLUpzz9Zzz2ebfuwAsBLB/tuWGwbodNXhw4hJPAaS2QZj2ItpOLTpgbRoOidn6SIlOIMpZvW0P+t/6IV6aEWyC++P/5mPonz71VBPLw3Mqs7l+0H45jYk1TAEirIzr2qi9mFFoXSIpTVrZXQcAzn/ya5z172k50EjlXpASwkpDgqO6Lh6amSHdJjFxQconrtQUIGWH4GyamFjlBn182bQNITCJ9ieeZ0OA1UZKc2z/7HVuEIQAFeQ3r8xcjZKIWHCE0543VtXiuemrrLEmXxN72Bo1P7zmnOnLt+HGN+ZlXPbSTbu1CxCZcF0s9Fz+bCWO+fPk0K4jiCeCt9HGQqgGAsZYBYDDAHyt+e5yxlglY6xy8+b8JEH89Yuz8cinS7FIE6EmEJNHVF7x6/8MTKYaqWSS4+05a63BXvx62WZjNfzBfHc1/4ot1XjRVMt/vMAwydU0OE00OqFJTBbLNu9GxbgJWBJwta4jFz5SmeK1Ciu1THtc8pHKXjiZv7bKKjdM1HQHuUh/ICsrB97+EQ667aNQy/cTXlZuqcZxf/3MFgwi8n3JE4fOzy8oSUtACfbjpKa/+DFlyWbc9Hpqokxyjk1VtVhuareCmJnEOalUKOEgFjpBxiYGhK6ROumhKbj1rfnYZSZ5lIvdWdOABz9enPW17KlsjP/zpZHyMp3mgt11cWzVuJ28NOMHnCuZPQVhCq4fL9iIH3IQoNNYHfW9CE2QYow1B/AGgN9yzh3OC5zzxznnQzjnQzp06BDWZT0Rg69Xx7R8L3zeXTrOplY+zjQb7f++WYtrX55j+ZSoeT3Vwfz9b9dbzrrnPj4df/jftzYTiG7otxy4NfV9d+46q1z7b4KTG1+E1GB+z4QF2BBA/S3jlf7AcDbPzqldR71k39+wszbrfePUppSJHOXVHrdLTt+M5WY16Nc0/jN1OZZvrsZ7UroLITDK7Tobx2/xroM+P3H+1t31gZP/XfDUDLxSmdLicg5c8t9K67OqtU0muRU5+s7cdZi8eJNk1va/nlyc37OxTHsBniFHyqQcliAitmQSxcn1uOu9BXhk0veYuGCD7qeBkfueEJjjIUcduiGeb76EgVF/nozD7/7EcfyOdxfYTLWCXGt5vlu305pHsmVvcnYPRZBijJXAEKJe4Jy/GUaZYRAJoD4WwpbbOZlER4lOlG6jFYOM24At12RTVS2uemE2fvWcMUBXmxP1TilvkW7s8zKX6SIY0yXBOXbWNFhpFrJBreuMFdvwn6krcMPrcwP93mt/KVGmkZDT+DuIlmJ7db3nZCWKkAfzYfd+ip895lwdpoN6zbfnrMPH36U34ajPQRZ6D7trYs4i00R/8HWQFV9Lp4nf6EwZGUUuumiY6uIJvD5rjeMZiI9vzF6T8XYUiSS3+Syqgv3nSzbj1EemYu2OGlzz0je46OmZknbQ+x5nrdqGVyuDm97T1ZiIIIdEMonnp6/CY5+HEz0p6iE/b7HYiCc5Hvt8GV74elVGZctmSCGI5mvTZ/FcdV2ppj4Rej22ukS9qoTh3B+EsY98gd+8FG4+wb2BMKL2GIAnASzknD+YfZXCQ3Qir0FDrHTDVKSkEnKm97uSmN0fwfq5phwxsQg/jJblJQCAHdImvDpNjE5oEGf5RTAGIZnkuOzZSvz8P19n7GNTa5okrbQMomzzc7qrS93gISbo+nhKI+WXpHDV1mocdtdEPP3lStdzRF3VJH/fZpAZurYhgdvf+Q6bdtXi2pfnOL5/dPL3aZWnPocw/NlqGxK2FAa76+L43sUx289kk/ItTJ0Xl96TdV7GtU09A1U8eWjiUlz/2lx8vMDu4BqGcJnkdv2E6q4johl3S5Gxqm+WWzX+71/T8Nz0lMDhV1tLYxLwvlILDo4/vjUf936wKNDv/LDGyKTzGAPDW3PW4cP5mWmm5LYiBOZMNWrj355vJcG97e35+N0rzn4oYwmImu8GjP8Qv38t2CIwLBwLg7xefd8hDI3UcAC/AHAcY2yO+e/UEMrNGtWh8cxHU1sqiKgJP41UJoiS0i2zxEWPr8unpGZPb14WA2DPpK1zsBTn1zYk8MLXq2wdTQyy5SV2jVQ6k0mCcyw0zRSZDl4DFd8cNaQ4qCLCev9KPUb+eRJuN8Ok69PQSIkIrskeCULFNcMI3X1t1ho889VKjHl4qlZLqQpr89fu9NQYqIKM+tkyIadRx/Oe+BqD75oIAPjmh+0YeNtHOOHBz7Vtxq89pCb51DGtRsqacNNHZ1ICYKU32VnToD0/CGu279Emj00m7X1IvbZoK/L78AsACUJDIunI0yUuEVSITi1ewtWkpDRjuns2xqdajY+n4KGJS1y/k/teNE3Tntpun522Ck9+sQIA8N9pq/C/b7x3wEhp2vTlBtm37sKnZuCOd8PZlFy0KcvXzqrHWny/ydsXNhuf0SlLNmN3jnJiqYx7Yx7mrQkvF1gmhBG19wXnnHHOD+GcH2r+y3wzuBB4c/YanPTQ51YCQNF45q5JaQVE1ISs/dDZtTNqSh7qXS9iSnIgtVPLdVGdRluUG4KUWN0CLhop8/+/fLQYt/xvPj76bqOjnqpGKp3bSCS5Q5O2fPNu7NijV0FvrKrFJc/MtO0wLiZcUc7SjbsxY8W2tELCbXVSblAOP5d9pPwQ57llhQbcNVJBEXs/JpMcCXNCcJvE1Guc9vcvcO8Hi1wFX/WwQ5DKYPKetSq1FcaP//mV9fcuzSDq95wts4h0LG4JUpKPVBaJWt1MW6IoN9NeEMY8PBW/fHqm6zUFanusT+iECruWNBOfmxtem4vBpsn2vXnrsMrcxQEIlqaE89RzCttZW6e1l/3XahsSnpFpf/t0qet3cr8QXfV/36z13c0hmeTWXoSZIp6r2o7ScaD/fMlmT623Dre8aup7Ex+vfXkOTnhwSlrXSIcLnpqB63y0d26kO2++PHM11m4v7ObFRZnZfGdNA5Zs3G0NWF6LqZRGyq5aVknn5Vo+IQF+JDshl0RdNFKaYsTkKjpGc1OQ2rmnwVudbR4SK3BZgBFk4yMlr77F8z/ur5/j9Ef1G6z+fdJSfLpoE97WrPSENuLrFdvw08emSRFUweqSmhzdz2lIBJ+iRDvy2p5FfOUXnuzGizN+wJUvzMarlat96yVfQxa2al02pA1q2stEQFEF5R3VznYV2LSn0ZLqBFNmHj/rX1+hcuW2QPUURat1cUukmI5W2W0FnuTcVq567bhOI2X+n+6iQb7OW6b2oy6exK9f/Aan/i21gXbQ+xLvIpTNw6X7U32k3pi1RnKOZoYgFXBjZRWds/lDnyzBj//5pe08Vdh5bMpyjH1EP04F3ZDdzbTnJ4hmG6Qzc+V2/Ol9Z141K92H+Tloc+acWxukj3/7u4zefya51+wEb/sluchQnAZFKUiJnDuio3gNGnHNalDG7Zd18YTr1gOiqNP+/gWemLrc9doff7cBB47/CHNX70AyyR2NQVxbpymoT9hNki0sHyk/jZQ4Jpu91FWLqpd2vQUHNQ0Ja4KWTYtuSQhTAQH+ZYv3OWf1jmAaH/NxJZIcVbUNeFuzMbXhbB5M8BXP0yv1gBDCM80Ovn6n8Zy27K7z1RCJNrCtuh59bvnAOu4WIaiLFpPJJtLotL/bJ6DtGg2kmyD1yswfMGnRxlT+NOm7lEZKn0dq5dZqVK7ajpsC5uXRvetb35qPVyvXOK6t+5wJCcVHSjX7WqY9jZnL2rw5g4qIcVBo3avr5cjHYGWI57TBJcFvUHbXxW0CjqqR+v1rc7HL9BEzTHtJWx/avCv4zhL18SQen7LM0EBJXWfLbnubVNvj3NXu5qGgG7LrnOgBY9cGLzLxV1T3PhXbXsnEExzTl2+1NMRBBegXZ/yAqUu32D6nS/buMsF/X6q593xSlIKU2B8q5dDo/kJSA6ucu8XYWmD82/NTCeyUl6r6UtjKlP722rJB+Nqc+Y8vMeqByb6rT/lb4ZAu6ic60S7JYVXnF+Aw7yirZcA5wMxbG9z+fPLDUyyNSCLJtZPnuh01lgZD3LOXGVL9vKs2jjvfC+5DkOQcN742D9e+PMeRI4vzlDpejPMNiaTWnCbq6LlhsOScmw419YZPiJXnKMJ80zLUmRPkR0r03h6X1SNXbkldJac0sumzRlGty4KU6s+nctMb3+LiZyq1EU/imcvaCVnAFIuPoKYny0dKehY2Z211DaGp84ot1Zj9w3bHcTc4t5ej9ku1Lxv1NN+9T9nCN1JQH09afUuYoHdptndS34WbOVg8p01VTkHm2pe/sfzj/Bh420e4Rorm8lq8MAC1cbtp74h7nCH+qTray9i0qw5/en8Rfv7EdM8xVf7ZhHnrbVtiZYrOPM05x8yV3u0lk/QM6t6nOmGiIZG0baPDeTAzo2yyBzLTmKmv9qvvt+DyZyvBOcdrlasxdelmPPXFirTL3lMfd2h/SZDKAWIlJjppg5cgJf7n3Nax7v9wEZ6dtspqdLvrEhh810R8KbZL8Xj3fs7Z4vt6KWnj6m01zt9pOqWgQTHtWVFokgAQRDjRNWJ1cJO1ST//z/TAzueJJNcmBT36vkk48p5PLSdO3TUB70lt3hr/KDhZnb3O1PSokYQcKd+461+bi911cRx17yQMu9cZ6i5WjbnwkRow/kOMuH+S5CfiL86Id71YSThb7aKRUp+xUyNlIl1bNv3OXb0DkxYF27ZBDnoQJJLcs+3o2oDQatq0Neb/kxZtwrEPfGacF3AiEte47Z35WmHZ8Yw0dTr54Sn4yT+/CtwP9tQnPDVS9Zp8d1z5340mpXYz/IaqWks7KITMIIKU21ghnnu95lm9PWcdtlXXY+vuOstxubbB0NSPuH8SjvvrZ7bz5YhIcTXd821IGIs7N2dzobUVqEJ0g/k8N1XVOfrqs9NWWhtoy9d+bvpK7bWC8P636y0tsDZgIkAzCSPzeqnGvKXOfZzzYIEwSp2/XbsT810ijznnqKl3bmGmvtvLnq3Exws2YseeBtzw+jz84skZuPO9BZiyVJ+g2y2R9pC7P3EEJJEglQOiEbu5KEjESZJzbcSF6KSLN1RhW3U9/vLRYgDePjC6fjP+7fnW36KzqZ3HYXpRVm3y3NqgRBuKesoZteXy1+6owc6aBkdZxuRmr+sTU1fAja+WbbWyd/uRSHLscfEbqU8kcdd7CyytnG5OcmikNJoKN96esxbLNldb57qZEJNJ+7Fnp63Elt112k2qheChM+1xbmyrIp7r5c9VOs4RfLJgI75b5xyUtuyul0w6/hqiBheztJtGSm1f6gT04tdO9f0ht39s/X3mP77Exc/Y78tNptSZ9pLKYkVFJ5i4Oe+q6CZ6AJi5cpv1Lict2ohNpolo9g879AkLHXXSXMvse3JWZ9mRW+XYBz6z+itgvLd3566zJiYxsW2W2lxqseU9djUtdfozivsVyTR3afwg1ffgptELIiyOuH+y5bgsNAVrttdg+eZqPPLpUivZqMx6M6muTpASJj3Lf1Wp21HKIicVmWZ8Fou3unjS0T7F2LahqtY2hrj1GT++WrYFV70wG/e+vwhVtQ2efn5eBDnHT3Oj8xNS2w9HsIhi9UrvzF3nMN8LVm7dgwHjP3TkM1NfbeumpQCA5VvsvlOTFhlzwLLNuw2XBvP4w58s1fo+6t6VTojMJzH/U/Y+xAAiOumTX6xwlVhT5j/J2VVqRqqvi/jGbeCWywRSkvKz01Lmg6nfb0GnFuWOVbTDCTXJcfULszHByjTu7iMlftvgopEaft8kdG5Zjs6tyh3XUPlOM/DJzF+3Ewd3beV5jijbb4ASq06dj4BzhZP622/gkfMuJTl3TcynOgLrHFwTSY5ohEmmPef1fvb4dMxZvcMy+3nNP5c+awgjzcti+PT3o9CpZeqdWH5YjEkThF5aEd+rz2JPnf6ZB9FCAM5n9PAnSxymO0FpLKJ1bq+qcQrQ8YTe1GvVT9OlxGLAb57RTQ4NiSTO/vc0HNK1Fd759QiHELhelyFfekY7axpsedkE+7dugrU7ajB/bRV6tGuGjVW1GPWXzzzrt0fSrsSTSStp4cr7xlp1l/1wRDX8Jr1yTWCIeMYimaafRmrnngY88YXelzOINkWndRY8OHEJHp3knu9Mv0G7cVAIUpt8/KMufHoGZqzYhpIoQ0PCrgVX+44QPKvr4kg2L7WOZ5rzTuRMe276Kjw3fRVeuXwYAFUj5f8QdeNwxbgJ+Ph3x1ifE5wj4mHsLdPk/7vuVXvk3NKNuzBR0gx+8O16nHJwF8fv3Oq8uy6OcW/Mw22nH2QdW2RGC6p5v9Txu02zEqzdUYPFG+yClGifx//1c5RGIxh1QGrnk9Xb92BIRVttXWR0/mH5pCgFqWjEPpl9tWwrvlrmXH0C9gg70ZblyVTNwyIIarppplkxXmSGSJ90YCfbcZ3pZcIC/f56Kb8K47MsSIkG/N9pq1AWi1pCz4aqWnRSBKnahkTaTsZB/VGq6+IO7ZUqmArnbK/koYKENOrWx5PYUx9H01L/JmwIUqbjrbpC4/YOr/q+LdpQhTEPT8XTFx0hmfbsnba2IYEZK4yVU5OS4BGPu+vieP/b9bhoeE9bXQFDkIoHfC8OQUox7VXXxbWbcrsLUvbjD3/iHmpeFotqBSmdqSIhaX11aBOnmofkd6TNUZXgeOubtRjRtz3aNy8DAKzfYQhKq7bqw943agQpueRBd3zs/J5zy5xW05DAyzN+wD8/88/2bdNyu/hI6c639t10eW46GTtuCVKmRqpOo5GS3v097y+wnO0d57lojO4w87A5rq25F69Fp658IQglkhy/fHqG78JO9D2jj3ObSVB1UheC1J76hE2ISzcqbfW2PejapgnW7bC3IdVHat2OGswMEFHq1hdlX6VEksNreCmNOr/85ge7f+vtynu78oXZ+OS6UejTsTkAQ1vesWWZ60LwnTnr8N689TbfPCHwqu4IahFtTI2U6qcqtwG1rXBuaHt/9I8v8doVR6FPxxbaepFpLweoPlJeyI6w4ny583nR9koAACAASURBVG3dnaUgVRZzHQRVgUQdb6Yrpge5nQo1qmrakxviu3PXOdMOiPPN8zJRaSeC2NgB/PaVOfjD/761HVNXx6mwc+czUrVUsjl1+ZZqHDhev6muTpMlOnlNvc5HKoWaa+aj+cbqbcaKbdbko2qRbWkIfHwdtiuC+X+mLLdFf6Zj2hM4BSn7Oz3oto9wxfOznQk5Xdql18Sn4rYStEVomf8bZtT0BKnUd6m/dWftrovjt6/MwXEPfIbXZxlCwZrtxrvcWdNgbfwto4tE8zOfxCU/r2SSY9yb36a9cavDR8rDV8svaEFrEudG3VKmPZ1GSrq+x1imexzf/LBDawZev7Mm7WhVXf1FJnEA+Gzx5sARe2Lc9xKKmpkCQHVd3Nb+92g3eNc/+2/X7MTIP0/G81//gA2Kv5b4ze66OP79+TJc/MxM7a4EKkHMbX7z2VuaqOQgyD5nlz5biTMe/dJ1CdeqiRkdLvlACsFV9UerjydtbUuY9hZtsAvGftaFKUs2Y/ueBs8FHQlSOUBoDPwa3oMfL7YEkCRPDRpbqyVByvzbWml5OF/qaF4Wc/WnUjuPOohX16vamxRCPZsy7SXNMn0GXvN/MdnWNCTSDq2+/d0FgfbBWr7Z7jcya9V2DFE22BSTma4v+QkIKhMXbMQFT81wPINEkluJDVUzhPHeU+ev3m6fFFdtM+6ha5smrs7msinM7/kfpkQ5rduprmhNjVSEWSKe335aqkAkPyeR6fyThRt9nc0F6TjKi/xlKt/8sANLNu6yaQcSPj5SQYN3vNprVW0c1782F0s27rK9y+P/+rnjXN3m10lu7GN58TPOxJqAMQ6Iy2e6xY68gBr550laoUSckY5QK5Pg3BIsqjTmSVlIaFqmf4ec87Qiqo66d5KviVMlzB0lhO+il6lRaKSqahts19aZw90meLHLwOeLN9v82gB7m7jvg0WuDtOAEbV96J0fG0Kdy7VsSZh93oWb9cSPbdX1WLGl2iawur0XS5CS0uyIgBR1XNxaXW8FgwAp68z3m+zzgqrFtGufgZbmNb222SIfqRwQi/j7qQDAI5LtXtZIyZOhyD2iao+CTjalsYjrCkkVpDIZmC2HesvZ3Lte4h6FcFejRBQF5b9frcR5Q3uk9Zs/f+jcp0vcsm6QSFeQusz0PVL9HZKcW5383bl2U2kiaZ/c1cFIaKgYmKVtev/bDWhSEsMJB3bEYd3apJW12A9R1vi3v8O5R3YP9Bt1shOmPc65bW80tXm5mWhrA2gV7n1/IT5dtMl1AJuxYhtOemgKRvVL+Tskkz4+UgHbfxAH6E8XbvKcUAG9jxQH8PdJ31sOsCoNyaQl5WSa7VsWLt3yq6XGIm8fMbfgzkSSWzsl+GmkdO4Haj1kdOVlSohdJ6WR8hSkjCmvqqbB1m90AqvbeCzMWrvrGhy+gOncz18/Xowdexrw9px1GNpL7wckv98QAvu0bN1tF3gA/z4ma6S2m3/rgnDW7jCi0RljVn+RFRWA0cYvenpGqj7SGMyRGve9qlRojVRRClJq1F4QklxKISAJI25OiEEFKc71amPAKYn7TSReEfFWBmjNgODVKWoaEhllhU03T5JXygBAbxJTJyrVLAfA6qSAMZDGk9wRMSb7SKkTpOFsnrrOdiVsX9xnXTxhva+dNQ146ssVeOrLFThj0H646ZT+nvcmEL4cXsi3/FLAJHjqc6qus0c9CV6eaS/PTagJklH6sSmGc3KPdk09z/t8yWbLZ8kv/cFni/Vh0DJbdtfhyhdm+553v0ZoV9moMe1xzrHNZTsjwN5n350bLNu1ShDHZvGYrIWGhx+fjnhS0khpBJ8F63figM4t0KFFmauf4d0TFuL6k/o5jrtt95QJYWqkxBhT67HgamJppOK+84Nb1cRQtrsu7hxr0ph0xA4Sf/jft66CgLzLRhibjOtQBRvA/d53m/52sqZNzQmo8s/PluGJqcsx+oCO2rLrE0lb8k+1fQtBym3nD4AEqZygZjYPgpxHStYUqZMRB7BpVy0qVwXbkiKR5FoBAHDm+PATzrw2kbQ0UhpBSp5o1Ueypz6BluXpN8J08yTFIsxTENSV59S0OAfI+kTSGpBKYxHE6xMOYSiZdI98iyfsDtCqcCEGTTfn2lmrtgfe0PWnj03zPSeTjOiO9AcNRntTk9b9Y7LdKdpNkPLaLBaw9ys3R24dCe6tkQqCW9BIJmytrne0uy++3+LZtuOJpKXBDSIY61BN9trrKM8paQqhSW5E4FrHXca4RIJ7pj/40/uL8NjnyzHr1hMdm5TLPKXZ802XIyxTdtXGQ9ngG5D8ID3ar2zu9BNM3NqqKH93bdyRJiUVYe2P7F8YZDy9/Z3v0LppSeDyg7JN2c6pZXnMVZDSRVAKrarbOChSBrndo3pcXciJ+dNrwU+mvRwQTcPZXLBzT4OlFam3CVJK+gNubE7qZo+eqiQXW7C+Cuc9od8eQG14meYyAfTaNIE8UAWN3PIj3Qk/ybln9I3Oj0ydTHTPZ1dtHAfc/SFuGtPf+l5dMSc8fD3U9AcyV7842zcx5todNaj0yVqcDm6pC9x4c/YavP+tktm8LjXQe+E2kfiZxNL12xGTjWpGzQSdUJANm3bZtVJ+WrEGH61aEIJopOqV/hVPclz78hxMXrTJJiC7JSKtro9bvqJupjhhQvEaJ3XjnOwfky33f7gIr81a7X9iAMRd1HhoVMWYYkTt+QhSPv1jzfYaxxglAh2CECRkXy7/nQw1oH6oC6curZq4tonxbzt3lPjCTFLtN3/p9nUFnJHU8tyydXcdHvh4CQBjMewevZrJfgzhUZTO5qk8UsF/89eJS6xcTzaNlKZTejn1iUYls1GzvYJ6HcA/BNerrXhppGThSn0k8Qwnhpr6BK57dY7n/lQyDQnu6Vuhe87ORJPO3wvzjGzKUd8P59xV8Isn3UPyJ8xbH2gD39+/Ntf/pIC4ZSV347pXndfeU59AXTzhCDNWcZtI/HxgNu4Mvu+ZTMLjWQdFl58qG9L190mkscm1G9UBhGVVGEgmOd6Zu87aM03Q4OI4c/R9kyz9ted2VpxbztNBCVMjBTiDUjJFjGNeJlexeF22ebfrxC5w6x8ipUumPnKCIJvDq1HPuUANRigviWTUxt32+LSu49LX1OvLc8EDHy+2/o4nkmm7lOSLUDRSjLExAP4GIArgCc75fWGUmympLNaZPXQ5O7jqeOs3jKaT2E1dTfpJ9B/Md98LKpVHylm/qySfElVoSiSTGdneq+sTeHP2Wrw5O7OQWxWdliPI89E56zp9pNwz0SeT3NOJM9vBMl0yTQwo8+mijbjiuTpM9tGuuN2bm6O1YOOuzDawlQM6MuHRSUuz0trqSPd5f70ie9Oi34QDOP18Epyjc8tyR8oGr61xNpnnevk0PTZluTZq0IuwBamwCNJXxTlfLduKMx790vNcN239vz/3zxsWhEgjUWOogrbYoidd/BYIbtpktX3Kc648nzUkktoFsZ//bT7I+lUyxqIA/gHgFAAHAjiXMXZgtuVmg1dG3yDIg5Uu2aDnb9NYrauryZqGzCdRL42U7FfiiNxKZG9uCQO1gzz5xQpbAk5Ar7G74vlZjmOqj1QiyV39fuJJ7rqqBzLbTDQbwhAUduxp8BWivl2zM+38R4Ktu/VJDv1IJDlufWu+/4kuPPDxEm2m8WxQ/cj8uOH1eRlNMuleU13AJZJc6x+jzc5uIlJrqP1BRs5yHZQwTXthEiRIQhaO/NwawozG1RH2oiBT1D4lJ3VOBz+XADdtsvP6+ms3JLh2QRwrBkEKwJEAvuecL+ec1wN4GcCZIZSbMWFKqHU+jUPlk4XBByZV0Aui8ncjofHv0qFq1BLJ9HLF5Ap1ELzrvQUOx82gA4+a9HLdjhos2ehMyAgY9+81YPqtcn9/ojOqKRvCDC334vRHv8CNr8/L6LeblSS1QQWpFVuq8clCb22XHxPmBXfmDUK6ghTgr5X2I0g7VgX/9+at980n5oaXaU/OnB2UxqqRCuK3mc7CyGs/1TAIEqWaD9T2EU/qW/jIvu09y/HT7rpppILKbGt31DjyEALFI0jtD0D2FlxjHisYMY8wyXRRO1OYuTzUASmbFYqXRkpGlgvaNC3x9BHKJzp/hS3KhO2WRkLl5Zl251WvLTySnHva3VWnX5W20n5dYZCOv4qcoymfqBqpJgEFKbFBdTYECf1PB1XoDkJNfXaDQJD0AbpFVdAM37mmsQpSQdaDfjsPyIQVTdjYUdtVfVyvkfLz6fLz8c2VYBorcMQeEI4gpZNaHG+BMXY5Y6ySMVa5eXNuJfFQNVLKy/dyUCzXbBqZDkF8J3T85qVvLIdNvzBasckmAHRv29RXI5Mv3LbikdmmyXeSLfEkd5gQZfw0RM1dskLng2zbW6ao76ppSbBnsGpLZqbEXHKrJgrJDzXkPV2WSc7VB+3XUntOug7g+STMPFL5Jp2x7qkvV+SwJo2XeDKpFUrlKEOdFijdQJmwKBaN1BoA3aTPXQE4wiY4549zzodwzod06JDblXQuH+ya7e4DXIvy7HJ8ZLralqNU0olqKC+JmhqpjC4bKkEmJ7cs0EG4+tje6N2hmeP45l11rmY/wHvn+bMO7xpo0+Rckc4GyWHy3HT79kDlATVSasTZvs57vxmBLsom4n5ceFQP/Oa4PjmqUTCC5MFqrKQTPPL89PSc8IuFhoTeSiELUi00W0Plch45+aBOrt8VOvUBEI4gNRNAX8ZYT8ZYKYBzALwTQrkZUygvfl3jSge/Xc6D0BBP2tSB+3kM1E1Lo0gkk43EtJfdJHv76UZ8Q4cWZdrvy2LRUDvcdSf2w1/OOgTNygojzADBTWq5QNbEeW0xQrhTFoukPVY1L49lPc7sy+Q7eMSPnw3p5n9SHimLRVxNmmXSwi1bpUG69OrQ3PW7RmDZy16Q4pzHAfwawEcAFgJ4lXOevr48RGIFiit1a1wlUYZ2zQxfmjvPPAg/HdI1Z3VQnc2vP/kA13Oblsawfketb7h7GPztnEMDnSe2E0mHv5x1CLq1NbYqcYs2KS+JeOSFT5+ubZqAMZaVaa9FlmZBr4zUANCnY3O0z9CHy89sKG/XENTZnLBTFoumPVY1KYlaiTYLSSOwpgSmLBbBoK6tAPhHluWTXx3TCz89onEJUq2alJhRe87v/DRSuaTEbHAj+7bHl+OOs30XLRKNFDjn73PO+3HOe3PO7wmjzGwolEaqpUvj6tephRW6XBKN4KD9WvmWdUjXVjjtkC5p10HtBCXRCNqaQpw6OZZEWVbmloH76/07dAzr1S7QeaUugQJumiYAGHtIF2uvJTf1sqGRClSFQIjrNctCGGqe5WCkE6QO7dYavz2hL4DsnGWb+ZgsZbOin0BH6CnNQCNVXhJtFD4hrZrkXiMR1jjevnmZtQH4ukbke1YSjTSKdynTojyG2oakNrG0LEjlu88Lh/LSaATlSkZ43WbJ+abwS5scEFbjVIv5048P9jy/pcvgIm+oyOC9Z5D1m2jEN9xUR5LbQ7pjEWY9j3bN7MJINivbt64ejt8eHzz03287BDExl7icV6FsjisLVk1KotZeS14aKb/tXvw4ZWBn62/xDoNqpHSCYLaO6jofqfKSCHqbavCGeBIXj+jpWUb/zi20x/0GytZNU5qudFanQbbFaKxcfkwvjOjj3SfTCQAoL/GeSHUm00SShxqVfE2G/lZhJqp1ewRhCVKcc3Q3xw+vvFv5piRqF6R/MjgV7H6JT7/NFV7uAnLfFeOtOKYbWn9ymHvwfrr+naLNx6LMMTYVRULOxkg0pIFGDfc890hvNWzbpnozSkkkYvnnRBgLtFO10ckyez1yZEo0wqxJXxUyshE4O7csT8uk4xc627eTMfm7CZk92tkdxR//xeHW30x6pm7De5DtGPwYK2kIdRopr/eqUz9nq5HSDUYMzCq3Iclx1eg+WPanUzHjD8c7zr362N4Y1LW1tmw/gecXR/Ww/vbTXslkI8yO6NMevzy6IuPfd/TQarpx2+mp3MI/Pmx/Rxk3n9IfH/52JE460HCGDbJIEpSXRD0nAV37qK6Lh6rF6CcJ0neeeZDnuXL7ziT/lhtu4ethmWw4jAjlQqOa8ktizNZeDu2W6ovXHN8X+7duYjs/H76IXuOk7CNVZi4YrHFQMwb86ScpxYMqsLdskt7YV2LOhbFoxDE2FY1pr7ER1kAjVpfNy2KYccvxYIzhilG9XQe/Ns30glQkIuWIYHb/EjdiURboPBm144ly3PYezEbgjEWZrWP54SVkTL5+tCVouk1EqkaqffMydG/b1Br8xQCQTHL06+R0TCwviWTtbD6ybyratMysZ1PpGbRzef+AftWk+tQdUdEGN45x92lT0Wk/kpxbA7Yw7UUjDB1bOoMOhvdp75pc0ut99e/cwjKVAOkJhNl0zbJYBLef4T3Ze5HJ6+/TMdWWSqIRx4r92P4d0b9zS2uVnM4u9GUxby2pzmy8uy4Rqo+UPAH6Cbll0r2dMWi/0OqgG6/POrxraOM458ZGvOmOp9lw8P5O943HLxhi+1yqaKTkv2MRZgkrggsyXETo5oV/nTdYe67XM5IFGPG3GHd1miz5/aka+XSd1cUcVhJhDsGbTHs5IixVnxgcW5bH0LGFMRGNO6U/Zt96IgBgWK+2tvPdJtJohFmDeISxQNqRoJP+L4+uwCPnHgZA35gjLGXakyc/IDuBsyTiXBl44fVOerZvhqj1fPTnqFEb5SVRTLnxWFxwVAUA2DRSL1w6DFeN7m07vywWDexsrgoRV47ujQV3nmzzCxEmSLkTt3HRSAKpSbyzJNAM7233G7vh5P64anRwU4tOkOVIDVINPjnFhvRo6/qd17tVB8V0TJTqZP3qr44KPClnO2Cq15Y1AG7IWr+SqFObLNq1WACko5FijHlmSRdCTv/OLfDur0cAAIb3aReo30YjDDeNMbRlgHv0rqwZ8Bs3xVZKI/u29zVxpoPufh44e1BoJswk54hGGDp4BLLc/aOBoVxLoFuIqM9XdrsA7JqVaITZNP5/OesQz/rLqP5rur7cVpmrhLbLy2JrM+2Zc5hYzOl2x5DvVw0iEv7EQ3q0QaeW/vcl+pVOe0kaqRwRVtSeaDiq5qZVkxJMvfFY3PuTQ2zH1cYpkAdwhmCOmlEWTJi69vi+GNzdmBB21Tbgk+tG4ZZTB1jfxyIR63mceGAnrLxvbOoaWUxMhq06vOYjnpGwPqoro36d7L486uAr3hXnxkR/ykC7o35ZSSSwRkJ9LCUR5sgXpdM8tPOIkBPXHndKf0tj1qV1E/z7/MHWe/BLpqqiqwPnPGXa8wj1/tOPD/bUOnkJ+1cfaxf20smlpb6DJiVRnONjMhdkuz5Sf/7Kr4a5+ogJxAIKMAZz9ZmJdlgaMwWqWHqV9Jq4xLWiEYaDu7bCorvG4PgBnQL12wgzFgD9O7fEl+OOw1MXHeE458YxB+Cwbm2sz34Tkth3tEV5LLCQE2SxJSbJy4/pZTseVPPml1dLPGKvgBV1vMnWf1H0zctGpnydHONKzFsjJSe6jTBm3YdftK8qzOv6uapFfuDsQbjm+L5aTZpAHhNSGinj/wM1iWXl+au98uyFP3EsyvD1H06wrtujnd4EK4rSCd2kkcoR6nP99PejMirHkoI1Hbpb26YOHyE3jdSyTbvBzGE8EgHaNHMKUl8rPixBfUkiEWY5/sYiEfTp2ByXSQNSNJLymVHzRWWjkYpF3TVrqjbIC7FiFp1B1FGdnJuURnFERWrQVzuP6NDi9+orK4tFAz9Tpky5uslONzi5CdJAamuh8pKoZS6KMGDMwC6WeVIVsJ/6pd0UABiTo0A3gCR5ahLw2ndRvHu3FGJuQtaKe091RGCmI1CrQkAkAhzdu32gJJOZ+FeNPy3l46QuTMpiUa0G6fMbRlt/d5RWyyXRiM28BaTuR4wRJWku4tTnf/1JqQAOMbmLawgNeZB+K9/r/q2bOAJNAOCq0X1sbchPQOvaxjARDe/T3nex+vwlQzF3/ElYdNcY37oKoUwNrglyn2MP6eKr0RTPWAhSh3RthYuGV9jOUYW2Zy85Eqce3BlB+Nd5g/Hnsw6xJY0U/UduX8ZYLWm1oxGbQKoKVXKiW7l6foKDGvmsC4JqUWY/1rFlOa47sZ/r5u4AbKZG9f7KYhHc82N3rZ6qkRJac3HPorn2dskXJfJ/6QT4osgj1RhRB8x0BzeBUCPu11qvFi9XBAk3Hyl54mFgaN3EeZ7a0IKa9qIRI5fRH8cOwLOXHOn4PhZl+Pu5h+HK0b1xYJeWym+N+7s0gwiRWMS5Ohdcf1IwP5+mpVH072zUKapopFTH+PJYBC9ffpT1WR30SyWNlO778jQ0Uiq6hKW6CViY9kb2be9YWYk9vkpjzBKqhGBw3tAemHrjsTi4q301eFx/ZzZf+dnqUkVwzi1BSucrJhDPR9zZIMXM5fZude1SjaJpURZznQRVYUh8DhIF5juBxCJ47zcjbMdOH7SfZTrQRXSq7eSf5w22BTbI91aq0UiJ3+smziCopj3ZtCsmG4dJsru/SVJ9UkE0LH6C1GHd2+DzG0bj50d29z13RN/2aNW0JNA4JoQyVSOm+ghp4e57uKWSXRrPuIOpXezXqQVuO/0gWxtVNVKGS0Swd3lEz7b46ZBueOwXqYWPzhQVZQyv/io1hnn5SDHGbP6XEcas9uv37IVv3eDurfHcJUdqg6RUjZR4Fl77vcoacPG3XBcv/0A1n50w7akC7JE97e4G5w3tjll/PMHy99S9EzLt5YlMbe2icfVxkZJbNS3BFaNSGoLSWAQXD++JB386yDo2Z/yJuPf/DrYmccZgW5UI1M4Rjeg3MXzh0qH288yCLx3ZSyvNRyMM+7VugpvG9HdMROL+3FIOeCFHA6qTi9uEN/e2k/D8JUOt5yN3WtE/xMSi7onVpNQe4aR2Hisy0fy9Y1BOw0dKJeGzXYJAaJQ6tCizDZj9O7dA51bGar40Gk1pzaQ6dgsYVSQ/2t4dmuNoxc8qyY138+KlQ/HCpcNcy1H7RElEfV7B24SXkz0Ay78HcApiYqUZD5Dzyk8jFWUMAxXTRGksZdpu0Ahr6gR66sHuuduMABC9ICW0cuma9tSmJfedlpYgZT+nS6smtvalQ31WQbSGfoIqgxE9y5iqs81c6w+k2qI6BgYNkdeNpwDwf4cbiY9VjZRuseUYfxkLrLHXLdRFMylVNE79OrXA8D5GnzXySDmFE4FbKgK/au3fpgn+evYgPH7BEIzs20EbUacK1mIR2Mn04XxRmWdEfVN/mxYWqZ15uQo0L4vhilG9LVO6pZES86J53uE92uDEA1MLyHt+fDDaNS+zFlo6Z3gy7eUJddIIGgYtdrmXI3dUzhuacuCOMIbxpx+Io3unVNStm5baTGCMOfNg6HCbNIb3aY/XrkgNon6LJi9pXTRAdRINSttmpXjsF4fjCSka5XQPNXurJiUY0bc9jqhwOjmrPlKqI7Wq/VPvWzxTsaJXO1d5SSRw2JZ6ms78pdM8iHxKdfEkOrUsRy9zb787zxwo/Y5ZpsJMHrssiEQizOGcLlatR/dp7+kToj5vdSJJJ9Fop5bl9tB55b5kk6V6z3VxQ5gOpJHyeV66lXpZLIJnLjoCV4zqrfVNdFvd65qK3kfKHr0kixiDuvon3vXankk4guvamt+zUOvPGMOPD9sffz7rEP0P4L+yl79WT3UzyQRBCCzqu3CLCpYd5zk4urZpirtMZ/FyjflJPONupmly/U4jKaf8XFWhiTHvBfjE3x1j/a2Lfhb+iU0kIUY8s4QkFNg0OkrbytRPi3NDiBRWDt1cIl/rjSuPsvJs/e7EvvjPBUNwtCaYQHYVEOOr/Nh0iy/h5sEYw7hT+mNwD8M9Q7Rth6mfMfznAqdLg1hokbN5AVFXDG5CipprRGxY27WNu7ZAnrDFn16DXNDJM8KY67wvCyJ+jchTDWz5E3mX8ZiUs0nl5IM623yDZG1c++aluPb4vnj+EvvqRrcNjDWxm5/PGLSfLRWAU5vm1AysvG8srjneyOqdjUZKPU+3Y7xu9SX8uupMp1ybkMKFjT9iCTvZJghlcL7foGkSLR8p8xdqVdIZxMtKIujVXppIlUqUxBhuOPkAvHL5MKu+Q00VvvDfCLIHmt/z0n1dGo2gb6cWGHdKf/ztnENtucAA98CUebedhG9vP8l+Hx5Re2ICl9vKw+cc5llfwNvZXAh+uiAGvz6re1YP/exQ190SDtqvpa/JiHl8kjn2gPQ2pS/RmIkAoImLFm1Yr3a4UMpjBgD9zMWu7CxtJek1P4sF8cot1Y7rqSYmQ5ByXv+4/h3x3m9GoK8U/KLTXK01N7fv2T41d4jrCdN+SSyimBft1/u95C/Hubs/I2Boch76mTH2qqepTfx3JxjljjmoMx786SAcLkXvlsWiNo2QzG5pP1SrfWk0Up1bluPhnxlbgt04pr8twEncb0vFR0qUIzfbbm1TaRuEYKpb9JNGKocIJ2bAubLQmWoAu5MpkFole6/s5b8VPaUGecXqFqEA2BvH2EO6YNrNx2HCNSMc5/kNfl6rKjGI+65EPb9NNf6yWMQaDF68dCgmXDMSvzuxH0YoTqQ6lbU1yJjvpjQW8UwFkI52Yowp7Hn9ZkiPNpbaWTU/6bQGekHKuC+hZZHrIp51LMKs9pdtcGmEMcf7DboBtdpu1ASLaQlSsajnsy2JRnD1sX0wtFc7q4/cdEp/vPvrEVY0ZjCNVHqLhvt+crCtHx20Xyv84+f2/Dlug3CL8hJHrhvGmMP8ojqCi+ffrllpIPOo1/sS129S4nwX8rNQhUOjrvoydc9w4Z1j8L+rhvuasmzRxx6nPn2R01fTC/EMneZIF809A47saZjHxOMT/VGOfFX9JnubgtQ68+bDgQAAIABJREFUM7u5bCaS+9FlI3uib8cW1qR91uFdca25QBtzUGeH+Vg3Bq/evse4pqSpE+Os6P8lkYinRqp101L82MwOnkhyK2nxgZotxiJM1jLb25Q6nl1rbiH1718cjp8MDr7vq7ydmKi2fC0x9vfu2Aw/cslqLu5XLKAsZ3PlvAV3noyJv0uZi8X5uoCeRiBHoWi3EZdXyKqkr8t5Abg7eAcxkRi/dx5TyxYvfcGdJyPCGJ6btsoWnZEq1/65S6sm6NLKmVjNz5nTbXDs1b6ZFOHmt9JPf/WrUw0HKeOIHm2xfHO1w/cn7TpJ9/RvU6N2zfF98cunZ2rPP3tIV6zbUYtFG3ZZnTrCDGFTb9pLlX/CgE74ZOFGS0BMaaRMLVSE2TQ/ovllmyBUzhEm8JKjItK11cG/qsYuSDUtSydrfcSzDckaYXHLpdGIbUK6anRvLFhfhbmrd7iWo7vEGYP2wztz1wFwLgiO6OmeJ0uQbuSqW/oDNWqUI5jGUecAP7h7a7RtVmb5jzQpdQpkcsm6MtyurKuTaLe+vpJZTliM6dun0PyoQqWbIMrg1Nbvb5rtTh7YGXPX7LT9XjyfluUluPCoHjjB1LjI2ki5jd4y1oj0FElsh/Zsi7OHdMNx/TviEI25VteGenVohvlrq2zWDNFHZH8fL40UkOovSc4x+oCO+OS6UZi3ZgemLNnseCZu7S1bzTdgPMuTDuyEu95bACDV14TWtFvbppZ52yuNi7hHN2dz0QTUqO0LjuqBslgE55ibPFf+8QRMXrQJN7w+j7aIySW21YbyoN00Um54OdPKbTRiCUvuL1Z81bQ0hvKSKC47phd+MayH47wIYzisu2FPPvvw4KsGXTkqC+8cgw9+O1Ka0L3L8GummXTUCdeMwJQbjpXKMP4/smdbfHfHyRh9QMe0y5TRDW6jD+iIw3u00ZxtdGjnFjpOc41A1kz86/zBmH/HyZZzrNBIpXyhmDVAMDArt8whHjlbgsCY0zTlnVAvJRxZg495vqqRSsfvwC9Dty1026WPdGvbFG9fPdzzOhXtmzmO3TJ2gOWv4hZM4cV1J/ZDL025bgxwRL7aNVJyW5Hv+/9cVv5JzZzz5lXD8cSFQ1BjCuQ6p2t5DNMNZ26Crafm0Ne0Jy0aNd+7JVYUr/oOTVb6N6862rquqpV0czbXVbNji3J8e/tJuFIJ/gHspq47zhxo7VDg5WwOGHmt7vvJwda7G9SttXbxozv2zEVH4u2rh9vKFW1eLOTVPFI6wVH1ZezTsbntfcc05TvL0B5Oi8V3n2ILiBH3PLh7G/zngiEYd0p/yyfUS8sl7tfhbO5Tx5JoBOcP62EJ3e2bl1m5qcLM9J8pRauRkhu32kluGtMfM1dsw5odNZixYptvWW57QQH2xpuaJDT10dTLC8aM/C+yfTkdSqIMDQmu9QERK9CgvjoDpGRr+7dugscvsPtMZdJRD9pPrx6PROyOzq2blmDHnoa0y3e7J7eqMsCKrNuvdRMs3rjLmAgTesFbfo8lUcOkmTLtmRoppHKfyELryL4dMn6v9jpofKQ8FgllJRHUmHliShT/kTMP3Q9Pf7nS9bcz/nC89VuVWDTimctFNtHI7zkd/nvxkdps2hGWiqRThb8gAv7A/Vth0vWjUTFuQqB69OvUArP+eAIOv/sT2zXLFDMS59x2/VtPG4A3Zq8BYCRD7d/FMGl6ZTYXiXZH9XMuKrifIJWBdsJrnANUZ3Pjw5AebfCQ6Q/z/jUjsbGqzvG7KGOIc46fDumGUwZ2wRH3fGJ9N7h7G8uspvrJuZn25HrI966aYq0UHy6PWF5sCz+0AyTfp5JoBOcou0EEpX3zMocvqGXaMweD0mjEMY6opNY7+puIRhjiSW6OBea5yqnOGMvskc2IwqeqrHnUd1wTgl8r09ncKfAHV3JY6SAKr5AqXo2UjCq8dGhehgd/dqjvJpBjD+7iadYD7IN3ykVKt2oR3wUjW3WsGES89tMTHdo3nLZ1Ezz9SyMzcseWZQ4hKIygCTdNxRc3HYc5409Mu7x0orEAo/uec0Q3PHnhEPzzfMOP5iwlfNoPIaAK1bacL0pon4JktQ+KzkfKq67yild9zgP3a2UbBGWn/yk3HIuOLcsdG0fLqH1MTIJL7j7FNkGI09KNtBnVr4P2nUYjTPKxsX8X1hYjKu2kCVJMBCLCTBa67WND6u+fD+2Owaa22UuDOLRXO8y/42SHjyEAyNkidJNsJ83eikY93K/n97yY5u9WTUosTUW75mXaDNe3jDV2WiiJRrRjjVjsxRX1nGhDfxw7AL8/MeV4zQKKBlFpstd+b1bm7h8NRL9OLbDorjF49zdOP9SwEIsHYcJ0y4Vn+43QYrm0EzmhpWhjanvIheVLlJmudUe8a+FsLgQrUcV0ikso+fgKSVYaKcbYXwCcDqAewDIAF3HO3Z0cGgniXfnZVv/hsrGjjM5HimnEUy//KX25gU5zpSQSQS2SnuYN2fTkhojy8RIERQfOpj27mSIyDQF2m6i9huBIhOH4AcbqauV9Y1HbkEB9PGnLNu2FsOur2YFjEYY7zjwI5w7tHjhfVBAizOkX4eW8LJv2xKQpJhn1cQnhp0e7plZotF9dZN648mhMXLDBmWMs5EEvKplN1TaUT9+JMo2fj11brf+dlwYRcG//sglRLeKvZw9yZAkXeGnE/RIX634aZN67aHhPXDS8JwD9+7//rEPw8MQlGNrT7hd5/ICOeOarlRjcow2mLduqrYeXRk8sIt3OEG1cCLVB0tJkg2iP4t2pY7MuRxKzBCkXYVCMvWCOpMZqGZly708OdhxL7USRXlkV7Zti/9ZNHM7m157QD5f+dyb6+WzZJGMpAhqBj1S2pr2JAG7mnMcZY/cDuBnATdlXKxwq2jXFmYc6oweCZogNAgvg/2E7P+Al/SacAzq1wOKNu1y/j2oSpqkkrUlUf84lI3riVnOLDU8fGJcOnA5iDMmmDBnXOSGNCa28JIo/nzVIc7aelI+U3dk8GjFyhwXZJDcddK/ES5CSc+yIaDlxtlrWeUO7Y1NVrW1LGpWbxvTHpEUbATgF1wM6t8ABmkEx05WszLlHdsNLM1Yb5Unpwdq5mFLygXDUFkoVDvvY4DbWpDsRpX4nCVLS8WxMxv4aKeei0U8QVNGNI/u3boK/nG30s18d0wudzTxRI/t2wKK7xqC8JIrpy+2ClNervf//DsZb36xzFSwEx/XviEUbdnlu7RQm4t7dBAC9Rsr4Xw6Qkm/HWqBH3E2Z2U5z6mb38nWDRgkLzjx0f5x56P7gXJgjjYJG9euApfecmlZZbgJpIcjKtMc5/5hzLrxUpwPI3Cs6B3x2w7H43YlObcIhXY0JTTe4XTGqN8piEdseXV7ofKS0Whux157HCPDeb0ZY6fz9pOzXrzwKU2881vX71F5q7g09lWFb/738U29ByqOiAVEHmWxxNe0pn4UjadCreuXIUU17osx0V0yP/vww/P1cIwfR9JuPdz2PMeez97qPe39yMA7t1hqL7x7jMDGK9vn1H47HjFuOR3lJFDefOsBzQ+IrR/fGa1ccbdUlCCmH22Dn65A3C49GGLq1bYo7zjgIjyv5zsLavDwIJRqNVFQzNqhkOonbNVLh9BlVI3J8f7tvlnwLYgwVmqag6LT1MjefOsBWpl5LlKqI7tZ/dkR3vHT5MMkspn8+vz/pAEy7+ThLcMs11hhn+fYogpQu2aRG8yO/bxEVKEcyOkx7ORA0olY/zqztMdO3MZvFTtCo83wQprP5xQBeCbG8nCCv2HSD27hT+mPcKf0Dl2fPI+VeroXHVwP3b2Xth+fXNnR5bmSG9WqH9+at90zbr9uq5MPfjsTjU5bjzdlrbR1S1EenvQrDXMOUQSZbXJ3NmfdnP7xy5AiNlIgu8xNU3TjtkFR2eK9B3kjaai/cO2lfW7zlExnn5lvjR+ANoV38ODJFXPfCoysc33n5B4aNEEKEgMO53uyvcvsZB+Gw7q1N5+TgQtWwXu3QqkkJdtY0hKbFVQXPJ395hM0JX76HDi3KMtJ+ZTpWyNowww/Lv5yyWAQty2OWj5ZKNMK0KWVyhWraS89HSqcxj+C6E/vh0mcrtYEnqTIyq++fzzrE8mVyr1dmZQNAl1blvj7IXujmr0LhK0gxxj4BoNsG+xbO+dvmObcAiAN4waOcywFcDgDdu2cWCRE2YZj27IOlqZHSFBvURyqI31IQHjh7EK4a3Qetm7oPzta1pOfQv3NLHLRfK0OQkjpJtnZ2P1IRJ7nVSA3q1hrTl2siNUO4bGksgucuOdKxOXQuomaMcp3TSbrPL6xJOGhfSpkqcn9dt9Xu+cO6Y0gP/xxTghtOPgBVNd6Ro0KbIGuK5Mu71aV5WQznDXWmP/GjNBbBgz8dhEv+WxmSSBrEOT+M8TKz34nHN7Jve5w/tLu168T5mtQx1rUiDPNuPzmzC2bIVaN747VZa7TfiTZwdO92eLVyjbWlFGDsx+mdRyp1TPw59uD9rHfGJH/JsHykfjrEudmxs16Zt753rh7hup9gEDqYpvy+Hlu45QtfQYpzfoLX94yxCwGcBuB47jGKc84fB/A4AAwZMiSsvh+YQd1aW9tSCELxkdJopDJUSAEwshQ/P30VLhmRnspcpbwkqo2gkeEuGhNdHa17030nRY5kSmq15n3eK5cPw7LN1f7luVTmhpMOwCkDu+BH//gSQBhTgx2RowZIDWjZyqD/Pv9wXPH8LMfxCGPWiu6sw7vi9VlrMl4hZlvHoF3piIq2+G5dletGs+niZRpw6993/8jpPOvF1ce6Z9gXiElQzoWkyyEUJmFMZjK6iVwmTBN+pgzo0hKMMXRqWR5KCpGwuXFMf9w4Rm/REGbNu340EFdKi9y5409CWUlE6+vjlq0cMBOc6s5Vz0vvFgIRhl9sqyzHgKP7tMeLlw7F0F7eyZvzQbZRe2NgOJeP4pzvCadKuUGX7C8MZ1SdH0QQx2w32jcvw8TrRmVdryD8+LCueGnGagzv3R6fXT/ax0k+Pz5SfpPC0F7tAnUcN7t5LBrRbiYblqlJxsodlWU5YwbqFMLGM2tWFsPK+8Zi4foqU5BK7z6EQOOW/DAoQf0Ubhk7AOce6R69+P41I1EaYzjhwSlZXzcdJ9SLh/fEfq0z95Xp2qYJRvRpjwuPrsBlz1YadQtg2ssGoekMz7SXqqRu8/Ew7iHTMsTPwtJYh8GVo3tj0fqqwOenco5F0VNKAuslUIgkpzafRvkRWBYM6dk6nM1z4COlmCkLRbo7aOSKbH2kHgVQBmCiOdFO55xfkXWt8kQYGik5iZ2XIMWsc7K+ZGgc2bOtdlWXbkROGB01qCAVBrJQeNbhXfHarDUYloNVzUH7tcTnSzbb0g6Eiey4mwouSK+Mcaf0R+8OzV03Kg1K0DZQEo1oo/kEflrUdEjHCXX86cGCS9yIRSN4/tKh2LGnHoBIyJn6PiemcdFPAZx4YCdMXLAxq+LksUwEO9gvF64rRDqkxqSsqxAaN7lontzIZL65eHhPtG9ehh9J0efWdlMwxvDB3Vvj5lMGpNqeI49U+G3PMtE3phdSQLISpDjn/jrvRkzY3v6ivXqW2ogEKTdcFjbGdx7+X9mgC/PNB0N7tcuZieDRnx+Ghet3Za3CdkN+7KnQ5/SeX9PSmNZRO13krtQmxHDywd1bp53Z/uLhPfHUlytCq4OO+35yMBZqtBEty0sw9uAuuPDoipz7Fcpmn8fOPzzrSU0XNXZERRvMXLkdQLiJd9PF0r5lX4WCkcm9x6IRx5YrwgRbXhJFs7IY3rzKsLa47dIhX/agkBYqqfxWoRS311O0W8QEIez8E1b6A12xAcx+jQXdBOA1QYeyUhWq4iLqmC3KS3BkgI1zM0VuSyLiqlADm1yXFy8bGlq5YpJIh/GnH5i1hskPt61DIhFmS+Q75qDOOHtIbrLCyL0uEmGIBOyHFxzVA0dpNLA6Z/PXrjgaT3+5Ane8uyCUNWBj0sjnm7Du/fRB++H7TbtxhZLjzU1rZ+ublw4LpQ6ZLtyKlX1akBrVrwOenbYqtPK8UgQw5f/GjNjrTo4qsRI3au4gjAEi27wkOm47/UAcUZE7QabQyANkKotzYQY2IQi3b15m2/F+X+ffSm6rMMnU3HXnmQO1x90Wlqmgiew7eqZlNEbTXlDEfqFhZdoviUa0Du1ulgSR1aJ105LQtONk2rOzTwtSxw/ohIV3jsGA8R+GUl6QjOaNIXmYHz8+bH/s2FOvDy3WVD8UHykr8Vx4HTPdZIF7G7rw+sJppMRfNLDmC7GoCavPuAk5jeGNjj2kCx6d/D1+PrRxpM5Jh/9dNRzTlm0NLERmuwOCqiXKRfoVMu3Z2acFKQBZ5bFQCdJPGr8YZahtLx3Zy3bMa6wOQ5ASUSlhvo9ix5Z6w2Xn93yRz+1YCIN8aWnc9mPMJ11aNcGc8ScVrgJZ0LN9M1uUnhfL/nRqxnOE2/uJhNhOvrn1RCQ5x+46Y0OTMw91Rnfui+zzglSYeK04LNPeXj7faN2/QtiJ47KRvVAajWj3dSL06LYnKpjPwl7ervPBjWMOwJEhmppTppz8vPNcJZYlUmRn/tM75LMQxwYRSNKueWaZ7YuV/G1G1YjZr1U5urvktQnCsxcfibMPD+ZQWowm5TCG19JYBJcd08s3KeC+iuyvJmCavwvls0CTrD9Xje6DIWEKUnkyr4zqZySZPW1Ql9xeiMgKXRZ0QNJI5bc6+xSkkQLwlcfGsEE4pl8HHNPPfTNbIPdbrOQar1VvarPmvfseGzNfjTvO2gxZIGukSsx9unq0C2ZCCJtCObnvyxzStRV6tm+Wdj6jdOnbqQVpH/YC3EZfa5ygLpozSJDKM3t7W85VHinCG90G1fJzb1legicuGILBPdrksVZEIWlWFsPk60cXuhpEY0PRSu8NKXf2dkiQyhN7fVPe2yXAIkTVcp6QZXbybMi3NnLy9aOxqao2r9ckiMaM5QvlOA7tcSI8yCElhxxR4dQO7O0+UroJUxwrL6HmtK/SumkJ9mtV7pqjKGx6tm/WKDYrJdLn6N703nKBFXygzDGkkMo9pJHKEZV/PAHNy1KPt5gbc5PSKG44+QCcfFDhNCJEYSmJRrL2NST2DV68bBgqxk0odDWKDvf0B5SFPNeQIJUj2jcv0x7fWxtz51blAOC6ue/Vx+7V2y4SBAHg7h8NRNsQ90p045/nDUbvDs1zfp19CTFGn3qwPboy4mLyI8KDBKk8sbdvutmrQ3NMueFYdG3TpNBVCY3WOdpMmCD2VrS7GeQAdbInsqdji3J8d8fJaKokNQ4zISehhwSpfFEEjbl7u+LZQ23mLSegjHy6CIIoIpqVafLNFbNfSSOBBKk8QU25cdGhhd70ShAEUUykEnLuxav4Rk4oS3LG2PWMMc4Yax9GecUMNWaCIAgiX6SczQtckSIma0GKMdYNwIkAfsi+OsULaVcJgiCIfENzT+4JQyP1EIAbsff6UecXekoEQRBEnnBL1EmER1aCFGPsDABrOedzQ6pP0UL70BEEQRD5JmJl6ixoNYoaX2dzxtgnADprvroFwB8AnBTkQoyxywFcDgDdu3dPo4rFBbVlgiAIIl+k8kjR7JMrfDVSnPMTOOcD1X8AlgPoCWAuY2wlgK4AZjPGdEIXOOePc86HcM6HdOjQIcx72Cu4ccwBqGjXFIO6tS50VQiCIIh9BNq0OPdknP6Ac/4tgI7isylMDeGcbwmhXkXHYd3b4LMbji10NQiCIIh9CFYEOQwbO5SRkCAIgiCKFNoiJveElpCTc14RVlkEQRAEQWQPWfZyD2U2Jwii0fHGlUcVugoEURRYQXtk28sZJEgRBNHoOLxH20JXgSCKgmiEYUCXlrhydO9CV6VoIUGKIPYyXrl8GFZsqS50NQiC2AtgjOGDa0cWuhpFDQlSBLGXMbRXOwzt1a7Q1SAIgiBAUXsEQRAEQRAZQ4IUQRAEQRBEhpAgRRAEQRAEkSEkSBEEQRAEQWQIK0RuCcbYZgCrcnyZ9gBou5rGB72Xxge9k8YJvZfGCb2Xxkc+3kkPzrl2o+CCCFL5gDFWyTkfUuh6EHbovTQ+6J00Tui9NE7ovTQ+Cv1OyLRHEARBEASRISRIEQRBEARBZEgxC1KPF7oChBZ6L40PeieNE3ovjRN6L42Pgr6TovWRIgiCIAiCyDXFrJEiCIIgCILIKUUpSDHGxjDGFjPGvmeMjSt0ffYVGGPdGGOTGWMLGWPfMcauNY+3ZYxNZIwtNf9vYx5njLFHzPc0jzE2uLB3ULwwxqKMsW8YY++Zn3syxr4238krjLFS83iZ+fl78/uKQta7mGGMtWaMvc4YW2T2maOorxQextjvzPFrPmPsJcZYOfWX/MMYe4oxtokxNl86lnb/YIxdaJ6/lDF2YS7qWnSCFGMsCuAfAE4BcCCAcxljBxa2VvsMcQC/55wPADAMwNXmsx8H4FPOeV8An5qfAeMd9TX/XQ7gX/mv8j7DtQAWSp/vB/CQ+U62A7jEPH4JgO2c8z4AHjLPI3LD3wB8yDnvD2AQjPdDfaWAMMb2B3ANgCGc84EAogDOAfWXQvAMgDHKsbT6B2OsLYDbAAwFcCSA24TwFSZFJ0jBeFjfc86Xc87rAbwM4MwC12mfgHO+nnM+2/x7F4yJYX8Yz/+/5mn/BfAj8+8zATzLDaYDaM0Y65Lnahc9jLGuAMYCeML8zAAcB+B18xT1nYh39TqA483ziRBhjLUEcAyAJwGAc17POd8B6iuNgRiAJoyxGICmANaD+kve4ZxPAbBNOZxu/zgZwETO+TbO+XYAE+EUzrKmGAWp/QGslj6vMY8RecRUcR8G4GsAnTjn6wFD2ALQ0TyN3lV+eBjAjQCS5ud2AHZwzuPmZ/m5W+/E/H6neT4RLr0AbAbwtGlyfYIx1gzUVwoK53wtgAcA/ABDgNoJYBaovzQW0u0feek3xShI6VYDFJqYRxhjzQG8AeC3nPMqr1M1x+hdhQhj7DQAmzjns+TDmlN5gO+I8IgBGAzgX5zzwwBUI2Wm0EHvJQ+YZp8zAfQEsB+AZjDMRirUXxoXbu8hL++nGAWpNQC6SZ+7AlhXoLrsczDGSmAIUS9wzt80D28UZgjz/03mcXpXuWc4gDMYYythmLmPg6Gham2aLgD7c7feifl9KzjV60T2rAGwhnP+tfn5dRiCFfWVwnICgBWc882c8wYAbwI4GtRfGgvp9o+89JtiFKRmAuhrRlmUwnAUfKfAddonMH0DngSwkHP+oPTVOwBEtMSFAN6Wjl9gRlwMA7BTqG2JcOCc38w578o5r4DRFyZxzs8DMBnAWeZp6jsR7+os83xaYYcM53wDgNWMsQPMQ8cDWADqK4XmBwDDGGNNzfFMvBfqL42DdPvHRwBOYoy1MbWNJ5nHwoVzXnT/AJwKYAmAZQBuKXR99pV/AEbAUJvOAzDH/HcqDJ+BTwEsNf9va57PYERYLgPwLYxImYLfR7H+AzAawHvm370AzADwPYDXAJSZx8vNz9+b3/cqdL2L9R+AQwFUmv3lLQBtqK8U/h+AOwAsAjAfwHMAyqi/FOQ9vATDT60Bhmbpkkz6B4CLzffzPYCLclFXymxOEARBEASRIcVo2iMIgiAIgsgLJEgRBEEQBEFkCAlSBEEQBEEQGUKCFEEQBEEQRIaQIEUQBEEQBJEhJEgRBEEQBEFkCAlSBEEQBEEQGUKCFEEQBEEQRIbE/E8Jn/bt2/OKiopCXJogCIIgCCItZs2atYVz3kH3XUEEqYqKClRWVhbi0gRBEARBEGnBGFvl9h2Z9giCIAiCIDKEBCmCIAiCIIgMIUGKIAiCIAgiQ0iQIgiiKIgnkjjz0S8wefGmQleFIIh9iNAEKcZYlDH2DWPsvbDKJAiCCMq2PfWYu2Ynrn91bqGrQhDEPkSYGqlrASwMsTyCIIjA1DUkAQDRCCtwTQiC2JcIRZBijHUFMBbAE2GURxAEkS67auMAgBgJUgRB5JGwNFIPA7gRQDKk8giCINKiut4QpCIkSBEEkUeyFqQYY6cB2MQ5n+Vz3uWMsUrGWOXmzZuzvSxBEISN3aSRIgiiAIShkRoO4AzG2EoALwM4jjH2vHoS5/xxzvkQzvmQDh20WdYJgiAyZlcdaaQIgsg/WQtSnPObOeddOecVAM4BMIlzfn7WNSMIgkiD6jrSSBEEkX8ojxRBEEWBMO1FIzSsNUYqxk3ArW/Ntx1bu6MG49+ej3iC3GuJvZdQRxzO+Wec89PCLJMgCCIIu4VpjxRSjZbnptv3fZ2yZDOenbYKa7bXFKhGBJE9tHQjCKIo2GNG7dXFSbuxt1BTnwAA1JNGitiLIUGKIIiioCHBAaQmZ6LxwDnXHq9pMAUpEn4bPckkx1vfrEUiqX+X+zIkSBEEURQ0mFqN2gYSpBobbnOveFekRWz8vDF7DX77yhw89cWKQlel0UGCFEEQRUHc1EjtIY1Uo8NNiyG0h3VxemeNne176gEAG6pqC1yTxgcJUgRB2NhYVYtT/zYVG3bmfsD8dOFGVIybgDXb92RdVtycrMnfpvHhJkjt2QdMe/d9sAgV4ya4mjf3FiLMiOJI7uX3kQtIkMoBf/jft5i8eFOgc2sbEnt9ByOKi5dm/IAF66vw4owfcn6tVytXAwDmr63Kuqx40piME0lOfhyNjITLGFdbX/yC1ONTlgHY+wV8sRl4MoO+9cXSLfj9q3PDrlKjgQSpHPDi1z/goqdn+p63aEMV+t/6YVE3MGIvJg8CvphboiHkLBCmPSDlL0U0DlxNew17V9RebUMibR+8WNSYZmvr9457dEP0UTeh2Ivzn/wab8xe46o06POH93Hdq//P3neHy00d7b8qW251r9jYxsY2BmzAdBMIvZPfF0gghSQk+QikQHogfPkIJAQCqUCjVUdNAAAgAElEQVQKJfUjgRBKKKaZEjAdA6a4F4x79+1ldyX9/pDmaM7RkVZ779q+dpjn4cF3VysdSefMmXnnnZm5vRrfzpQPDKkqSyXo0qqtfu2UWQs2bK/h7DBp7ih+UFSvh1Ioub1+dg/MXYP//uucKo1oxwmFCawqaCJuPH1gSPUtKWdIdRd3jfd19PXPYPIPHqvoN5nAAOncxZMgKLTXm6VVdPTzoOR6uO+NNT0/8U6WDwypKkupAtjTCUIRNEF3VekqOph29RP48cwFAIBF61vR0lWs2vk9z8NDb63dpbOxZlz3NK5/bKH2u4n/8yg+8psXenX+S++ai1nzdz2DnDbYaqwBvlnHKewPZOcIfzfc2dzV6khtbO2u+DeESO3qhlRvQnskFH7vjTwxbz0emNu3jK4PDKkqixrrX7W1Az9+eL528u0uyn5ToFyemLceAHDyr57Dp257pWrnf23FNnztzjdxTWCo7YqypqkTv/33stjv563tPUdoVxRCpKphSBXZGtsdODee5+02/EluSHUx9KnrP4BsTr0fd/X6ZhR970loj6Qae96F//c6Lr2rb4UBPzCkqixqSOHr/5iL259/D++saY4cWy1C7MaWrp0aytjU5htSg+pzQvHr7renQsp2+ea2qp2zr0i1lWslc2pdcye++Y+5kdRzAzsOIaXx9kY5k5R2s9DeEdc+jWNu+PfOHkZVhL/fIkMlOnYhsnlPjVrb2j1Ce7SkeoVI7QbrUicfGFJVFlUhUKhPF/KrJAwYJ11FB4f+5Clcft87vT5XT2VjUFdkYF22KvekSj5jAZA92V1JkhTwmqbq9hirxIC48oF5uO/NNXhmoT7DdEdgIWRIFauwkXKy+a4SKkqS9S1dWLm192Uh+oI47N3wjVhwpHaBOlI9rU+WIbL5Lm5IkW6pNiK1O6CuHxhSVRZVgQfOiLb2BlnnvZlIVBH48XfX9/gcvRXiDQyqy1a0kZ/8y+fwtTvfLHscPZ9dFRpPgrPXJhhSnufhucWbxMbjeR5ue245mjvj+Wfbw5DdnkLrohrj5vyLnYVIbWjpwotLN++Ua/dl4ZuvHObre4hU3Pra0lbo0fnIkNpV9ReJMKR6sVZ163J3KFXygSHVS7l7ziqc8qvnxN+kEIiYR/8vaTbTkkLAfGrBhophUzExdyJffWOLb0g11mQqioEv2tCKh95aW/Y4OmfXLuC16iQJHWnv9hvt6rL/n1qwEZ/546u4/fnlAIAXl23BNY8swJUPvBt7vkqQnb6Q4yAQqSoYPnw9FUs7RzmfedPz+OTt1eMH9kXZ2NqFsZfNxEvLtqT+Dd8sHQ3ZvLuPIIgPv70W0656Au9qqAlU2btSsXeTrD1aX70pyLm9IjM7Wz4wpHop373nbSxc38o2BErnlg0pDl1vay/gmpnzJaj3n3NW4wt/mYN/vr6qouv3BU+uveAbA57nbZcYeMHZMSnSa5o6sa5ZRoiufWRBKtQsSboTFGionKLfEfds+aZ2/zzBHGpKQKSKVciK2ZGirpveSNHxkLV9lUZzZkcLobO9DVf0hoeyveXNlU0AgD9U0HONG1I0RT3P63NNi99437+3F5dFUUVu7FfyfnaXrL1SFRAp3f6QxonqKJRw7aML+mx4tNeGlGEYow3DeMYwjAWGYcwzDOPSagxsV5OOwJgQiJQhG1Ic1v3RzPm4bfZ7eJSF44gLQehOWukLCoi4SyXXS70hVrLRFAJ0Ic0i2tpewAs9DK3MuO5pHHHt09Jntzy3PBVqliRJiFSSUhJopnJM0qPTIZ8A8PLyLTjzpue1XBT1fDsSqSJ0oiqIlOOiNuvz6Qo7CZEi6S1Hi5yTvigZi+Zl+nvUIVIFxxUORF9pWjysMQcA2KDRw3wdVvJ+6Xn1VSMgrZBur3Rqc12v2x/S7Bm/f3Y5bnl2Oe54+f3KLr6DpBqIVAnAtzzP2wfA4QC+YhjGlCqcd5eSDqUeii0QKf8RX/3wfLEhUzjHlSaY/7uMXdkr6QukWlIQjuul3hArUZx0j2k8uk/f/go+dfsrvULGVlWZ4MuNXdWATIK1aQ6V8wA9zTxS5fL73sE7a5qxelt6cvuO4IDScKuBZDquh9ogMWFnZ+311jBo6eq7hpQd6LRKnrGMSHn4+ysrpdBgX3AIAWBAbRaAz3VThd9DJeh4Xy1/sK29gPvfXJ36eDKcK91z+FrQGd9p1j7tmX2Vl95rQ8rzvHWe570R/LsVwAIAe/T2vLuKkPdOL5oUgkmGVPD9uuYuESIiC5zXzqHP7ApbZdD1dibdhQypkuuljne3VrBREO8njbKdv86vx9SbjazamVJ83Kox6CR49YRI0YYVdyg/Z5x3R5uAxebcjixzECcUIik4Ht5cuQ1jL5uJZZt6Vuai6LqoyfYRQ6qXYejWKha0rbbYYl5WUHxYIZt///538DnWRquvGFI0Tl1kgOu2uCzDrqKDLW3yb8nw7GnWXyXylxdX4Pw/pOPoXXLXm/jGP97Cyi3p9B297ySqgk74WtAiUin2DAE0WDtfZ+mkqhwpwzDGAjgQwG7BtpyzYisuv+8dbGyNeickpFRokRQVREotNNjSVRTHcJuJLPVMhb0y+jIilZTSXMlGQfdYScipN4ZUtVOx+Vjau+VzJxmeNBfICNKR7UuOKymquHBLJYUvd2R3d9q4So6Lh95aBwCx5RjKScnxUJu1AfQBQ6qXc6i5o+8aUrTxVYIixpHNSZIMqV88sSgxwaKaQvekW2vc6YnTL5+47WVM//GT8u+C+23r3v4o45UPzsPsJemoDVR6JS2fkNZUpbqVrwUtRyrF+XoasdlRUrVRGYZRD+BeAF/3PC9SptkwjAsNw5hjGMacTZs2Veuy21Wuemg+7nx1JV5cGp+dQt5GHCJlKgjT+be/ElEanscQqQot7rSe3NxVTTj117Px9uqmyHeL1rdiwvcfSe2ZqCJzpJK9D5JKlEpRGFLpn01v+AjVrlfFFY8apksK25HRE3qC8ri2thcw4YpHcevs5eKzuGw1Qn6SjKRlm9qwamtHVYtklhMaV8n1kMv4a6mnRnDR8QQipZ7j7tdWYexlM3cYT6XcPTiulxhCXryx7xafpY2vEtJxubAY32yfW7wJYy+biaUbWwEANz69FH95acdwY5Iy0zj/MO79EhFf/p1/bEtCksjOlLTLnO6/ckMqeU9Iw7UjzmOlQMOOkqqMyjCMDHwj6m+e592nO8bzvFs9zzvY87yDhwwZUo3LbnchwmeSd1sOkVI5MW+tbsbmAPotOOEmEkKX8isp51mL0F4ZI+PdNc1YsK4F1z4S7ff291feR8n18GQPmyeT9+a4rqRsnARDqpLQnjBOK0Sk2rpLmLNia/ofBVLtzbaQwBHgz0udK/Q3ecKql0whsPtZs8+4rL2kwrD0yfE/fxYfuv4Zoex2RBViGm+h5CJn986QctyQbK4q7Gsf9dsLVbMHZJKUC+3d+NQSfOj6Z2KNqbnBhjyiX77qY+utkE6qKLTH5p0OjebI+n1v+Lydt1bJJQg2t1Xe565SofWoW0ZOitCeTug57ai5B0QdbM/zMPaymfjZ44six6Zdb6S7Krl3Nwjjkuj0U5p5pO6rfU2qkbVnAPgDgAWe5/2i90PqO+ImbD4kliUbUqQQwrIH4cT53JFjAQCrAsJvt+AWuWLT4tNk2aY27H3Fo3jknXWx10+LSNH5OzTZQDR28uYrFSJRlhwFkUrwNCoypEQotDJE6soH5uGc379UcfXwamcQ8U1CfSRJjXZV44eQMjqqKQj/1ObC9xaXtecKoyz6vep9l3qwUfZUxNxxXeRsQpMqM2RfWrYFnQUnCO3pOVJivu2gqGW5eyCi9bpmPW1g3lrfiOiLxQppPqfN2vvJIwskh0ZFo7OWKemx9mBO1OVs6bilOwClI52lRaQkQ6rysGZLZ89Cew/MXYOZb8fvATpp7Spqs+VufmZp5Ni06y0OGU+SuaubpFCjtp5iBYZUXy0hUQ1EagaA8wEcZxjG3OC/06pw3p0utHDSIFLtSvkD+pwriD3610if0f952QDX8/D6+9vwwtLNAiZOQoo4f+ilZVsiREf1OB3hkSZnT639bgb18803aROohNvVE0J9d8nF6m2+t78gZUNgstOqjUhxcqYaLpOKSCrPRC1WqY6LCgTWsw0nDkVyhFEWfk/367hyc9yS5lgA+PY/38JJv3xWe/6eCnHGio4nEKlKiMdrmjrxidtexnfvfdsnm2f0HKkkRG57SLmN1krIyCw5LpZvbo/9fmdLiFiWH5vnebj1ueX4+azF4jPVkGqsyciGVPB9reLY7YgSCYSi68Jd/F2Um6OSgxSsI45IdRWd1O/20rvm4it/fyPVsSTTf/wkfv9sGPJPyhhMaxiRbtGXUPG7Lmxrl4uWqlX+dfopaS/wPA9LNrSGhhS7j77UWqYaWXvPe55neJ431fO8A4L/HqnG4HaEvLO6WXh/qrhiI0tKUQ8yMogjRegJGVKOi8a8jW+eOBFTRjZKvyXF4Hnh5Cy5Hs7+3Yv41O2vCAOnJhOPFBWYEfOJ217GZ//0qvY4ugetIRV81tOsEp61xzewpE0rKVuNZMXmdry7prlsj6f5a1siRkZ30cHogbUAgHkpDSnKaKs2R4orCvW++d/NnUVJUagtGcggIwXSFBhSddnQkIpTSsKQ0sxlx/Ukb5kMKFXR3/P6aizeUD1UwHXDgoxFxxXFNCvZMOl5vbumWUKk4ja6NJt/NaTcRptkSK3a1olCyUVd1qoaT+2njy3Eq+9VHubWiQjtpVjDOt2plnboX5uREzKCd+pB3izT6IzeChHp+XP/2p1v4sK/zqkIkZL0oCa0N/kHj+HLf3u9orGt3taB/X/4uOCOlRMKkQLJSE7ajhFJiNTcVU245pEF+O69b0ufb1ba6ugy9JIoBP98fTVO/OVzeDpIQOHJOn3Jx+ibzK0dKGfe/DxOv/F5rUJLUyyQFOIPH5qP3/57qSBickTqkLEDccnxe2s8rHBSdLLMN5KuQnpDiry8OPibFr4utEfX7mlWSRcPUbpcgcQ/tzRho4vueB1n3PQ8lm1sD84X/U1HoYTTbpyNryoeW1fJFc8ybWsHCh1WO2uPb6rqI+HK+cjrnsbBP57FjlVCeyUZmRKhvWya0F70eoRIlVxPVFHn59jeoT25bIMbPv8e1OgpOi5KLjOkYuZeJZXf1zR19ripdLmNlhwtnaFEvKm9htQLhMRxPfzx+fcEWlOp/O7fy/DxW17q0W9VIX1YSUiGS5tqSMUgUiXHleYIN0jikPeuotMrpIKMNT7uh95aiyfmb5AMuXI1oWRDisjm8n0/Pq8yTurKLR1o7Sph1dZ0c5JTNbjeV/eAtOstKWuP9IqKSKnP6ZI73xR8RfW3OpkfOMF0SEcx6vD1BfmPN6RI5q6KZlukKRbIF+31jy2K8Hm6S6GnnVcMIo586FAhgUglcJeoRxUNozZra4+jRdDSVYooGvIAuZJ+7N31uHtOunY1ImvPkUN7SQskjRImo/D1ldvE+dSxU5bakwvklPnuoiNIrWlT4WlTE1ykKqABt89ejpeXh1mf5bL22tn7p+cnyh8E84HGR61i+HOOUy6Oci4uJceTNiYRBtvOZHNevbvkeD0is6r8MVpjcdmLlSBSM657GjOuezr18VzK3UNYbFUT6gg2qrqcJe7v9fe34eqH5+M797xV8Viq/R5pfLTWf/rYwtiQr+55c7K5ZRrYY0CNtDkTul90PMnoorl72DVPRUoMAP4mPvkHj+E2lsXqeR6umTkfbwQ6pJzQeHWIIl9nKnF8W3sBYy+bKf7mepBQmJauIlzX63H7H47ephG+33CDVG2+nBaRovsvOG7kHogVojoGOiTsFhZydF1PW/yURK0b1cEQqb4U9tbvuv+BolrSQLgp6Txz1/XgeJ7IvCMhhZ5lfA/ifqjIEle29DteDDKNIaUu+Dj0iocA2wuOxKsh5IsjUhfd4cPOHz94dOy1AblfllpHKm7TOuhHs7CVPW/P87RZh7RwueJ1XE8qERFnOHSXXBFCSLPgXNeLGCzVQGR+PFP2vtSxJIc/ZWQoNKT8/4uGr2weqfNRPZfueTmuK5GeBdk8Zmy69/XO6mbsPaw+4iwkCfdWC06Y8Umb6pqmTriuJ0K0OhFecvBMchkTphG/2ZTbhF5/fytytoXhvcyWK+flJ6Fv9I5ydhjaozn/yDvrI8eXHct2Sp6gcf7u38vKHsvlt+z4PfrXoDZrSceRHiq5rqSTaK3EhalWbPGR64ffXocLjx4PwJ/3t81+D7fNfg8rrju97L0VBRobHXcTq+2lljIgTlt4nigi5Xk+ItpTA0AXtVDFNg3xnDhSzdfa5rZuaU1VikgB/nvNm+H5qTyBamDp3lWW1YL65ZOLcdPTUQI8CXUGIZGcrz5kSO32iNRtzy3Hc4vL161q7Y6mptIE0y2qS/8xF3tf8WjE8yREiTaaAkOkVIOIb9S0OW5k1jlNfspmUuWuV1fiRw/Plz5Tw4ck3OBqVpRAb0J7cvl/TzKe4oycrYrRWm5BdBXla3CJUypdRUcou3teX42xl81MLALKQz50T70pdup5XmK4WPydhNopyBCNq1MxqKTnE8eREoUvWWgPYS+/91kNMbpO3LlUA3NbewFn3vw8vv3PytASzncoOeHzork647qn8aHrn0k8h5rNkzFNZG0z1mDSzbX27hL+8uIKuK6Hs3/3Es646Xks3pCOhxIn5YwXQqS6JGfKwX1vrBY6JJ8xE5HE3oxlY0sXfvfvZanOu2JzO8ZeNlPUoCO0r5JCinEyZlAtcrYlJWTQuis6siFVbqyUmcmdxEqdIceV1xoXHuZVdag6tjiHsuR4PeZghhmuHrqKDr5255tYq4SeuZFSkxaRKjp4ZuHGsnOe35PKp+U8Wd3nXPJsjI/PizoG89e2iPB2IiK1g/iOaWS3N6SueWQBPvPHV/Haiq044OonYisGq/Frz/OEktMpX+qbpy64zsBiDonqrqgNleStdytcJyCchHEhpsvueyfyWRx6xReBGrem6/SEfyETqdMhUkljS/oMiL6LOCOsu+QKxUrHJLV+kYrtVdiR/v9eWoF1zbJC+8WsxRj//WjOhRrKSXpGjkL6VjNXSJlxZRV3vqQN2XE9vL819KhbyyB5aiiA/n6lQjJzR0HmO9B76kmNHvptxjKQsUyl5ATfyKLv9JZnl+HKB+fhgbfCelxpDIyOQim2tlG5eyBuJW2qbd0lzJq/Ad+8+y18827fIM3Zlsio5ON5e3VTxPN/ZfkW3PbccuhEN5afP7EYP31sobaK/LrmTnzuT68KY+G5Jb4j+n9BUcxKKlyX0wGjB9Yia5tap6XoeFpEKk5o3jbkbSzZ0IquolOxM1RUjHku6wKjxTSiiJRqMMihvdCZLiq8r0qEc1Efn7ceD721Fj95REa8eR1Cbkhxw2dLuzxnu0ouLvjzazjpl8+VuX74TA760Szpuzi0TMcl4/ugrk3VaTfOFg6UpWSSd3Bd9wEitWOEv9QfPjgPTR1FvKtk6JFnqC6MguMK3lHShqp+RxOWV4emaySRxkk5cS+9oxBvyMVJudCebsydwpCqfIEXFESqHEdK56HovMY4gri6EfJ3zA3OLsaRSrpO+F14XjIM0hhSm9u68YMH5uEC1jcMQCxcrer1pEwktcoyjZ/g7TC0J0PuSaJ7JyVXrrLdIrhlMYaUohxps6yUi8OVe6HkiWdRCTVNNbgztomsZUbCEOHx0ZPTJrdgXeiRp1lz//WbF3GwhqsDpCeb03o46qdPi16cJEQJeGNlkzTPz7r5BfxGqQd07q0v4xplUwX8UOWld80FILdYGlTvN+d9TVOw9qanl+Lfizbhwbm+YalmnQmyueuVXSPl5uMBo/sja5noKrpiDgqkNMKRSj7XVmYgnPjL5/Dde96W5kEablKJoWGqkH4cWJeLIFJqXTzVoSS9XHDcHpdXEfuB4wmDSTVUOSKVZ041v6bIpAt+mja0lzRu+k6tv6UzGqmDAZDc9uvuOasiJXk6KkAod6Ts1oYU30iJ0MYnmud5IuShkge7EvqXJZHjOpQJ5TieUJoZy4hY2CTCmGFeepqYuCpxob1utrBvm70cDwaIGhAupLSe0uvvb8MdL8veqT9OOWuPj3tbewF/fuE9bXXfcnwELkmIFN+8uopOJFSZNouQnkcaZIQUmQqxx0kajhSNU1RZ9uTPu4o+z4IyWGREKlkp6jajkuNibVM4p0MkT38udZ70lFNGiFTONiVESj1LEulfnTtZy/QRKTYXyvUiHFiXAwAsZ82Sda0+VFkUhELomZdrg8KFIhYicUAz38lzP/t3L+LOV1dK3815X0+eVp/VJ297RZQ94A2rqdglNfnmQmMnSgGhrRQS4sZRubo+cXPouMlDMbAui5OmDBM6mVCIMJtUz5HSya+fXIIfPDAPQLheXn1vq+xApjD0Q+clupZINw+qy0YMKVWv0XU9z5OySYuOp0VpHn1nnbZ9Fxe+H/BsVS79ajLi33lbj0gRtYKeR1qyeVfRie0uUQkixT9LKrL83XvexnOL5TpUHVIyTnW5f72R3ZpszpUT/ZtPBI46qaE9HrNXM4A+cdvLsdfsVBCpEpv0hmEgb5tSZhaJLrymbqhpJDa0xxTK/W+uwf1vrsGR4wdhQG02XFApDamzf/ciAODTh49JRqTYIr/krjcxe8lmDO9XEx2bRsHF1bRSnwU3DLhXuLW9GKkzkqRIyyFSrutF+iYCjKeUMgyoKhpdBeX2goN+NWYka49vJJ1FRx/a02w23GjWfV90PGxs7cLYQbVYsaWDZTt6mLe2Gcs2teMShpaQ0vQ8D39/daUoNFtpo2Aaf7+aDIpOSMJVN+SOghOpci3uR+ORZ2xDNoyd5OdD497G9MWNTy2JHPfy8i1o6ijglP1GSO9xc1sBw/vlZeOtzOZEc2nOiq044toV2mNyzOmbr9RC05Ux8T+Xn1XONoWDwZ04+mz2ks14e3UTpo7qHxk7HU9GttoGC5DT0dVEECA+e/LDk4bgj587BEB8f9HV2zolPk2SQ/nLJ8OCn/x+5d6fbtlkCD6fio4HTk8l3TywLhuphaWi32GY2r8+8bZKjqudGxf/zS/fkkSIF1l7bohIqQkhHHXzmEtC+1Jt1hLRF8G5TFk/sLPooF9NRqwTnnRC51BfEXe66nM22rpLaO4sit8qXPLI2lcNVq7rPkCkdpA0sZegTmxARp1Usjn/Tq09k9RslAqHEdLleJ6UeRDPYQrCNiy8FlYMT79BxVn4OiNiU2u3NDF1nKykyeoyaN82jShHiv120Xrfe9cR2nXKNg5ZIS/k2kcX4KAfzZKuwc+t8gCA5FCdpEBL0bkSVxiRG13vrmnGTU8tSURQIpXNY2pjAeF7D7NH2QbWXdKG9lRUaMG6FskI4tcjI25TWzeKjoexg+sAhE5FyXFx+o3PS78HQqU5b20Lrrj/XXznnreDcVam2NolQ8qLrT6uKlMu6rzOWn5o7/4312DsZTPhup6MSGmeN82LpIbOAHDerS/jojv8DW89Q6UJseFjSVv5+qmFG2PbxMSlrwOynrju0YXsc3l95dg5JEOKne+sm1+Q9ICoORd8RiRrUYiTrVfu8OgQybi6XdxIjGsXdetzy3EjC5GXnGj5E520BUZNxlINqRShPTbeTa2yDmkvODAMYGB9VqA6RcfFDx+ch0Xr5fp9YbkZfywUSi06LjoLrhhfJUIhdUeTESiu67rYK1jHjuJ4AcDwxrxYT/TOk9aXdP2iK+1lHBCgOaM6U51FB6fsOxx/+fyhePeqk/G9UyajyAj36n6lEvHV+dNZxmncWbLbGlKfvO1l3KzhqXClypUJbR4bW7pw1E+fxvx1IZdKXYBJ6dgktN4d1wPvQ1zOI+KhPZqo3Ov4y4srcEFM9XJA3ihWbe3AL2Ythuf5Bk9WaYhccjxpYtIkTrshtHaXxLE1WcuvBSQZUuG/twSKR0fO1Rl5cYuE7u+WZ5dja3tBut/L7wur6uqu05UQKpV4NBrDJT47MDzm0394BT+ftVhCNlRReRq6825u9Z9V2KKIOEjhsd+4e67YNPkmqCoyNWNVrjklhyXHBPM6TG/X33NTZxHNnUXxO1LElXqIxHdQESn1PE0dRdz7+mp9bR9lbWaC0B4Jn6P+8dFz0PeVFALtZOuUnAR+7koqX8cJNzZUhJav298/G5YTUB2VPOOj6BCpycMbAADLN4XJBjSfiJ9EhmIx4PdsZfxFqRK/riFtzHPgmchxxTVVcVwv9rkOrs+JfxNaZJmGSMsH0nEe+Xw6+oZnpO/au0uwTQND6nPCyHpzZRP+/OIK3MuqiAPhfdO+MigYX6HkiecbR/OIE3rnvIOEOv9LjofpYwZgcH1OWr90zcH1OWHc0XxPymZWr8/nLTfAaB6s3taJd1Y3S5+PGVyLYyYOARBST8hZ5E/ANg1p/wM0ocIPEKkdKy8u26LtUaer3QSEnsNDb6/D6m2duH32e+I7VfmSxZ8kPNuGW/FcOeqEO1zkWfEJc+WD8/DMok2xYTi+eL5255u48aklWLqxDUXHRX1eDo8UXVcsAJ/w6f+7U/I04mHfls6iUE61WT/DqCCF9qLIlurlAXoFpy4SUjpqXJxvHC8vD4mzaoov4G9Gv3lmKSZc8Ugke1OuyC4bMEA8WsHfA23gC9fHt6TRcbxUEPHioHUEpfeSUua/fWHpFqFU+CnVuapuwI6Gw0bZjKqDEBdSvuBPr2HaVU8IJKVBE3ZT+/fphMbWkLelhtfqde+eswrf+udbuPnpMNz2xLz1uPnpJVGOlG1KPMjmjqJkIOlqY6llJdII1x1/eN7XFTJfz8GvnlwsUDFV0qAjnJSrjo02ou/dI7fkUBNGOE/GlgwpBzqvU4AAACAASURBVEMacvjx/9sPAKTK9vRe2rr99b0xWLNdRRdTf/gEZs3fEDkW0M+XuPvkBh4XnaFLx5ZcLzbkv8eAkDJAoSvbNKGG9spJUnmVjoIDyzQwtDGHtu4SOgqlWD1MxjkZG4PrssH5XalUR5xcetebEtIIAJ3FUA/Qcy04Lp5asEHoaT8cafoRAvbsC46fOdhYk0FzZ8mPJjiysQfEG5sUfTh8r4HisyZuULPnMDfgermB4csToEJDysH+Vz6Ot5jR5XqeVN4AiM4pGQHtOxyp3dKQSlLgUmiPcQHeXt2MOSu2Ck+Tb246ZV1OHNcTGxwneWas9I+clGKh5OKmp5ZInlucQtFtlG3dJRRKLhoUQ6rkeGIB9q/NCKXQoYFsddLSxQ0pO6gjFb3+I++EncvV9hAA8OKyzZHP1GcuOAaKolNrUpEQAlaXlcMjNzy+CJ4HbFZCfxSuMIzwGrp7IfE8Dz95ZAHeXRMqAjISCaHQia6yeW2k4r2crckLIPK5pw+lhJ+1dhXxgto0VINILd/UjnzGxIF79leOTVZURLZWDUHP8zD++49EipGq0lEooTZribpPcYjU+sBg29ASvrML/+91/OyJxRE0U0WktnUUJGfgt88slSrNA+HmkeSZv6cUXKTrjh5YI9DPooJI/epJ3/BTkZp7X1+NN1NU2ubotbrBNXcW8b173sY/lO4DUUSKh/bC59Jd9AsFD2nwkRLu4NBzaO92sKGlC57nG2HrW7oiz5sjCNoyJrGhvXBcl526D0YEBVC3dhQi758I1I7rxnLD+tdkMHpgDaaMaBROsWkaMrquGR/pRhJVv6j3ZJsmhtSHzyyu/EXJ8YK6ZD6flBApQvUAwEoI7T0wd62ENAIy/5bGNXdVE77wlzn4SbDWSq4rkpr4vRRKLnKWicYaGy2dRUmvc6K8LhkICPfKA/ccgL9/8TAAMiLVVXSEwUshyFZN82nqvNFRcMT3JK4Xnb/q85fbbX2ASG1XSfL2uHdKE5oWxjm/fylSUFN3vjTepOuFLS84mVKNCcd5ZkA4qZ5euBE/n7UY17CNSS3XQMIXD03glq4SCo4nNbcFfEOB4vUDarOCMC0ZUppwB4UIWzpL4lnkM1aQtce4RsG/v/y3sA8eV7xDGnLYe2h9ZGMDooskJGvKn8eFBUjBDQg8QUAJQ2i4BYBfPoIMKLkWkXz+TW3duPW55VpjIalJcjRrz0WN8l5GBIR8tX5UyfGkrBxV8hlTCqVcfMcbkewuTujmSMlh4wahf21WOrZcksMbwbm3qP21gnVFSI3nedrOAR0FB7VZC3ZQriDkSMkPO8mg05LN2Xrb1lGQlO/C9a0471Y5WaSghGFUeXn5Fhz7s39Ln9G6aMhltKFXvm749ZdsaMW3/vlWpJmrTpKcrq6iGzGiAA1HyuahPTb+kk+8HlwfNaTIgWvtKokM5T0VtJLWI0claJ4WSi7GXjYTf3z+vYTQXjiYgXVZ/OCMKQB8JFk1ZmjOl1w54+3XTy4RtbOKjothDXnkMqZAC23TkK6vQ1v2u/JxfPr2V8TfEc6R8rePSPlGX5IhVXRcyVghjlSh5Ak9Sw3vy/FQSTqL1DrHjRiF1EzccTxYpm9IcRS96LjI2Cb61WQCQyp8jpyjFldLkJ5pTcZCY/A++HrpLDroX5MNjnWCMfmO1vgh9eK42pwc2lMljrSvkxeWbulxu51qy25pSCWFo3ShPfLKAFaZPPg7p6mSnAZSdFxPbL48Fq7GxQcqmxcXMqTII+fGXXydpaghtbGlCwvXt0RCeyU3LDravzYjPB0+yXXPkoy/lq4iCk6YDaLWldGR5LmRZpsG+tVktJV+aXMihR2HSKmbOAnpkIExhpSqVEnh1mTC/ma60F5rVxGX3PmmVHNIlZeWRQ1DEl1l85qsvAy7RSFYN7h26IXGGd62aSBrmVjf0iUUma6/WNHx8M85qzDu8kckwvSgumwk7Fyuwe/CAHlTAWDVq7ziX+/iwB/NioRBfEPKDuo+eVKDXnXMgL7mTEGZn1nLRJahHc2K960TmsNxWZ1LlEbgPPOqIW9HWqYAStsedv0TyxQ9JMlYRqSGThpROSYckbI5IlVykLNN1OVs1GUtbGwN5wK9v7buovg3d0iAcF3xEHqYMOP/5ldPLo7dCHPKPB4UnG9zW3fk/TfkMzANf17wENIvn1wsamdR4WPOA31nTTOuZeExVW9T5OJVVktLNcxVPWGbBgbXh2PlBuhHDhiJ6z66v/87x5XW+qCgxEbJdQViE1fCgAs/Bxm4alIPXQ/w12wmCO2piFTWMtGYz6C1uyQRxVs0SVmq0HPPZ0yhizuLHI30kM/416VjiSu1/x79xHGEvqtZjyRJ9bhU+eljC4WztrNltzSkkkrwq7WGAGAoM6TU8FZDPhNZXOUMqROnDJMQKR7aU3XjwPp4Q4qEFsmA2hCNiKuz5Lge/vzCexh72UxhtP3238vgeYjUKSkxjlT/4NxdRUdCVHTPkjIPmxWOVGtXCQ+/Habar97aGUmt5R6PbRnIZUytsUbKlK5FRiB5jHRvOi4Uf8YcweFVcdV3SAokn7HEe5NCe4FC+92/l+HBt9biFgV25yG3NQk1pciD2tzWjRseX+gbExnZwA1btMgeZcn1MLRB3wMuY5kwTQMPv70O+135uHRPXBzXxa2BF89rX9Xl7EgrIl5IsBLhPB3P8/D3V/waSKqSbO/2Q3u2aWDl1g68/N4W7biT1luzgiJlbANZjki1F2J5H0s3tuGzf3w1FomKk65SiDY05G0USi48Ty79kZRJqZNLjt9b+ptQhUpFNWK58Ul21CPvrMO8tS3CcB5UnxMh8vlrW0TIpq075ACpSCghLDy0rhazdL34d6fONQp98fAtSX3Ohm2aEsmai4/QeMjYppSlCPjGFD+Oi063lVwXR00YjBP2GYbB9dnIu7MC5w/widW3zX4Pe/SvwW8+eRCu+a/9ceT4wcG15Gr0PGtPJZsnGfr8HITWlFwvgvQVmM6wg7nDHdmi4yFjG8K55hxRHmKLQ6FJj+czlkCVbnl2Oc66+Xks39QGx3VhWyZqMha6ii5eWb4FVz88H415WyB4QFi/rCkGCFBDi+WcILXH4c6SqhhShmGcYhjGIsMwlhqGcVk1ztkb4Z6v6sF3a6BejtSQAdXU6b9o7nGSJCnGuqyFYY05uB5SIVIDEhApVbhXSONTpei6oqo2bVzE75gRLHJxrBMiSKQcVm3txOWs9YzOyKGQQ3t3SZDLyfPlIYufz1qML/5VrvjNPcqMafp9trSd1v3PyMMkL0iEEoNNQFfmoJEpfd53qzOB+0VKNp8xww7wUmjP/4wI1mrBxuGN6ZrckpHwx+ffw2+eWYYXl22RKhADYViIK9GfP7EIW9sLGDuoDtefMzVyXk4uLblebJf5kusJYjHfWGpzVgQl0BHhSeL2eMf1JGOZe74qItVZ9EN7meBdUr8/FZGg8+nGoiKzWYUj1ZSASF398Hw8u3gTZi8p34uTS0ehhGsDJIQjpVJBTo2eiQtDHD95KL554kTps4xp9siQUo0DbkRahoHlm9rw5b+9gXXNXcKYyWdMMedOu3G2OL6tqyTV+uLSn8I7bOML69GF8zct2ZxQHl2x4/q8HRgG+qy9Ta3dKJZcZC0jkpnMRf2tDtUvuX4trLGDatFRcCLGl20aaMj7905cyDOnjcTpU0egPmcjY1NVdrk5MdEqCiUZVbvj5fcx7aonYsfMry8K5Tpu5LmSMe+P35873CgiRMoOng9PGJDvX79WuoqhIUX3snB9K95e3Yx31jT7JHfTQC5joavk4NwgfM6zKYHQMdaF+oFoaLFcpmVSZfQdKb02pAzDsAD8BsCpAKYA+IRhGFN6e97eCF8wnBdkGEqhTY1383xAziXEpyFvRyZX0XFjK4ibpgHL8Be9QKQSDKlBdekNKR56iUOk3lzZJMJdm5T4/W8+dZD0N8+Uqs/5yuH1932Ym+BYneKiyVt0XDHR4+7jhaVymIsvFCsIR+l4WKQECCkjY5eUEyFA29qjz4GUfk3GkjZVbhSqiohCd/mMhaLj4Z3VzdIxoi5YcH01iyqtIUWbKQ858vdqGjy0F17/ttnvobXLT7+eNKxBfE4kXdsypIrgamhB3IfjibnD768ua0dCeyWF58FlzCB95mrRcaV3zBWmeq727hLqcjYyypooKRl/ap2bpO9Usnln0RGhO1XosmWbyCrP8ZmFG7EiMPpoXhYdV6wlw1BCe0603hcXNeQO+O/TTsjqihMdx4eMvYxl4llWDoMM57hed63dJTHPVUOKNkSePEJrlu5dF4IS11YQqcZ8BrZpaA2pugC19PVVdE6vb+kSob2krOj5a1skDo7OkPINAhM1WQudRSfyzizLEM9zQxDWO4xlsolCmcyQ+tFH9kWWDCzXFfOt6Lj4Y5nQlIxIhb1D1fdVYBzDjECk5Kw9f2344+AFTLnEIVJkSNVkLNRkLMmA6So6KAXnr8maUgspdb+jfbMphuNbaR/CHvga20WqgUgdCmCp53nLPc8rALgLwEeqcN4ei4xIhQuWV/kFQg+KpwgTVM07iRdLHja3dWPsZTNx/5urA0NKX2nZMg2YpgGXeah8Mqlkc5XgmyRSy5WEWkUk61jbj2GNuUgNq5LrCkJ4Y41/P5QKf/GHxwPQI1LUC6tQCg2pA0aHGV9JXoKabaiG9rpLDn7xxCKh8MYM8kmuImzg0mblX0QtpAr4ShnwlT3nmRQVD40LKZCcbWJzWzfOvPl5/JOReenZx5VBGNYvnSGlGmSAnJZel7VZIdbotWzLkBA32jgs05TG1l1yI9wlIJ4DUZu1It48taLRCQ+Hc+kuuRJPh3PY9BwpK0KqdhUkg/gUhZKHpo6ChHKpIYKcLRtS3UU3YqhTuJJC7uWUt/oI2ljokhyQYiksKFqftRWyuWx8q0YJ6ZK5/3siPnHongAQoAqJw4rcD4AIL2ZtUxcOHTcQZ0z1q7Hz9Ud6L2tFw+uWaaCtKyz62qiM2TQM5GxTCiUWVUTK8yKGHYlq8JimgYF1WcEH5ZK1TViWgfbuEq584N3I9xuaQ0MqKaP6xzMX4MK/vi7+JoeCZ/aWHBe2aaAma8HTZJHZAVLYkLOxMTD6+P5BJQ0KDtf/pjCKedPikutFQlmeJzsRajcDIIYjVQrXqhXw67gjVSi5kbUBRJHBOESKdFLO9ikEPNO4q+gKJC9vW1LLGVV/0FyPAwLKOjWKJLWY2ZFSDUNqDwA8fWR18NlOE24s8XBFzrbQXijhmUUbMX9ti8gq+MKHxsWeqyFvo+i6WBzAuHe9ugolx0N9To9IWUaASLE+fnYCIhWHbOmEL6q4GDMXvkFQRoV0PieMtRNcTeEVavuhQ4uo9UChFHrh08cMEN9bCZOboxWu50WM2/veWIMbn16KXwctOqi2EdWyWdvUCZeVWdBVReaIFM+Y5ItaVUT0HTc2l7EihaRf4gwpQuTKEYTpHXbEeG21uTDUqVNqGcvE6AE1+MShe+Lhrx0lWo1Ypjy2uHBBnKKsy9kwgs2RhObP52dE14cK2ZMUHVcyNDjCwN/z759dhoXrW4N3FA0p8nESGXbJxlYccPUs/GpW6E2rnq26mXaXnIj3TmiKkVIJR7k14f1RSZFuJwwD1eVsbdo9/W6EYnSTIdS/Nivmro8qpFPP/Rl3suj4zX8LJRffuectrG/pgm0ayFg+x4iPnXRjzrYijsXwxjzaWPX8Rg1qVpu1JNLwFfe/i2Wb2iREqhCDcKhcJroPXfKIbfok5n/MWSWQQC7NnUWfA6SQzXXyEssQJkSKI4LNnUX0q8kIQ0FFPGmtNuRtQTTn3SootFdkiLBlQoSviyVPREWKjhshXXNkCdA7U0VHTzanzygsrOo7IqFzIUeAJA6RondK762WUSa6gkKdGULyCk5schDtd3HJUpU2dN6dDCndnUTehmEYFxqGMccwjDmbNlXGSahUePjONAz86ysz8MJlxyFnm7jj5ZW44E+v4bQbZ+M3z/iE4X41GeEJcjENSocP49q1WQuFBETKZLAqTUozwZDK2VZkcuuUFiCnjHJCbxpCcL/aaNp8yQ0XHxVVXLm1A/1qMsIDXdPUif/51zuiujHAIHwW2hveL48j9hoEANqedCTcuPM8RDhS9CwIcTtz6kgAwMemjwbgK+s/vvCeSCHWGVJ1uZD7wTcjrnyufmi+BKuT0uOGBP+3DkniMiooCBjXSobEFYYUI91zRCpnB3NHjwbZpgHbMnHtR/fHfnv0E4rENk0tAqVKXPVuUnA6j37s4Fp8eNIQaV4OjkmSKDqu1KF9I8tqonW5rb0gig2q5QqAKLeGlDGhpbez96YWVs3apkQ27yq6kTnS1l3CL2YtTh0WUDcDHq5syIfcPVoX+YwpHBIgRD9pkzhu8lDpfDxrk56FZRmpESmOcLV0lvCh65/BZfe+jUffXe9ft+QGnBlX4gnS/M7aZsSQqsla6Cg4aCuUkLEMrb6rzdpSaG/RhlbcPvs9ub1WDCKlcyBztqVNv09q9g4EtaAcF1nbiPD8dEJjCukb/vPzPA/bOgoYUJcVxpFaZsYWhlRo9HH9S4hPyXEFZ9Eywzle4IiU40WeezdD+flYuTiuniNF84/CwhGOlAaRUvcaHWL9lb+9gUvvmgsgylkFgGsfXYiXl28NEaliSH1RdRiFF9WIypVn+mygSkN7fcSOqoohtRrAaPb3KABr1YM8z7vV87yDPc87eMiQIVW4bLxwaLHkuDhgdH/s0b8mdpH5nkz4RgjuzAccGw7H1mQtiXegimUEoT3PEwhBEiKVy0Tj+nHePs8u4hvxBTPG4pzpozAyIbzUX1N/qOh4IrRHG8KqrR0Y2pATY/rxzAW44+WVeHn5FpQcF5ff97YgXBdLYaw+a5s495DR4hmo8qtzDwiaiIYLy0MQbg2e7Q8fnBep5jt6YC1WXHc6DhkbIl68q7tad+TVK44X6e81WUvapLlSWt/Shasfni/+pgXPuRv8NsLQXuTWAAD7jvQ5ZeWMGcf18MbKbaJ0ACAXSqR51V2KKksAEfSGnrVlGqkMqThuAnEJaX7yOZuzTfz5gkPx1pUnic8GxczRQsmVwiGbGCJF6/JFVh4ia5sRT6zkutqQkC4coHq2GUaoBfwG3Tc8vkgyEAslFzc+tUQqppokqvHJawfRcyuWXIGirW2Sw1M0V0mHTBvdH987ZTKGNfrPkBspFAIyjZ4hUqQXZs3fIEJWbV1FZCw/Hb5TQ3vI2ibeWt2Mk375LBuH/1Y2tXYjn7EiBrZh+Blgamh93OBaKUwYF9rT1cjK2WakfAOAoFJ3cr09Qlx0ek4VMqwJ1adMsvaCg6LjYWBdRtR2I0QqDKGHiBRJjVRiggwmT0KksszACgvuRp/N/730vqSndM6UWmYGCKIDom6hjEh1Fhws3dQWrA0FkVIMqesfW4h/vblG+mzmO+vEM6N5oDOEbcv063iVHJFE9dXjJkSOy9mW6NpBQnSMtA2USXYnROo1AHsbhjHOMIwsgPMAPFiF8/ZYuOLjSl0lOJJkbVn5Us2PfMbPKCo6npT+WXI8kQKqiiWRzctzpHJ2NK4f18uvTZMNdev50/HtkybhZx+bhiOUrDwu5LVyO67kuJHQXnvBQf/aTMS48zw/S+POV8MobsFxxILOmOF96JzHrB01GF3PCzhS/jn+/OKKCLRPiokrXt7dXjU2hjbkhdKqyVja/mJcwgbBgSHFjG3ujZJRHJd5NWVkI4AQmYoTx/Xw0d++iNlLworjKkeKxqrPmJQfbhjaMxKb7q647nQ05u3YbJmMHW7ggByuoHXDQ2FqlXySouOKkDkgp7PTuuThkqxlRbxgvnbKierZZixDW/Vf26cv5TU6ivLmzjNTab4UWCZVNMtX5g7lMxYu/vB4HDZukPibhG90ujDxS5cfh08dJqPnPGxP99nNUPO27pKodM0NKVpHtG6pqCMAnDN9FADfkPKTNuSxGPA3U7VTgecpDd9TlH4gyWXMSIsbICRP66Qm44+hFIT24gx8LoR60dyhU9Pa6F+bFcYRGVuE0NM74ZyxPEMUDcMQzZIljpQgoYfvQPdsbnh8UWKldUBOEiLpLjlifeVt35B6dcVWHPezf+NLd7yOpg7fmFYNWHUdv7W6GV//x9zINUlIh6vFnQH/PdVk/NCeYQAn7ztMG+nJ2WYEJaY5eNdr0SKzSbLbkM09zysB+CqAxwEsAHC353nzenve3ghHpHgMOi6jI2MZkgIbUOcvkrxtImMaMiKV8REp3UQCfBTDNMIiikBy1l7OtiIk8ANG99duVHxjpVY2tVlbbKZJ/BzyIPhC4nVZ+PVythXhMJRcL7JRF0pukA3io3BJ/ISsJqPG50hZkdRxLvReeC+tpGrwQLgo8xk5bKoLa63e5ocsSwKRYoYUmzuifUmMsdKvJoPnvnMsrg0K8sWJ7vc034Bwc+suOegsOBFFoc4f+rOcIQX4HmNcAVOaT3Q+7nHqnnfc/O8suLjvjTU4YZ+hqM/ZUnkKWpd8E8japqbae3y2F5fxQ6KZg4Zh4IsfGocrz5wSaXmjSrkaNSSql8yLMNJ6WrmlQ5zvwqP3ko4nBEKkkAdzjOYCRzT4GtKt50F1OYwaIDtafO3SMy6UXBHibusqBaEemXhP6Ke6Li/+8HgMD9DtzW0F1GYtre6sCWrHcSm5nqSnKmnjkbMt4SzecM5UfOEon5tna7g94h7yNrYEtcIylillw8YJGdqEZtIYKdFoYG1WzHlCQQnpIt3CHQ2VWpGx/A4DQv8HxhXgG9lJhOoD9+wvzUvd89ORzV0vdFAa8hmhJ5ZvbheNy7tLbsQgjqOoxIkwpDRAgm0ZyGd8qkZn0YmlnGSVJIWJw+rL9qAFwufMp0JanuP2lqrUkfI87xHP8yZ6njfe87xrqnHO3khce4a4l5W1TJFtYRihh0ehPc4tqM36xEzySFSlSVl7QLhhcCVw9kGjpONztikUIY2vsSaDi44Zn3hfpAwkIy2hdxMZRlnFkCIDgivjrG0KZS+OdbyI91kouUHPLplfo9OdfghTXljrm7vEPcfVCyFInxuAbRqvVboWKTuFyNylQXjoHelCe1zi+sD5Y/Sf+56DagVEHSe63xMCCkAkMRQCZaRmS6keJQ/Fxe1Zp+43PPitEam7NX3MAOw7slGgmaSYuILVEYMnj/BLMMyYMEj6vKWriJLr4bBxg9AQbHIk3SztmyRrmxGv2/PSGTnHTByq/Xz8kHpcMGOcFGK+7TMH471rT8MFM8aKz1QicZyoCBevCE9z/ot/nYMbHvfD0uceMlqE7QDg4r+9gYffXhumkAebMKGbnCNFjoPnRTPlAATEcXmd10nE3/C5cUSKKl3zLDEyllW9mLHC6tWbWruEHuTy2SPHiP6aXBzXk8aQFvWjcZAeaKzJ4KA9/XD+fns0xiJSTR0F3P/mGp8jZRmi8GWS0CaulgHZGhhWA+qyQg/QHKHwKYX8uB5VHWEi9nNHmvaXkuPFEqr36F+D5o6ihGjqyN8lDUcKCItTNuRtreHZWXAiIdJKyu8AekOSxDZN5DMmOgu+E6g7hs5BBvivzj0Ad3/piFT9a8l443Ohj9hRu2tlc/1EjdskfTg2QDFsS3gjuQz1AQvThqnOUH3OwvyrT8blp06WzkVZe0C4QHk475T9hmPFdaeza5girEaTuuS4uOiY8fjFx6fhYJYNxzcXGk+5UEB47yGxlKTEyOL1EiJlijg7ieNGM0z+NXctHn13XYSo7MHDRceMx9//+zBxbNYyI15M0fHEuLRlFgx50cz+7rEA4ou50aG00ajlD5LqVYVZe/olQWiPDvThY1SVqio6Q6qxxhbPjjbFVVs78d7m9sg7Vf82GUdKJ7ecPx03fuJAAP77USvB7zOiATMv+ZAI/dLc5d6krmjsiH41WHHd6fjsEWOlzykcms/4DgK/ntqMGQCylqF9Jmmydw4a4yNOcaUYaEO66qx9ceKUYUFWYuWV2lVESg5NhvNl1VYf3cyYZsSofeP9Jim0B7A5x8bEDX9dX0XTjLaO4YThLil0R+vS12MdBUcKKYvQnmIkZS1DOFab2woB1zA8Zuk1p2L6mIHajVJFpOI4UjrhBp1tGjh96gg8/a1jcNzkYbHzmxsUGcuUnJI4oXA+he1ojKRXBrJ2SfSu+wXOdQ3V3rLIwYuGyzKWX5eLG1L03lq7iloeGOCXqFF7Q+p4VCUnWkcKAOat9Tl/9Tlb+7w6i460X/zhsweLJKQ4zq8qooirZh3Zlr++KIITpwuzVohITRnZiP612VTrkhwDSV+kt9O3q+yWhtTogbU4ed9hkc+TMjpogmVZm4F8xiehF125yGAp6GdUm7Uj0KLJEClaECrBDwhRr5xtCaVFpfSLjp9l89GDRkneJldQNB6+YJIImaQY+KKnNFo7iG2T0KbOFVvJ9SI1VQC/0rfKtXA94LJTJ4t2CfQdedgEvw9tyIlnrUMg1A1j9MBajBpQI7Wl4ELPIssRKfZMdIgUKapyiNRZN7+Ad9c0JyJSQPmwo+N6kXBdTcbChKCxJxmln/7DK5E2E0CUbM5DezoZPaBWvPNMsJnKY5fPR5svD+3pvFa6T3UzJU8zl7FQn7O1BTl5e4usppclkK6ezIF7DsDtnzkYV39kX+33IbohOwnl5PSpI6S/45Crb5wwUUuati0jwqXrKJQkegAQGuf8HLw4qWpI0Tu2lGvWxxhSJHddeJjWyaLwrIoG+IhUeO3arEw2p3HonqXjyqGrOKNBJ/waNM/3CtaFToeqcz5jmxLxPk6Ih0WIVMn1sGRDKxYF3L4BtRmxV0QQqYzsNOqMhYzlN0tWy9/UZi3c/vx7wuBWZVhjHts6ijj112F1eS1Hyo22iAGAx4IsI6FzUAAAIABJREFUzfq8rX1enQUngqTR33GZ4uo8FnuD5r5t088KpEhFXGiP78N0/TSIFOkkPqRbnluO79//TswvdpzslobU8fsMwy3nH4zrz5mKh756lPg8SYkSipGxTGFt5wNPzmPx52JQXVfd0EgsIyRGkiLXZRZQuxc/tOcv0o8fPBqfO3IsPnPkWHEc1xXc2CAvmStI3eIhoYlKdU6AIDvK9UmaeQ1PQ0r/d71IhhyJQKSC33ka2CZrmyLsZRoGnv/esXj00g+J3+jQIp1hWJu1BLdB5UPQc85a/nhUD0x3jaKCSCXNkesfXwTH86QCfkA6ROrzM8YFhF83glbkMxb2DcjqqqFz5rSR+PyMccwQlt+x2FxjDCn+jOhZTxvVT2R4qr8jY5cbSGrDWiA0ONXsHQod5TMWGoIGqSTXProQ1z66QGSK0ph4BegrTtsHgFzCBNAbczUZCydMGSbQAlVo/TUwoyBNevyVZ8iNGajbAZeJw+px6Ql7azcA2zIiXDjet47GoONQcr2iPls6Tq0Ef+CeA3DKvn74lhsxXUUXMyYMwoShDVrdQAkzqvOQsUzJOFM7BJDzmGHr80cf2VcQ2rtjOKrlhI9DvUddBqO6DjOWiWGNefz+0wfhhH3ksO+kYQ34clBkmJzQJqHTXZz4y+dwy7PLYRp+BhmtFWFIBesirxhSOmMhY5n45+ur8f9+8wKAMCGEGx/q2AHfkFJFpTyQDulSPj9ir0Gi5EZDztbuOb4+DJ8jL9Cpq64PyM4n7/+ocxgzloGMbQTdBOINKW7M6Zz2OInTrdTLc2fKbmlIkXz84NHYf1TYeToJPqQJlbUMKexGCog8K1KG2RijxTB4CiwZO9HHPDAgGLueJ7wBx3Xxw7P2lXg23CPp1nh6cUR2UsKD6kLkyx83D+15AUnTkIq1hZM7fF5FDUeKpE4hrerCXzmGSNmmgVEDajGoPic2FV1oT+dF12TtkBQaY0hRnZ6Jwxrk0J4OkYqE9uLnSFNHAZ7nSSghIG9+Osj73ouPxP+eOQWWYYiN7jsnTxIht2mj++MHZ07Bl47eC6cEfCaSfjUZ/O+ZU0RJDHUuhXWk9PORe+j0fqaO6i/esfo7MurzZZS+CJ8qDZdp4+TcPy63PLtcCvdk7TBrL88KqKroIVW450LrVDUuSboZ34YkTgfwjUHnbauSjTFsAd/AcBwVkXJESEmEKIJDeN01Op9pRIm0FHZVnbh+NRn8/vzpmDisXnpu3SVH3K8OOYtFpGxTCvXUZG1t6IcbZ/uP6o+87d83N+Zau0qpG1/nNIiU+FszvxvyGSmsSzr5lP1GRErIPP6No3FBUFiW3gPpM476DqjNwjQNMQfC0F4Q+lZ0ZBwipRs714t8XyKhIshc1LpK9Tnbr2uoIH17scSL+jiOVNFRypqEBnJNbPJItO4YoL9v2zKQs0LOYxJHSj1nGkOqXLHVnSl9d2TbQZKIabRwM3aIzuTtEPqkCUWbsU4xAb5hFBZzixo7JEOChd7aVRI1iAZq4vucbMgNAVr7/NzkxR2+10BBgqdwoS60R9lRgh+WkT1U7r0vWt+CWQv0jS7rFI4Uzx6ry4bnJIPRUhazf29RtEhHnq9h5RLGKpsrnXf/Uf3wxg9OxJeO3ksuf6BBpLqKDp6cvyHM2ktALLZ1FOC4XmRTke6H/Z7mG31vmqFizNkmzpo2EvOuOhkThzWgMZ/B5aftE8mioXdCm1YlHKnHvv4hSeGF7zlMx44gUsE74saOLjOGPlOfV6uCSOlEznozBGF9yshGcX9qaG+PARpDyqZno39nBU1GalwIgz/3JIVN5S1ESCImtKdDpJo6irBNQ6wJh3pxap7vnppehgKRiiGb26bc56y76AoDURfyovUaMaRMQzakMqaWr8V1CSHxJdeTQqEtncWy4W4SPpfUeamb3/U5G499/WjteHQInMhi7HakivfcQeSRAsA3pHK2KXQ6rTe+llRR94YQHQrnxDnTR0OVPTXOgorM1gcFe3UGFuA/J7/sS3RcHQVHGls+EzrPqrO0sbULNzy+UEIU+TzRcqRMueBnXLguy36bU/Yc/fHpw387S/ruyLaDJCWQkBFSkwnJ5nyiUchFhNRiDanQqycyo04J/M8ZU3DeIaNx4pRh+MSho3Hnfx+O0/YfHjluGuthV45HRGMyDQOXHLc33r3qZFGxnDcoJSk5rqi/QverHkPyr7lr8fbqZgyuz2LWN46WvqN2AXQe/pw5GtCoeHVAqLB0FY31ob1Qwe+3h+zVUUFQwEerbMsUhiSgf35XPjgPX/zrHMxZ4TdrTtpEmzqKcLyop6UWrwSAYyYOiaBFfKOjZ6WiW5E6Ueo5KgjtTR7eKP3NkcZwTPrQHs33tF4gjZs4UnkFkeIGjETWtk3814Gj8OYPTsS+I/uJDUANaeiQHzPGsCApaBCpw/capD1Wrk4d73ERCprVOCbh76MlHToKJdF+hIzQ8w7xa+xMHF4vjlsVVG+fOLQeqlhsHnGpD9ZExpbbLXUxROrsg0bh+6fJiTECgdaQpS3TEKh2TcbSGmL8OVmmX3HfcT1sag2zGlu6ipIx//3TJuO+Lx8ZOReghPZiUB0u9XlbQqV5eEqnO6jZ7sqt7VK9Kh5+HlgrG1IdBZ80Tc+ebCLe41IVdU7QmqUp8fOPTcNoTb05XZFL1WDyW5Z5EQoAPeParAXDiCYkAMDfvniY9FxztiV4YUco6+Ksm17Ab55Zhjfe36a9L04RCb83RD06IF530LMzDeZoJxjbDTk9ctqXpO+ObDuIjrtDYjNURnCkgoKcQBjS69SE9njLB9f1xIunGLxukxtcn8N1Z09FPuNP/CPGD9J6/hcdsxeOnTQEWUVJkvCFHNYgcmEGXiV5xsQb4pO7SIiUTeTReGSJpCGfwd7DGqTPVESKy5Vn7ouGvI0hDTkRsuRoBy0qHZdCH9oLlc3+zJCaf/XJgl/DZfLwcKy6TJc1TZ2x36nS2lWC63qx3BXAR2qe+86xuOX86YLfRsaQaTADJUYpqBsAGQN7D/XvQ712WJCz/FKmceRskyFZ8u9mBAkCew/zN/Jy5N1xg+rwuSPH4g+fPQSAjEjxNjJ/++LhOP/wMQBkAjK9/wFKr8KIIWWakR514rsYdEhwpNgGO3pgLcYMqsW0ILSy91CZ5A/E882A0POna9KSHc4Mdr8Uhb92hjTkYBhAR7eDps6i1KrpzGkjseK60zG0IfztyfsOR8428engWf36vANEyCfOaCakJWMaEtmcI1L5jIULjx6Pu790BD4WFNuMy3YknUf3WpO1Y0I5MoJEiNSm1m7xPFu7SuJZjeiXx4VHjxdlDVSR2zMpzoouNKk4IRwB5RszlZIxDAMThtTj3jfWiB6QKtJG851fv7mzKMJyIQ+TDKnofcQ5QzQnRg+slcZ+5rSRuOzUydoQqIrMNuRtn9CvGFI1Ck9VVQc3nDMVh4wdKBlDuYyJzxwxBkfsNQjnHiojZFTig3dC4NOOUNTPzxiHE/bxE7tsS+51GAc2kO5rZE5FksNGBvIHob0+Ikn1CkPOR1ggM5+xBKGSNkCa2HxC/vZTB+HigMjoep5Q3HcFVcCTFHM56V+bxZ8uOBQTh9ULmFfXkgAINwyuTGnxakN7TlBQ05QXHx2r62+r40rUxnAtAL/cwzs/PBn5jCWyp6Rq8xlSuFEiu5Ygy+59EjOSeGFSLuMGR0Mkh44bGMnqpPdbtlee50U2FXr3JHsOqvUNZMgokm2ZwhCPCw2rSpgy2n5x7jTc/MkDcazSp41uuVyzZBo7gMB4hzQ2ktOnjsDs7x6LDwc1mlQe2qcO2xOTmCFtmgZ+eNa+2GeEj34JRCpj4TxW1bghb+PI8b7Xy+uAqXNGJGoohm3GNvD0tz6MP11wSOS+VG4fyQ0fm4oJQ+sFYkPy7HeOxQNfPQorrjtdEHx5E9a4In/3ffnICB9wSEMOtVkLPzwrzBwkgwIAHvzqDJx3yGi0dZfQ3FEs28Jk72ENWPTjUzE2mLcfOWAPfPxgf5OjUUXQmmAu2ZYhkZC7S27EIDl03EBcd/ZUvHrF8QKtXbGlXTqGnMQahkjphBPCLdN/D47rYmNrN8YEocmWziIs08CfLjgE9395RuK9c0NKNeDVunYAsP8eMuLKUc+xwfXPmDoC3ztlkvj8S8eMR6HkYslGv4r7AOU6ZIypz1jVCjTXdGFZVd+rHKmGvC0Z7jd94kBcdMx4rbGqlt4QHKmiI4UV6R3RtXlHASBKEQD85z11VH/ceeHh2qb2QBhVASD0Gb+OB0+8q4wpI1JxyG4umK/ciE1CpGjP4dm3p+4Xjd7sTKmsrOkuLl5C0YmQdMfrSJkCraENsEuzEeYzFkYHHA4P4WIkqz7NJldOLDNEpGqzlhgPX7SE+MiGFMS9AGpoz5NCexyxAPQ1THSLQ5y7jMfA+8iJ3wbXog340HEDsbapE6u3dWoNUK6A4qpry+M1cdtnDsYfnl+Ol5f74bvPHDEG+47sh8fnhZyvdmqjoZCEazKWBK87rmxIvfL947XZNkCIVoSIlCEUYxwipRpYZEjVZm2cETRw5sJ77RlGsrMgjOqMGeFvcRk9sBZLg41GLXB4zX/pK7fTuw+z9kwpaSJjm2Ke8DBuXBhERaTsoLP8EE0LkLC8g3wvZ0wdqX1mXOg5NGgcBJI7vnAYpoxsxMC6bAR9rc3amH/1Kco5w76HtVkbtVkbG1u70dRRjBQwTSOqsRvn6ashxa6ioyXxWqYhoWDHThqKv770vnQeINRbvGBo3Dgs0xS9NDe3deOA0f2xYF0LuoOGycdO0hdP5cJJ/ipSpIbT7/jCYTh8r4HSZxyRmhggqiu2tEuGMaF7y4L53a82C7AG01QQVzWmKZqhcqR0zpva5obWGK2/xppMWbSdRE26qMn6yRkdBb9Yb1fRN5jIkAqbvsslYoQhxaAqTpOIM3puenqp9nO6J84Z9RGp8DxxziLpAa4fkvaOfUY0Yt7aFowfEoa7f/fp6Tjjptl4d01L7O92pPxHIVI6hIWEZxqIOlJ2WIdIbfMQVW7hYlFTSXuDSJFkmJfLF5wtGVKESLEbFYiU/5vLT5uMaaP6YUhDLiSb2+FGD4SbhK6Wj85bXxc0aSWlrSOmAuFiL+pCewGEfN4ho7X9mcQ52OLPZyzce/ERkaKoqpw4ZRgmMhTFNqMcgs6iE2wE8j2rnrHreZIXmvRuVSL4sMYc3gu8/zjFoc4rNYsvcg0K9xgGHrnkQ/hBkLo/WFPhmfbYvB2iZTqPGggNIl0xTp3UZH0eCTXsVb1rv0WQ/xk3pNQ0bXpW6nsQ4YBA+X70wD0iv4lT3GkkrnfgiutOx1F7DxbInBpCiROaFnVZS/CeCo6L/imfJ5fQ+/dFLQ1Aos7p7pKbKgPx2MlDseSaU8Xf3Kn0/69/NnyuWgEvZ3NbN4qOJxAp3bjiJKlaONEtPjxpCP7+34fhqL0HRwxKjkgR/YD6GZJQ65tlm3xDSkUI1XAhCRnGNF3jsl6BKK8pLBng30N91tbyoTjy98tzpwFAJIRnm37dte6SK83ZfHA+StD5xccPwG8/dVD4vcbZ5c5cpa1WuCFF88SAwqOKC+1pECmdc/D/DhiJ1644IZY6oqv6vrPkPxKR+sYJE/Hs4o14Y2WT+I4mbN5WQnuWPrQXJWgGhpQbVcrVMKT4OTgSwz8nj0yX3UeTcPLwRjzw1aNwwi+eRTEI7ZGxKGqkBPf2208dhA0tXfjm3W+J89HlTp86AjPfXocvHbOX4FwYhoHrz56KQ8fJniKJaI3B5r8I7XWH3cXpWerQFa6AcraJ6WMGYvoY/fW4cE/MNKLViNu7HdFGI+56QGhwkcQZIkCodEnZ7j20HvPW+h5UVkPWBGTl88Q3jpYMQJ0IRMoysM+IRuwzohF1WQtHjI8iHx5DpOgW4uYmIYRqGnmcZG0Tk4Y1YP46//7UrB7ea1FX2JUkjiPF2/Dce/ERmDYqTMIghbo9DClV1DpCXH72sWl4Kshs/ddXZmDW/A2wLRPHTR6KJ+b7n8c5GUkShoaCAo/BfX712An49slh2Eq3GaVJK+fXAMLn2F9U8/bv+SMHjJQq1XMdaFk+R2p9s29I84zatPovLl0eCMnN0/ccIBX65SIltuQzePWK4yOOAPHClsaE9uIMKbUIadigXYdIyfObfnvHFw7DQ2+tRWONrU184oYUOR1qvSjbNMT5OQJXoyBO4wbXSbSGGk1or1LhER2OspGh01l0pHURh3JlyzjcJGMG1QUcQ7oW8PtPTxfrIK6t2M6Q/yhDiibvpOF+Mb27X1sl0CNRdTgb9pnLZ8JNvVMhm0dCEsEE9jwvEnKqCiLFrlcTQ4ylGDJHkghOVjf84Y15rN7WifqcLRQiKRWCXmdM8BUWN6QIybjpvAPxq3MPiDyHjx8ikxa56LwwFZHitU10ZHd+Dh2sHid8UdtKk2rAz6ri7X361WTQ3FmMKNamjqJ03aT+hiKkR4YUM4qI/K+KbkNLErIP+e/Oi0H06HHmbFNYeXGK9aMH7YH561rwjRMnlh0DybTR/YQhRXPonOmjcM/rq6Vei0mGFJHfCZHKWn67DW4kqIbzyP55HD1xCC45bkLqsZKQko4r1aCK2g6JyznTR+GcwKmYOqo/pgbG3nmH7ok/vvAeFm9ow5AYgneSxJUCUA0P3cZVrmURCUck6DxEjKdH/+vzDpR+YysOhW2aInljzKA60bw9LSLFQzeqkH6NC2sCUaORhy9J6nI26rKW4IWpCKGOA/r414/GmEG1WNvUiS8f68+xkGwevTc1o46OmTS8AZOG+4avbtnx95kVDry8VmzLEIk5jUrR1LjxAHqOVKXCy/OQnvQRKTsYq5MOkRJk82Tzg+YhTU3P8ySEXm3uXI19tqfyH2VI0XMmpaHb9PvVZLSIFG1CnTGhPYFIeRrFV4XOinL1bFP7eYOGI6VC0iT7jmzEn15YgX1GNAhjkrw3TiqMCPF+TANm0nEa0Sn1rMKRoj5/cZLktSYJf1+mYUhVmQFfCfSvzeD8I8ZgS3sBQxtyuPrh+RHjr7WrJGWvJG0SgocU/IOn3sd5a7akiMo/33K99riEHClLvLm439Vmbfwkhg8VJ3sODD1g2tSu/ej++PZJk/x2FAkFW0no9rsDQ0qEUhKehW2Z+OvnD61orKqkRaRow0pcIxqhe47j0yWJQKSCv2le6JoNq5IWkdKdhxADqocXGZcma4+M5OH98hhcn8PG1u7UGxwvKqlKmLEY//u04alcxhJFfdX+nzpnj5Ja/odVvCdEWW9IKYhUwrimSQWjw5sjB47a2Ihzmayxcz4scEw8tjh9JIrXpsjujRNesiE0zEzxzNQWNHGG1LoAtSy3Fmh+xa01MtoBaqvWs72hGvIfxZG66qz9cN4ho/HhSUMi3517yGhcdMx4fOXYCcyQMiMGU1dMfR3ymGizuv7sqeK76iBS3JDiHKlwHLQZ8PCUq5AkSfYZ0YiC42ev0DmIDxTXWwxAhduHLGqxSYCXP/CvmbVDwqIuW0in6NIIT/O3TVOLJFmGgXzGwmWnThbX0RHa03KkVGPloD3DcFQ82Tw8X5p0X7HBpNhEXIZIqWHHagjnZYk2IpYpeCm6TV1FaCgkSJu3qKO1nVKf6e7TNm2tEVXJK+NnEMI2vAeGlFqigtZrtJ5ZdQwpQhOnB2UK4ja8aB2p8O8hDTnxu6QeoPL5/PDw2QeNinxH81RXpeTW86fj6yfsneoa6rhVHVNprSJdaE8N28XpiFevOB53XXiE+JsbgqTLVUOKr9ewPIXFEDv9tQgNrgTFV2UUK4p7+tQR+NIxe+F7J4e6siNlaO/AoDbiuQqQcYbS45LulVDe4/eRM635Pq7rSbgj5T8KkRreL4/rmIHDhTZQIFxcNaypIwllUWSUBcfJ5kBYh4d/1xvhi5EvfqmyecDH4BP0uMlDsXB9KwY3yBA2wfYcjh0U8GGSGo3qFEda0RlB9HzJQ6xlneZ1CJZABCocBifomqbegODPkjbKWs0Gy5VR0iYR1ngiiJoZSSnqSKUK7ZUJ0XEhVZOzOSJVPQOlXNiKpzgfMnYArv7IfhEOGJVReGuVz1+spLxDT4ReSWPK0B559moLmHJCPR2HNVYe2lPT52mDUnlovQntcaHMto8etAcmDK3HVE07E39cDJFiPUZrs37DauIjVTLFHleK/YrzC0MqakmdtO9wnLRv+nR4NeOaC7+n+pwdW0eNDLo0TnLcMbrQIwnNR9KL44fUoSGfkdZ5/6DNWG3WEvoqbj2rRrcuGSVJDh0XdssA/Gd4+al+3T7SyZ2FUqrQ3qcPH4Nzpo+OjOnmTx6E4yavxq3PLcfC9a3i91NGNmLFdadHznPr+QfjttnLccPjiypej9WWXhlShmHcAOBMAAUAywBc4HleU/Kv+r5MGdmI7582GUdPHILFG9qk70ghqoo9RKT8v/kCrUZoz45Z/Oo4/vg5uc7Ot06ahM8eOTayaLkSJpj6wqP3wua2blE4UZVDxw7EdWdXFu6RrqlR6oZhIGebDGq3w6whnSEVIAJp+3eR8OentjIgkQyp4EXWaq7D32eSHiUjhxeCJe5VHNrEN0PVWE+6RhqF7gllawijrpoGSllDireGsC1hNHEZUJfF2EG1gmuVsU2g4FSMFFQqaUN7FBqpFJH68KQh+NsrKxM3zzgRWXvBNccNrsPnZ4zD0RNlZF1nTPcEkSKKgGEYUmcFVfj8tKwwXE7zYGiFiFSS0DytBvKQlB3I19Hc/z0x9hykH3SO5cC6rNBn6jnTCvGHqI7TA189CvU5G9fMnC+OGUE10LK2aF107sF6jiq/zzv/+3CMTwij6uTuLx0R+92REwbjgNH98e2TJ0l1r+IMKcMwYikaHz1oFF5bsRUL17eWdQ6zrHtCMSklfwdIb2f4LAD7eZ43FcBiAJf3fkg7XyzTwIVHj0dt1o6FJ+PbAESb3/Ymm0icP4YjVQ6qtUxDC83zc5Ciq8/5vJg44u1NnzxQSmuuVOLCcjnbxJZA8dQzQyqvOZ7OUWmITw5D6JUb/2xCQHw9eGy0CjPfF5J4GZS0wHX/6IG+wourpK4j/SYJTa10oT1S/tGwYzWEajzFGT1yU9r46/K2Pv1Eo+vtG9pLu0ZpvbkVbuhXnrkvZn/3WKmyeVqhZyVaxFgm/vfMKRHDVZfAkKb8QU9FKsjJEClCogj16E04SZyfDNgqGFL8XasGNM+mta14vqZI4tF8/dDXjhJlSPxjKrv/vYbUibDdtiC0R/qfI06k12syFoY25LH8J6fhk4fpE014QdMjxg+S1hjJ/5y+D677aNRRvooVm9VJfc7Gv74yA5OHN5btd5hGCKxIw+civbCzSyH0CpHyPO8J9ufLAM7p3XD6npTLPAiPk+F3bqj0JOVZFb6RJDV4TCs9MfR6axDGF2izRCaKT7IMjFHNhizCrhUaUlKGUcwC5cccOWEwnvrWMdhrcB2+c8/b0nFpw5t//cJheGDuGglG/92npuN3zy6TqoPHSRpFEtfqRSci8YAx3aqJSA2qz2Hy8AZceryeryIZUgnj5QakMKSqEB5PEvWVPvjVGdr3TFO4UmQka5sYPTDalDaN0LPScQy51Oeia0K3huLkc0eOrSjko5LN6R2RgUc6Jqk1V/prVQ+RyjCiOOdAfuGocTh67yh/ViczJgzGpGEN2qzWPfrX4JiJg/Gj4O9KIhLzrjpZ9C2szVoiA1DXsJrKPZBTqTNYxw+pw7JN7ak4hl/80F5o7y7hsvvekT7/7JFjU4+fr/GetnShFmJp1jwdo9ad29FSTY7U5wH8o4rn6xMS38ojmWzOQ2fV8Mj4htfTzDUu3JCKq2mkyvYKr9DiMww/lEblG3T3STqpNlPZ1JWUfoxiU99TXDp2Wg9zwtB6fOukSdJnowfWps6GSzNvTIFSlD/2a8ftjYvueB1jB9cmVjbvqVimgce+rue4AP47sEwDjuslzjluFJIhVQ0kQieGCL/Kn08dpQ9pWT0M7fVG4sodqKIWAgYqQ6R+WAZ5UMVWyOYhIiUnF1QDLSCjtpqIlG0aqGXGJ0eRykm/mkwsnwuQ0cGkEimq8HIrDXlbGFIhIuX/vzFvh10PEhIl/nnRkZEWQElSKWVClTQcqXJSdOV6acnXq56B3RspO1LDMJ40DONdzX8fYcdcAaAE4G8J57nQMIw5hmHM2bRpU3VGvwMkjmMQ4UhFEKnqQupcaakk056ILrRXTrZX00h6xnVBv7xOTU9BElLS5x0aX69KJ9wIjDMe0qIzvSHcV1usCjhSp+w3HCuuOx0N+UykD+COkqzYxBIQKak2mm9I6XoxVkPoSmnVMD3vSkN7vRGal+XC2bpikvmEHma9FY6YmkZoMKmIlK7VVKVCJP1KSdI6oXFnLDNVm6meiKRveqgviHCu4zT2r80KXtSJU4bpTwCfrxXXJFonvXX6MynD90ly2n5+9t7UPfRJDlzC0F4fR6Q8zzsh6XvDMD4L4AwAx3sJGK7nebcCuBUADj744L5T272MxFno0dCejEj1hOSZJHEcqZ4KN8bSh/Z6v+lOG90/0iOLQpVU04XacUwYGkWEhjTksPBHp1T8fHMpDKm0BlJfMqRoc61YWQtEavuSuFXJZfzGzUlK1taE9qjO2M6WySP8kOxxk8v3jquWEKJRDi3QlXCoBg0gTvh7MgxDlDAZFKxfWnPFKiBS/3XgHrAtE6dVoVmtFNpLWfaiUknjuJWToY05LNnYJv2eUJrarIUJQxsw539OEM97e0ilY+eh5J4iUqdPHYHT9j8tVV2wjAjt7cIcKcMwTgHwPQDHeJ7XUe74XVHikKVoaE8mm1cjnCedP6ayeU9F4kilDO1V2o9JJw98JdoBnu6HlNpJU4bhTxccgmNi+Ao9QfsoG/AHAAAPb0lEQVT4hhKnHFZv69R+roplAnsOrMXKrTt/ypPRqfb3KieCbL6DjcJ+NRk0dRRju80DMlo1LkhuSJtVV6nwqsk/+9i0snzG8UPq8e5VJ6euO1UNIfSrHCKlN6S2IyKl6MC2wNilkgG0TqvBXzEMA2dNS25AnVZ4k2u1IGe1pBqG1NRR/fHC0i1SOFMN8aVt4dQT+f2np+OIvSprss3b9PTG8U671whEaidn7fVWG9wMIAdgVnDjL3ued1GvR9WHJDa0F6lsHs3QApK7ylciEiJVBS+T31dvqt1WQ6hxKG0EhpGuW3wlkoupBg8Anzh0T9z56srE1iX+uPzQrWkaePiSo0Rbm50paYqo6oRQtR0NrtE6OUSTDUnC19ZHD9oDQxpyOF0p1rc9hAr/lZMdaUQBYcuRcg6UPrS3HbP2FB1ICSP9AiOZrr29+G09FZqDlmmUJfD3VOrYu+qps0KhLf78RObmdmyHQiT34f3yFWeZVoMjVYlYuwpHKkk8z5vged5oz/MOCP7brYwowN80dZM2UtlcNC0OX+i9Fx+JJ791TFXGIXGkqoBImaYhFOGOmPBJQot1e/EVACAn1ZGS3+co1vogSeg5mYaBxnxGqvS7s4QQlEoNqRCJqfaIkuUHZ0zByH55HDlB33gWkBEp2zTx/w7cY7vN0UuO3xvDGnOxjbb7glBtnpoyCRY7GpFSeW5t3f4cHFBHiBSF9vpOc1lA5unVVUGX6oQjKj2NTqh9AIEwMrE9+8pR4U1dFmglsj2NPZLM7lD+4D9FLNOIWLyqYreU0B4ATB+TnuRXfgysiFyVlKOPSnipQ3vbS8gY6ElD17SShEilbduRs/w+Vzs6HJYk5P03d/TQkEpNs66OHDNxCF68/PjEY7gCNrazjT91VH+88v1EGuhOFwoTjeyfPE93fGhPXgeUbUthWwqn72y0QJXQgTS2W+uhaogOgaS1sT3Hfenxe///9u4+Ror6juP4+3u398CDHCDP3CEHIvIggkFBsQSRglIVa0ytJa0PRJpGU2w0xIe01tiHtGm0bdKYGK3a1toHatTYpMZSk5IYtWqL0mILVItYLaKAxgqe9tc/5jfH3t4euzc7szO7+3klm7uZndv93f72N/Od3yPnzZtUtI/qYMTRFaSU3mkxst7ZXIIv7+GCfYUX4zAyTuqU0dKns3lzb7oq0Ts3ScpNe2EglWR7f34fqbDmK+cD5LJntc41weH4+79VImzaO/DBhyWO7CsctVftGqly9BlWn6GgNS3nnzyJ9w71FF1kPV+xpr0kL7gDvfaRPlLZqC0o1FKFWh2Ar58/m189tyfy3xcbXDCYtTWjMrOKg6hq6e1srrX2si84YRy9M2/h9Adxy5+LJLxDrXToerFJ3oq5aMFknt+9v6L3KkfUBYnLkd/5M7zTG96e48B/e0ouxfL4tUt591APVz/wApCti/v0scM5Y/qxXLey/8SAR3OkRip78mt7szRCMi3NTcbnT59a8rhREWZNr8RANchHFn2Pr7N5nMLyHn7PJoxoZ/ms+EdhXr6km8uXdEf++2KBVHiurva0JVlVM9MfyJGan9sunMtXH95W9Jik+xnl1z713lFVeJHpDaRKBBK3XzK/ovcpJWwSSHLOmz4z7vrfh7f5QMoXxokdxZtOZk4IhryHn1eGKqRozTXx86sWR/77OGadjlt+TUHKlaU1pdrNVIVNifddcSpP7Xq7d7s9o017rQU1Uk/fdPSm5rS0t/bPz7CLRzX6H0V10+oT2bx9b1XeK1cP0x80ijCzWo7y5U36i53fsbPwRBBV7zDglK9WcyYFi9cONJt0HIrNpxNeCHLNxsu3nVNyBFtvIJVwXl+/8oR+oz+Tkq1LXEBNe7Xj5M4Otu45CMCymeNYljfaNqudzavRzygOxWqkiq25lzXrl05n/dLpVXmv8BpW69MfNITDHwWZNKwtx8/WLWLrngP9jkl6WGr+xSXXHM+JIDzRpd3Z/Lx5E5k7uYPuMdEXRC6l2PI2+XfU5QwTL5zDJSnXLC++Vl2cVs2ZwJYd+5iW4GceVd8ZsxVIDcaj1yzh2Vfe4Ru/3c4VS6Ym/n6bvnTGgNMb9HY2z1ofqbBpL8O1OnD0c1KWa6SqafyIdr590UnMm5zcTXg5FEiV4YAfETV97HBmTxrBmTP6D902M25ePavoc3HIr5GKq7NkWPWe9vQHZpZoEAXFRy+Fa5O9X2L+qFBTBpv2olq7aApr5k/imPbq9qspR9+mvTr4sKtoXudI5nWOZO2i4xIdsRdqaW5ioOt9OFI2q/NIZf27Vey8HDaTDmb9vnrWMaSFS0+bknYyKptHqtFMG3v0i/1VS6cxa+KIRN47/w7kyDwoFQZSvaP/6v9rUOyiMnP8Mf658jq553oDqdo/iZlZJoMoiGcpokY3pLU59UChLddE95hhfPfieammo1BrDX+/PvZNWKqRyhbVSJXhEzPGsGXHvkRnCS6l77pWwc+Ka6T8HWNryk171VCsGfS6lTOZ1zmSJceXtwxCGEAl3bTX6LLed0XKY2Y8ef2ytJPRT29NT7YqysoSNpPqHJQtCqTKcO/lp6Y+8iS/4ISTfhbr9zMYYWBYjYnTsqg11zSopUfCYFYnsWTpbluSFJ43P87giNVSwmZSlZFsUSBVhlxzEwkuol6W/PbyrlFDuXJJN2sXV9Y2HDZpHe7J1qiarApHyjRq4FktukhIksIJgMvtG5klvX2kGqA7Ri1RIFUjCjvgfu382RW/Zjgx5aGeo082Wk8GmiuqHGHrqobkJ0tNe5Kk0cOCJWyysOh4OfKnQVgwJRidtnL2+LSSI0UokKoRSXTA7fKL9SY5EWaWbNl4FiOGRO9gHTaFqsIkWaqRkiSFgdR7h7JfI7Xt1lV9zjdzJnWw85vn6mYjYxRI1YiwKrfSflH5NqyYwdQxw1g1Z0Jsr5llXaOHVvT3J3V28NSut3n9wAcxpUiK0UVCkjRqqA+kaqBpr9hC1Cof2aMcqRHh5HGtMRaitlwzn1nYpT4/ZTp3btAxfdyI6M2DUpqmP5AkhTVSInGJ5apsZtebmTOzZGajlLIXGJbkzO8ayZaNZ/G5DEwAV880KlKSlOTi6NKYKm7aM7Mu4JPA7sqTIwMJq3PTnoW80VXaPCilNcIEsZIeM+OLS6exeHp588eJlBJHH6k7gI3AIzG8lgwg7IAbZx8pkSxSrask7cbVs9JOgtSRiq7KZnYB8LpzbmtM6ZEBhJNBxtlHSiSL1LQnIrWkZI2Umf0eKDas62bgJmBlOW9kZuuB9QBTpqiPyWCFy5OoaU/qnW4WRKSWlAyknHMriu03s5OAbmCrH/XVCbxgZqc5594s8jp3AXcBLFy4sPbm5k9Zz8fB7OMtDbAunjS2dnUGFpEaErmPlHPuJWBcuG1mrwILnXP7YkiXFAgDKd2tS73TqCoRqSW6KteI48cdQ3OTsWHFCWknRSRRQ1s0T7CI1I7YzljOualxvZb01zGkhV3fWp12MkQSN7RNNVIiUjtUIyUimaKmPRGpJQqkRCRT2nMKpESkdiiQEpFMadI8UiJSQxRIiYiIiESkQEpEREQkIgVSIiIiIhEpkBIRERGJSDPfiUjmfHrBZEx9zkWkBiiQEpHMueOS+WknQUSkLGraExEREYlIgZSIiIhIRAqkRERERCJSICUiIiISkTnnqv+mZm8B/0r4bcYA+xJ+Dxk85Uv2KE+ySfmSTcqX7KlGnhznnBtb7IlUAqlqMLPnnHML006H9KV8yR7lSTYpX7JJ+ZI9aeeJmvZEREREIlIgJSIiIhJRPQdSd6WdAClK+ZI9ypNsUr5kk/Ile1LNk7rtIyUiIiKStHqukRIRERFJVF0GUmZ2jpn93cx2mtkNaaenUZhZl5k9aWbbzeyvZrbB7x9tZk+Y2Q7/c5Tfb2b2Q59PL5rZKen+B/XLzJrN7M9m9pjf7jazZ3ye/NLMWv3+Nr+90z8/Nc101zMzG2lmm8zsZV9mTldZSZ+ZfcWfv7aZ2YNm1q7yUn1m9mMz22tm2/L2Dbp8mNll/vgdZnZZEmmtu0DKzJqBHwHnArOBS81sdrqpahgfAdc552YBi4Gr/Wd/A7DZOTcD2Oy3IcijGf6xHriz+kluGBuA7Xnb3wHu8HmyH1jn968D9jvnjgfu8MdJMn4A/M45dyJwMkH+qKykyMwmA18GFjrn5gLNwGdReUnDfcA5BfsGVT7MbDRwC7AIOA24JQy+4lR3gRTBh7XTOfdP59yHwC+ANSmnqSE4595wzr3gf3+P4MIwmeDzv98fdj9wof99DfATF3gaGGlmE6uc7LpnZp3Ap4C7/bYBy4FN/pDCPAnzahNwtj9eYmRmI4ClwD0AzrkPnXMHUFnJghwwxMxywFDgDVReqs4590fgnYLdgy0fq4AnnHPvOOf2A0/QPzirWD0GUpOB1/K29/h9UkW+insB8Aww3jn3BgTBFjDOH6a8qo7vAxuB//ntY4EDzrmP/Hb+596bJ/75g/54idc04C3gXt/kereZDUNlJVXOudeB7wG7CQKog8DzqLxkxWDLR1XKTT0GUsXuBjQ0sYrMbDjwG+Ba59y7Rzu0yD7lVYzM7Dxgr3Pu+fzdRQ51ZTwn8ckBpwB3OucWAO9zpJmiGOVLFfhmnzVANzAJGEbQbFRI5SVbBsqHquRPPQZSe4CuvO1O4N8ppaXhmFkLQRD1gHPuIb/7P2EzhP+51+9XXiVvCXCBmb1K0My9nKCGaqRvuoC+n3tvnvjnO+hfvS6V2wPscc4947c3EQRWKivpWgG84px7yznXAzwEnIHKS1YMtnxUpdzUYyD1J2CGH2XRStBR8NGU09QQfN+Ae4Dtzrnb8556FAhHS1wGPJK3/wt+xMVi4GBYbSvxcM7d6JzrdM5NJSgLf3DOrQWeBC72hxXmSZhXF/vjdYcdM+fcm8BrZjbT7zob+BsqK2nbDSw2s6H+fBbmi8pLNgy2fDwOrDSzUb62caXfFy/nXN09gNXAP4BdwM1pp6dRHsCZBNWmLwJ/8Y/VBH0GNgM7/M/R/ngjGGG5C3iJYKRM6v9HvT6AZcBj/vdpwLPATuDXQJvf3+63d/rnp6Wd7np9APOB53x5eRgYpbKS/gO4FXgZ2Ab8FGhTeUklHx4k6KfWQ1CztC5K+QCu9PmzE7giibRqZnMRERGRiOqxaU9ERESkKhRIiYiIiESkQEpEREQkIgVSIiIiIhEpkBIRERGJSIGUiIiISEQKpEREREQiUiAlIiIiEtH/AfXoelQYBaJ2AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from statsmodels.tsa.arima_process import ArmaProcess\n", "\n", "# Plot 1: MA parameter: -0.9\n", "plt.subplot(2, 1, 1)\n", "ar1 = np.array([1])\n", "ma1 = np.array([1, -0.9])\n", "MA_object1 = ArmaProcess(ar1, ma1)\n", "simulated_data_1 = MA_object1.generate_sample(nsample=1000)\n", "plt.plot(simulated_data_1);\n", "\n", "# Plot 2: MA parameter: +0.9\n", "plt.subplot(2, 1, 2)\n", "ar2 = np.array([1])\n", "ma2 = np.array([1, 0.9])\n", "MA_object2 = ArmaProcess(ar2, ma2)\n", "simulated_data_2 = MA_object2.generate_sample(nsample=1000)\n", "plt.plot(simulated_data_2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compute the ACF for Several MA Time Series\n", "Unlike an AR(1), an MA(1) model has no autocorrelation beyond lag 1, an MA(2) model has no autocorrelation beyond lag 2, etc. The lag-1 autocorrelation for an MA(1) model is not $\\theta$, but rather $\\frac{\\theta}{1+\\theta^2}$. For example, if the MA parameter, $\\theta$, is = +0.9, the first-lag autocorrelation will be $\\frac{0.9}{1 + (0.9)^2} = 0.497$, and the autocorrelation at all other lags will be zero. If the MA parameter, $\\theta$, is -0.9, the first-lag autocorrelation will be $\\frac{-0.9}{1 + (-0.9)^2}$ = -0.497.\n", "\n", "You will verify these autocorrelation functions for the three time series you generated in the last exercise." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "ar3 = np.array([1])\n", "ma3 = np.array([1, -0.3])\n", "MA_object3 = ArmaProcess(ar3, ma3)\n", "simulated_data_3 = MA_object3.generate_sample(nsample=1000)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlMAAAE/CAYAAABin0ZUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAbRElEQVR4nO3df5xddZ3f8ddnZjKYENggJEhCQliJLNFqoHmA1nU3rroF64Ltw3XJtor7YA22srtW2110LVpa7Xb72GpdWStbWNCqSHetG20sblEeUiuUgBENaZbZLJgxQAIyAhIymbmf/nHv6M0wk7mZ7/09r+fjMY/cc+45537mfudk3uf7/Z47kZlIkiRpfgY6XYAkSVIvM0xJkiQVMExJkiQVMExJkiQVMExJkiQVMExJkiQVMExJWvAi4sGIeO08931VROxudk2SeodhStKcIuL2iHgiIo47hn0yIs5qZV2dMP37ysw7MvPsTtYkqbMMU5KOKiLWAq8CEri4o8XMISKGGlknSc1kmJI0l7cCdwI3ApdNraz1Vv1m3fLbIuJ/1x5/o7b6OxHxdET8Wm392yNiJCJ+GBFbI2Jl3f4vjoi/qj33aES8r7b+uIj4aETsq319dKqHLCI2RcRoRPxeRDwC/NlM62rbviEidkTEWET8n4h46UzfbEScHxHfqm33cER8PCKGZ/u+pl6vbv9zau/NWETsjIiL6567MSKujYj/ERFPRcRdEfHC+TWLpG5hmJI0l7cCn6l9/f2IOHWuHTLzF2oPX5aZSzPz8xHxS8C/A94MnAY8BNwMEBEnAP8L+J/ASuAs4LbaMX4feDmwAXgZcD7w/rqXewHwfOAMYMtM6yLiPOAG4ArgZOCTwNZZhi0ngX8OnAK8AngN8M9m+77qd4yIRcCXgK8CK4DfAj4TEfXDgJuBfw2cBIwAH5rxTZTUMwxTkmYVET9PNZDckpn3AH8D/Po8D/ePgRsy897MPAS8F3hFbRjxDcAjmflHmflsZj6VmXfV7XdNZu7PzANUg8hb6o5bAT6QmYcy8+As694OfDIz78rMycy8CThENaQdITPvycw7M3MiMx+kGrx+scHv8eXAUuAPMnM8M78GfJlqgJryhcz8v5k5QTWgbmjw2JK6lGFK0tFcBnw1Mx+rLX+WuqG+Y7SSam8UAJn5NPA4sApYTTWozblf7fHKuuUDmfnstH2mrzsDeE9t6G0sIsZqr7ly2n5ExIsi4ssR8UhEPAl8mGovVSNWAnszszKt3lV1y4/UPX6GaviS1MOcmClpRhGxmOqQ3GBt7hHAccCyiHgZ8GNgSd0uL5jjkPuohpqp4x9PdcjtB8Bejuy9mWm/nbXlNbV1U3KGfaav2wt8KDMbGVL7BPBtYHNmPhUR7wLe1MB+U7WujoiBukC1BvjrBveX1IPsmZI0mzdSnT+0nupQ1AbgHOAOqvOodgD/KCKW1D4q4PJp+z8K/Gzd8meB34iIDbW5Sh8G7qoNpX0ZeEFEvKs24fyEiLigtt/ngPdHxPKIOAW4Gvivx/i9/Cnwjoi4IKqOj4h/UJurNd0JwJPA0xHxc8A/neP7qncX1ZD5uxGxKCI2Ab9CbW6YpP5kmJI0m8uAP8vM72fmI1NfwMepzmP6CDBONVzcRHX+T70PAjfVhtXenJm3Af8K+AvgYeCFwKUAmfkU8DqqweMR4AHg1bXj/FtgO3Af8F3g3tq6hmXmdqrzpj4OPEF14vfbZtn8X1CdF/YU1RD2+WnPH/F9TXudcaofH3ER8BjwJ8BbM/P/HUu9knpLZM7UQy5JkqRG2DMlSZJUwDAlSZJUwDAlSZJUwDAlSZJUwDAlSZJUoGMf2nnKKafk2rVrO/XykiRJDbvnnnsey8zlMz3XsTC1du1atm/f3qmXlyRJalhEPDTbcw7zSZIkFTBMSZIkFTBMSZIkFTBMSZIkFTBMSZIkFTBMSZIkFTBMSZIkFZgzTEXEDRGxPyK+N8vzEREfi4iRiLgvIs5rfpnHZrKS3LbrUT522wPctutRJivZ6ZIkSVKfauRDO28EPg58apbnLwLW1b4uAD5R+7cjJivJW66/ix17xzg4Psni4UE2rF7Gpy+/gMGB6FRZkiSpT83ZM5WZ3wB+eJRNLgE+lVV3Assi4rRmFXisbt+9nx17x3hmfJIEnhmfZMfeMW7fvb9TJUmSpD7WjDlTq4C9dcujtXXPERFbImJ7RGw/cOBAE176uXbue5KD45NHrDs4Psn9+55syetJkqSFrRlhaqaxsxknKWXmdZm5MTM3Ll8+498KLPbilSeyeHjwiHWLhwdZv/LElryeJEla2JoRpkaB1XXLpwP7mnDcedl09go2rF5GTI5DVlhSmzO16ewVnSpJkiT1sWaEqa3AW2t39b0c+FFmPtyE487L4EDw6csvYPkDX2LZ6Df5483nOvlckiS1zJx380XE54BNwCkRMQp8AFgEkJn/GdgGvB4YAZ4BfqNVxTZqcCBYMraHJWN7eM05p3a6HEmS1MfmDFOZuXmO5xN4Z9MqkiRJ6iF+ArokSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVIBw5QkSVKBhsJURFwYEbsjYiQirprh+TUR8fWI+HZE3BcRr29+qZIkSd1nzjAVEYPAtcBFwHpgc0Ssn7bZ+4FbMvNc4FLgT5pdqCRJUjdqpGfqfGAkM/dk5jhwM3DJtG0SOLH2+GeAfc0rUZIkqXsNNbDNKmBv3fIocMG0bT4IfDUifgs4HnhtU6qTJEnqco30TMUM63La8mbgxsw8HXg98OmIeM6xI2JLRGyPiO0HDhw49molSZK6TCNhahRYXbd8Os8dxrscuAUgM78FPA84ZfqBMvO6zNyYmRuXL18+v4olSZK6SCNh6m5gXUScGRHDVCeYb522zfeB1wBExDlUw5RdT5Ikqe/NGaYycwK4ErgV2EX1rr2dEXFNRFxc2+w9wNsj4jvA54C3Zeb0oUBJkqS+08gEdDJzG7Bt2rqr6x7fD7yyuaVJkiR1Pz8BXZIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqUBDYSoiLoyI3RExEhFXzbLNmyPi/ojYGRGfbW6ZkiRJ3Wlorg0iYhC4FngdMArcHRFbM/P+um3WAe8FXpmZT0TEilYVLEmS1E0a6Zk6HxjJzD2ZOQ7cDFwybZu3A9dm5hMAmbm/uWVKkiR1p0bC1Cpgb93yaG1dvRcBL4qIb0bEnRFxYbMKlCRJ6mZzDvMBMcO6nOE464BNwOnAHRHxkswcO+JAEVuALQBr1qw55mIlSZK6TSM9U6PA6rrl04F9M2zzl5l5ODP/FthNNVwdITOvy8yNmblx+fLl861ZkiSpazQSpu4G1kXEmRExDFwKbJ22zReBVwNExClUh/32NLNQSZKkbjRnmMrMCeBK4FZgF3BLZu6MiGsi4uLaZrcCj0fE/cDXgX+ZmY+3qmhJkqRu0cicKTJzG7Bt2rqr6x4n8O7alyRJ0oLhJ6BLkiQVMExJkiQVMExJkiQVMExJkiQVMExJkiQVMExJkiQVMExJkiQVMExJkiQVMExJkiQVMExJkiQVMExJkiQVMExJkiQVaOgPHeu5JivJ7bv3s3Pfk7x45YlsOnsFgwPR6bIkSVKbGabmYbKSvOX6u9ixd4yD45MsHh5kw+plfPryCwxUkiQtMA7zzcPtu/ezY+8Yz4xPksAz45Ps2DvG7bv3d7o0SZLUZoapedi570kOjk8ese7g+CT373uyQxVJkqROMUzNw4tXnsji4cEj1i0eHmT9yhM7VJEkSeoUw9Q8bDp7BRtWLyMmxyErLKnNmdp09opOlyZJktrMMDUPgwPBpy+/gOUPfIllo9/kjzef6+RzSZIWKO/mm6fBgWDJ2B6WjO3hNeec2ulyJElSh9gzJUmSVMAwJUmSVMAwJUmSVMAwJUmSVMAwJUmSVMAwJUmSVMAwJUmSVMAwJUmSVMAwJUmSVMAwJUmSVMAwJUmSVMAwJUmSVMAwJUmSVMAwJUmSVMAwJUmSVMAwJUmSVMAwJUmSVKChMBURF0bE7ogYiYirjrLdmyIiI2Jj80qUJEnqXnOGqYgYBK4FLgLWA5sjYv0M250A/DZwV7OLlCRJ6laN9EydD4xk5p7MHAduBi6ZYbt/A/wh8GwT65MkSepqjYSpVcDeuuXR2rqfiIhzgdWZ+eUm1iZJktT1GglTMcO6/MmTEQPAR4D3zHmgiC0RsT0ith84cKDxKiVJkrpUI2FqFFhdt3w6sK9u+QTgJcDtEfEg8HJg60yT0DPzuszcmJkbly9fPv+qJUmSukQjYepuYF1EnBkRw8ClwNapJzPzR5l5Smauzcy1wJ3AxZm5vSUVS5IkdZE5w1RmTgBXArcCu4BbMnNnRFwTERe3ukBJkqRuNtTIRpm5Ddg2bd3Vs2y7qbwsSZKk3uAnoEuSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBVoKExFxIURsTsiRiLiqhmef3dE3B8R90XEbRFxRvNLlSRJ6j5zhqmIGASuBS4C1gObI2L9tM2+DWzMzJcCfw78YbMLlSRJ6kaN9EydD4xk5p7MHAduBi6p3yAzv56Zz9QW7wROb26ZkiRJ3amRMLUK2Fu3PFpbN5vLga+UFCVJktQrhhrYJmZYlzNuGPFPgI3AL87y/BZgC8CaNWsaLFGSJKl7NdIzNQqsrls+Hdg3faOIeC3w+8DFmXlopgNl5nWZuTEzNy5fvnw+9UqSJHWVRsLU3cC6iDgzIoaBS4Gt9RtExLnAJ6kGqf3NL1OSJKk7zRmmMnMCuBK4FdgF3JKZOyPimoi4uLbZfwCWAv8tInZExNZZDidJktRXGpkzRWZuA7ZNW3d13ePXNrkuSZKknuAnoEuSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUwTEmSJBUY6nQBC93hyQoTk8n4ZIXDta8jlieSSuYxH/fY9+g/OY/3DTr/3s2zbHWNhdeAzf6Z7cV3sFnvwXz/32qnbqtw2ZJF/NwLTuxoDYapFjhcF4TGJytMVH76eHpY6oHzRpKkrtUNv0cNUw3ITA5P5nOC0LOHJ0lg18NP/jRATWZXNKwkSWoPw1Sd8YkKD//oIIcnK4xP1MJTZfaAND5RAWDsmcNtrlSSJHULw1Sdw5MV9o092+kydIwqlWTH3jEefPzHrD35eDasXsbAQHS6LEnSAmGYUk+rVJIPf2UXI/ufZnyiwvDQAGetWMr7LjrHQCW1mBcyUpVhSj1tx94xRvY/zaHakOuhiQoj+59mx94xzjvjpA5XJ/UvL2QWHsPz7AxT6mkPPv7jn8xdmzI+UeHBx39smJJayAuZhcXwfHR+aGcXq1SSex96gi/cO8q9Dz1BpeJtgtOtPfl4hoeO/DEeHhpg7cnHN/V1bAvpSEe7kFH/qQ/PyZHhWfZMdS2vAhqzYfUyzlqxlJ3ffwwGhzhu0RBnrVjKhtXLmvYatoX0XFMXMofqAlUrLmTUHRwFODp7prpUv1wFtLpHZ2AgeN9F57D0/i+y+G/v4Ld/aV3TQ06/tEU72IO3cExdyDAxDlnhuNpFRjMvZNQ92jUK0KvsmepS7boKaOWEwnb16AwMBMOPj8DjI5x3xu817bhTvCJrTLva20mwjWn1+zR1IXPF77yHyaWncuU7ttgWfawdowC9zDDVpdrRhd7qX379MkHV4YzGtKO9HXJtTL9cyKh7GJ6PzmG+LtWOLvRWD1/1ywRVhzMa0472dsi1Mf30Pjl03D2mwvPih77JeWec1PQg1ctt3VDPVERcCPwnYBD4L5n5B9OePw74FPB3gceBX8vMB5tb6sLSjquAVg9f9UuPjldkjWlHezvk2ph+eZ/siVw4er2t5+yZiohB4FrgImA9sDki1k/b7HLgicw8C/gI8O+bXehC1OqrgFZPKOynHp1Wt0U/aEd7Owm2Mf3yPvVTD5uOrtfbupFhvvOBkczck5njwM3AJdO2uQS4qfb4z4HXRIS/bbpcq3/5teNOO3WPdrR3PwX0VuqX96lfpgpobr3e1pF59DHJiHgTcGFm/mZt+S3ABZl5Zd0236ttM1pb/pvaNo/Ndtznn3FOvu59NzThW5jZju/sAGDDyzY0vE8lk6cPTTS8/QP3fw+AdetfcmzFHYNWv0Zm8tcje2BwmJUrT2PpcYM0Owf3w/vUrtdopczk6UOTPHt4kuctGmxJW0N//Mz2g3a9T61s76eeneAHYwep/zUVAauWLeaE53n/VL1eP79L2npoYIAlw4NNrWcmt7zj792TmRtnrKGB/WdqjekJrJFtiIgtwBaApae9sIGXnr9jCVHz1Y5fqq1+jYjg7HWtbYt+eJ/a9Rqt+o8qM/n+Dw/yzKHDQBADweJFg6x5/uKm/4fbDz+z0PpQ2Orjt+t9amV7Lz1ukMWLBjl4eJLM6i/XxbWg0Ey9fjHWD+d3u9q6VRoJU6PA6rrl04F9s2wzGhFDwM8AP5x+oMy8DrgOYOPGjfn5K14xn5pb5seHJrhv9EedLkMLVKWSXHHr9UwuPZU3/J1fbuok93sfeoKPfe0BiOrIfiZMVpJfeemqnpqQ3E7v/Ox7Abj6d7f25PH7RTs+V6wdbdHK1+iX83u+bb1sySLOOe3Eltd3yztmf66RMHU3sC4izgR+AFwK/Pq0bbYClwHfAt4EfC3nGj+U9BNTd7I8vf6NMDjEx772QFPvZOmXu7vapVJJxk8+i8mlp3LvQ09492YHDQwE551xkj+nR9Ev53cvt/WcE9AzcwK4ErgV2AXckpk7I+KaiLi4ttn1wMkRMQK8G7iqVQVL/WjqThaGhiEGmn4nS7/c3dUO9cH24Jmv4mNfe4APf2VXUz/zZiqsHTzjlT33eTrqPp7fndfQDL7M3AZsm7bu6rrHzwK/2tzSpIWj1VeWU3d3Tf8Ml167u6sdjgi2NP+T3FvdC6mFx/O787wdQuoCrf7Ay6mPLfBv2s2t1cG21WFNC4/nd+cZpqQu0I4ry16ej9BOrQ62/TK/pV/0y/w4z+/OMkxJXcAry+7R6mDbL39mqR+0a8i1XwKbZmeYkrqEV5bdodXB1vkt3aMdQ67OkVsYDFOSNE0rg629kN2jHUOuzpFbGAxTktRm9kJ2h3YMuTpHbmFo5A8dS5LUd6aGXI8bGiCgJX8Q2s+AWhjsmZIkLUjtGHJ1jtzCYJiqE1H98g/hSNLC0OohV+fILQyGqTpLhoe44Mznc3gyOTxZqX3VP56+nAYvSdJROUeu/xmmpokIhofiOWPcM8lMJiq1cDWRjE9WmKj89PH0AGbwkiSp/ximCkQEiwaDRYMDMDz39jP2bk0khyuVIwPZZAX/7qkkSb3BMNVGiwYHqsGrARO10DU+WSHn0aVlLxjM9y2Yz/vdTDZdb1uI5142+6e2B9/DZpVc+vPT9LboAccNDXa6BMNUtxoaHGBoEBbT+R8SSZI0Oz9nSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqYBhSpIkqUB06o+6RsQB4KEWv8wpwGMtfg11D9t7YbG9Fxbbe+Ho1rY+IzOXz/REx8JUO0TE9szc2Ok61B6298Jiey8stvfC0Ytt7TCfJElSAcOUJElSgX4PU9d1ugC1le29sNjeC4vtvXD0XFv39ZwpSZKkVuv3nilJkqSW6tswFREXRsTuiBiJiKs6XY9aKyIejIjvRsSOiNje6XrUXBFxQ0Tsj4jv1a17fkT8VUQ8UPv3pE7WqOaYpa0/GBE/qJ3fOyLi9Z2sUc0TEasj4usRsSsidkbE79TW99T53ZdhKiIGgWuBi4D1wOaIWN/ZqtQGr87MDb12S60aciNw4bR1VwG3ZeY64LbasnrfjTy3rQE+Uju/N2TmtjbXpNaZAN6TmecALwfeWft93VPnd1+GKeB8YCQz92TmOHAzcEmHa5I0T5n5DeCH01ZfAtxUe3wT8Ma2FqWWmKWt1acy8+HMvLf2+ClgF7CKHju/+zVMrQL21i2P1tapfyXw1Yi4JyK2dLoYtcWpmfkwVP9DBlZ0uB611pURcV9tGLCrh3w0PxGxFjgXuIseO7/7NUzFDOu8bbG/vTIzz6M6tPvOiPiFThckqWk+AbwQ2AA8DPxRZ8tRs0XEUuAvgHdl5pOdrudY9WuYGgVW1y2fDuzrUC1qg8zcV/t3P/DfqQ71qr89GhGnAdT+3d/hetQimfloZk5mZgX4Uzy/+0pELKIapD6TmV+ore6p87tfw9TdwLqIODMihoFLga0drkktEhHHR8QJU4+BXwa+d/S91Ae2ApfVHl8G/GUHa1ELTf1SrfmHeH73jYgI4HpgV2b+x7qneur87tsP7azdOvtRYBC4ITM/1OGS1CIR8bNUe6MAhoDP2t79JSI+B2yi+tfkHwU+AHwRuAVYA3wf+NXMdOJyj5ulrTdRHeJL4EHgiqn5NOptEfHzwB3Ad4FKbfX7qM6b6pnzu2/DlCRJUjv06zCfJElSWximJEmSChimJEmSChimJEmSChimJEmSChimJEmSChimJEmSChimJEmSCvx/Ibh67xRjaiUAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from statsmodels.graphics.tsaplots import plot_acf\n", "\n", "# Plot 1: MA parameter = -0.9\n", "plot_acf(simulated_data_1, lags=20);\n", "\n", "# Plot 2: MA parameter = +0.9\n", "plot_acf(simulated_data_2, lags=20);\n", "\n", "# Plot 3: MA parameter = -0.3\n", "plot_acf(simulated_data_3, lags=20);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimation and Forecasting an MA Model\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Estimating an MA Model\n", "You will estimate the MA(1) parameter, $\\theta$, of one of the simulated series that you generated in the earlier exercise. Since the parameters are known for a simulated series, it is a good way to understand the estimation routines before applying it to real data.\n", "\n", "For simulated_data_1 with a true $\\theta$ of -0.9, you will print out the estimate of $\\theta$. In addition, you will also print out the entire output that is produced when you fit a time series, so you can get an idea of what other tests and summary statistics are available in statsmodels." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " ARMA Model Results \n", "==============================================================================\n", "Dep. Variable: y No. Observations: 1000\n", "Model: ARMA(0, 1) Log Likelihood -1405.231\n", "Method: css-mle S.D. of innovations 0.985\n", "Date: Mon, 08 Jun 2020 AIC 2816.462\n", "Time: 22:54:07 BIC 2831.185\n", "Sample: 0 HQIC 2822.058\n", " \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const -0.0055 0.003 -2.068 0.039 -0.011 -0.000\n", "ma.L1.y -0.9162 0.014 -67.856 0.000 -0.943 -0.890\n", " Roots \n", "=============================================================================\n", " Real Imaginary Modulus Frequency\n", "-----------------------------------------------------------------------------\n", "MA.1 1.0914 +0.0000j 1.0914 0.0000\n", "-----------------------------------------------------------------------------\n", "When the true theta=-0.9, the estimate of theta (and the constant) are:\n", "[-0.00545793 -0.91623848]\n" ] } ], "source": [ "from statsmodels.tsa.arima_model import ARMA\n", "\n", "# Fit an MA(1) model to the first simulated data\n", "mod = ARMA(simulated_data_1, order=(0, 1))\n", "res = mod.fit()\n", "\n", "# Print out summary information on the fit\n", "print(res.summary())\n", "\n", "# Print out the estimate for the constant and for theta\n", "print(\"When the true theta=-0.9, the estimate of theta (and the constant) are:\")\n", "print(res.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Forecasting with MA Model\n", "As you did with AR models, you will use MA models to forecast in-sample and out-of-sample data using statsmodels.\n", "\n", "For the simulated series ```simulated_data_1``` with $\\theta=−0.9$, you will plot in-sample and out-of-sample forecasts. One big difference you will see between out-of-sample forecasts with an MA(1) model and an AR(1) model is that the MA(1) forecasts more than one period in the future are simply the mean of the sample." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Forecast the first MA(1) model\n", "res.plot_predict(start=990, end=1010);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ARMA models\n", "- ARMA(1,1) model:\n", "$$ R_t = \\mu + \\phi R_{t-1} + \\epsilon_t + \\theta \\epsilon_{t-1} $$\n", "- Converting Between ARMA, AR, and MA Models\n", " - Converting AR(1) into an MA($\\infty$)\n", "$$ \\begin{aligned} R_t &= \\mu + \\phi R_{t-1} + \\epsilon_t \\\\\n", "R_t &= \\mu + \\phi( \\mu + \\phi R_{t-2} + \\epsilon_{t-1}) + \\epsilon_t \\\\\n", "&\\vdots \\\\\n", "R_t &= \\frac{\\mu}{1-\\phi} + \\epsilon_t + \\phi \\epsilon_{t-1} - \\phi^2 \\epsilon_{t-2} + \\phi^3 \\epsilon_{t-3} + \\dots \\end{aligned} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### High Frequency Stock Prices\n", "Higher frequency stock data is well modeled by an MA(1) process, so it's a nice application of the models in this chapter.\n", "\n", "The DataFrame ```intraday``` contains one day's prices (on September 1, 2017) for Sprint stock (ticker symbol \"S\") sampled at a frequency of one minute. The stock market is open for 6.5 hours (390 minutes), from 9:30am to 4:00pm.\n", "\n", "Before you can analyze the time series data, you will have to clean it up a little, which you will do in this and the next two exercises. When you look at the first few rows (see the IPython Shell), you'll notice several things. First, there are no column headers.The data is not time stamped from 9:30 to 4:00, but rather goes from 0 to 390. And you will notice that the first date is the odd-looking \"a1504272600\". The number after the \"a\" is Unix time which is the number of seconds since January 1, 1970. This is how this dataset separates each day of intraday data.\n", "\n", "If you look at the data types, you'll notice that the ```DATE``` column is an object, which here means a string. You will need to change that to numeric before you can clean up some missing data.\n", "\n", "The source of the minute data is Google Finance (see [here](https://www.quantshare.com/sa-426-6-ways-to-download-free-intraday-and-tick-data-for-the-us-stock-market) on how the data was downloaded)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Preprocess" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
01
0a15042726008.2900
118.2700
228.2800
338.2750
448.2875
\n", "
" ], "text/plain": [ " 0 1\n", "0 a1504272600 8.2900\n", "1 1 8.2700\n", "2 2 8.2800\n", "3 3 8.2750\n", "4 4 8.2875" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "intraday = pd.read_csv('./dataset/Sprint_Intraday.txt', header=None)\n", "intraday = intraday.loc[:, :1]\n", "intraday.head()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "DATE object\n", "CLOSE float64\n", "dtype: object\n" ] } ], "source": [ "# Change the first date to zero\n", "intraday.iloc[0, 0] = 0\n", "\n", "# Change the column headers to 'DATE' and 'CLOSE'\n", "intraday.columns = ['DATE', 'CLOSE']\n", "\n", "# Examine the data types for each column\n", "print(intraday.dtypes)\n", "\n", "# Convert DATE column to numeric\n", "intraday['DATE'] = pd.to_numeric(intraday['DATE'])\n", "\n", "# Make the 'DATE' column the new index\n", "intraday = intraday.set_index('DATE')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### More Data Cleaning: Missing Data\n", "When you print out the length of the DataFrame ```intraday```, you will notice that a few rows are missing. There will be missing data if there are no trades in a particular one-minute interval. One way to see which rows are missing is to take the difference of two sets: the full set of every minute and the set of the DataFrame index which contains missing rows. After filling in the missing rows, you can convert the index to time of day and then plot the data.\n", "\n", "Stocks trade at discrete one-cent increments (although a small percentage of trades occur in between the one-cent increments) rather than at continuous prices, and when you plot the data you should observe that there are long periods when the stock bounces back and forth over a one cent range. This is sometimes referred to as \"bid/ask bounce\"." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "If there were no missing rows, there would be 391 rows of minute data\n", "The actual length of the DataFrame is: 389\n", "Missing rows: {182, 14}\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Notice that some rows are missing\n", "print(\"If there were no missing rows, there would be 391 rows of minute data\")\n", "print(\"The actual length of the DataFrame is:\", len(intraday))\n", "\n", "# Everything\n", "set_everything = set(range(391))\n", "\n", "# The intraday index as a set\n", "set_intraday = set(intraday.index)\n", "\n", "# Calculate the difference\n", "set_missing = set_everything - set_intraday\n", "\n", "# Print the difference\n", "print(\"Missing rows: \", set_missing)\n", "\n", "# Fill in the missing rows\n", "intraday = intraday.reindex(range(391), method='ffill')\n", "\n", "# Change the index to the intraday times\n", "intraday.index = pd.date_range(start='2017-09-01 9:30', end='2017-09-01 16:00', freq='1min')\n", "\n", "# Plot the intraday time series\n", "intraday.plot(grid=True);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Applying an MA Model\n", "The bouncing of the stock price between bid and ask induces a negative first order autocorrelation, but no autocorrelations at lags higher than 1. You get the same ACF pattern with an MA(1) model. Therefore, you will fit an MA(1) model to the intraday stock data from the last exercise.\n", "\n", "The first step is to compute minute-by-minute returns from the prices in ```intraday```, and plot the autocorrelation function. You should observe that the ACF looks like that for an MA(1) process. Then, fit the data to an MA(1), the same way you did for simulated data." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "const -0.000002\n", "ma.L1.CLOSE -0.179272\n", "dtype: float64\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Compute returns from prices and drop the NaN\n", "returns = intraday.pct_change()\n", "returns = returns.dropna()\n", "\n", "# Plot ACF of returns with lags up to 60 minutes\n", "plot_acf(returns, lags=60);\n", "\n", "# fit the data to an MA(1) model\n", "mod = ARMA(returns, order=(0, 1))\n", "res = mod.fit()\n", "print(res.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Equivalence of AR(1) and MA($\\infty$)\n", "To better understand the relationship between MA models and AR models, you will demonstrate that an AR(1) model is equivalent to an MA($\\infty$) model with the appropriate parameters.\n", "\n", "You will simulate an MA model with parameters $0.8,0.8^2,0.8^3,\\cdots$ for a large number (30) lags and show that it has the same Autocorrelation Function as an AR(1) model with $\\phi=0.8$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlMAAAE/CAYAAABin0ZUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nO3dfXRcd33n8fdXY8ux4xgBsV2cOAmF1GunC07qE8P2ySXQJmybdDmUxt0G6HEJ7DZ9gt2WUhZodul2u9ttD4HSphsKzRZClrKtw6ZLu4BPabZx4wRBsbPCrgmREImcB+E4lj3WzHf/mJEzkiVrpDvSjMbv1zk6mvu7D/rO9ZXm43t/93cjM5EkSdL89LS7AEmSpKXMMCVJklSAYUqSJKkAw5QkSVIBhilJkqQCDFOSJEkFGKYknfMi4pGIePU81/3+iBhodU2Slg7DlKRZRcSeiHg6IlbMYZ2MiJcuZF3tMPV9ZeYXM3NTO2uS1F6GKUlnFRGXAd8PJHB9W4uZRUQsa6ZNklrJMCVpNm8E7gc+CrxporF+tupnG6bfHBF/W3/9N/XmL0fEsYj4yXr7WyLiUEQ8FRG7I2JDw/pXRMRf1+c9HhHvqreviIjfi4jh+tfvTZwhi4gdETEUEb8aEY8BfzxdW33ZH42I/ogYjYj/GxEvm+7NRsTVEfF39eW+FREfjIjemd7XxM9rWH9zfd+MRsT+iLi+Yd5HI+JDEfG/IuKZiNgbES+Z3z+LpE5hmJI0mzcCf1r/+pGIWD/bCpn5A/WXL8/M1Zn5yYh4FfAfgTcALwK+AdwFEBEXAP8H+N/ABuClwOfq2/h14BXAVuDlwNXAuxt+3HcALwAuBW6eri0irgI+ArwVeCHwh8DuGS5bVoBfBi4EXglcA/zrmd5X44oRsRy4B/grYB3w88CfRkTjZcCdwG8AzwcOAe+fdidKWjIMU5JmFBHfRy2Q3J2ZDwL/CPzUPDf3L4GPZOZDmXkS+DXglfXLiD8KPJaZv5OZJzLzmczc27DerZk5kplHqAWRmxq2WwXem5knM3Nshra3AH+YmXszs5KZHwNOUgtpk2Tmg5l5f2aOZ+Yj1ILXDzb5Hl8BrAZ+KzPLmfl54DPUAtSET2fm32fmOLWAurXJbUvqUIYpSWfzJuCvMvOJ+vTHabjUN0cbqJ2NAiAzjwFPAhcBG6kFtVnXq7/e0DB9JDNPTFlnatulwDvql95GI2K0/jM3TFmPiPiuiPhMRDwWEUeB36R2lqoZG4DBzKxOqfeihunHGl4fpxa+JC1hdsyUNK2IWEntklyp3vcIYAXQFxEvB54FVjWs8h2zbHKYWqiZ2P751C65fRMYZPLZm+nW21+fvqTeNiGnWWdq2yDw/sxs5pLah4EvATsz85mI+CXg9U2sN1HrxojoaQhUlwBfa3J9SUuQZ6YkzeTHqfUf2kLtUtRWYDPwRWr9qPqB10XEqvpQAbumrP848J0N0x8HfiYittb7Kv0msLd+Ke0zwHdExC/VO5xfEBHb6+t9Anh3RKyNiAuB9wD/fY7v5Y+At0XE9qg5PyL+eb2v1lQXAEeBYxHxT4B/Ncv7arSXWsj8lYhYHhE7gB+j3jdMUncyTEmayZuAP87MRzPzsYkv4IPU+jH9LlCmFi4+Rq3/T6P3AR+rX1Z7Q2Z+Dvh3wJ8B3wJeAtwIkJnPAK+hFjweAw4CP1Tfzn8A9gFfAf4BeKje1rTM3Eet39QHgaepdfx+8wyL/xtq/cKeoRbCPjll/qT3NeXnlKkNH3Ed8ATw+8AbM/P/zaVeSUtLZE53hlySJEnN8MyUJElSAYYpSZKkAgxTkiRJBRimJEmSCjBMSZIkFdC2QTsvvPDCvOyyy9r14yVJkpr24IMPPpGZa6eb17Ywddlll7Fv3752/XhJkqSmRcQ3ZprnZT5JkqQCDFOSJEkFGKYkSZIKMExJkiQVYJiSJEkqwDAlSZJUgGFKkiSpgFnDVER8JCJGIuKrM8yPiPhARByKiK9ExFWtL3NuKtXkcw8/zgc+d5DPPfw4lWq2uyRJktSlmhm086PAB4E/mWH+dcDl9a/twIfr39uiUk1uumMv/YOjjJUrrOwtsXVjH3fu2k6pJ9pVliRJ6lKznpnKzL8BnjrLIjcAf5I19wN9EfGiVhU4V3sGRugfHOV4uUICx8sV+gdH2TMw0q6SJElSF2tFn6mLgMGG6aF62xki4uaI2BcR+44cOdKCH32m/cNHGStXJrWNlSscGD66ID9PkiSd21oRpqa7djZtJ6XMvD0zt2XmtrVrp31WYGFXbFjDyt7SpLaVvSW2bFizID9PkiSd21oRpoaAjQ3TFwPDLdjuvOzYtI6tG/uIShmyyqp6n6kdm9a1qyRJktTFWhGmdgNvrN/V9wrg25n5rRZsd15KPcGdu7az9uA99A3dx207r7TzuSRJWjCz3s0XEZ8AdgAXRsQQ8F5gOUBm/gFwL/Ba4BBwHPiZhSq2WaWeYNXoYVaNHuaazevbXY4kSepis4apzNw5y/wEfq5lFUmSJC0hjoAuSZJUgGFKkiSpAMOUJElSAYYpSZKkAgxTkiRJBRimJEmSCjBMSZIkFWCYkiRJKsAwJUmSVIBhSpIkqQDDlCRJUgGGKUmSpAIMU5IkSQUYpiRJkgowTEmSJBVgmJIkSSrAMCVJklSAYUqSJKkAw5QkSVIBhilJkqQCDFOSJEkFGKYkSZIKMExJkiQVYJiSJEkqwDAlSZJUgGFKkiSpAMOUJElSAYYpSZKkAgxTkiRJBRimJEmSCjBMSZIkFWCYkiRJKsAwJUmSVIBhSpIkqYBl7S6gU1WqyZ6BEfYPH+WKDWvYsWkdpZ5od1mSJKnDGKamUakmN92xl/7BUcbKFVb2lti6sY87d203UEmSpEm8zDeNPQMj9A+OcrxcIYHj5Qr9g6PsGRhpd2mSJKnDNBWmIuLaiBiIiEMR8c5p5l8SEV+IiC9FxFci4rWtL3Xx7B8+yli5MqltrFzhwPDRNlUkSZI61axhKiJKwIeA64AtwM6I2DJlsXcDd2fmlcCNwO+3utDFdMWGNazsLU1qW9lbYsuGNW2qSJIkdapmzkxdDRzKzMOZWQbuAm6YskwCE0njecBw60pcfDs2rWPrxj6iUoassqreZ2rHpnXtLk2SJHWYZsLURcBgw/RQva3R+4Cfjogh4F7g51tSXZuUeoI7d21n7cF76Bu6j9t2Xmnnc0mSNK1mwtR0CSKnTO8EPpqZFwOvBe6MiDO2HRE3R8S+iNh35MiRuVe7iEo9warRw/R9836u2bzeICVJkqbVTJgaAjY2TF/MmZfxdgF3A2Tm3wHnARdO3VBm3p6Z2zJz29q1a+dXsSRJUgdpJkw9AFweES+OiF5qHcx3T1nmUeAagIjYTC1MdfapJ0mSpBaYNUxl5jhwC/BZ4GFqd+3tj4hbI+L6+mLvAN4SEV8GPgG8OTOnXgqUJEnqOk2NgJ6Z91LrWN7Y9p6G1weA721taZIkSZ3PEdAlSZIKMExJkiQVYJiSJEkqwDAlSZJUgGFKkiSpAMOUJElSAYYpSZKkAgxTkiRJBRimJEmSCjBMSZIkFWCYkiRJKsAwJUmSVIBhSpIkqQDDlCRJUgGGKUmSpAIMU5IkSQUYpiRJkgowTEmSJBVgmJIkSSrAMCVJklSAYUqSJKkAw5QkSVIBhilJkqQCDFOSJEkFLGt3Ad2sUk32DIywf/goV2xYw45N6yj1RLvLkiRJLWSYWiCVanLTHXvpHxxlrFxhZW+JrRv7uHPXdgOVJEldxMt8C2TPwAj9g6McL1dI4Hi5Qv/gKHsGRtpdmiRJaiHD1ALZP3yUsXJlUttYucKB4aNtqkiSJC0Ew9QCuWLDGlb2lia1rewtsWXDmjZVJEmSFoJhaoHs2LSOrRv7iEoZssqqep+pHZvWtbs0SZLUQoapBVLqCe7ctZ21B++hb+g+btt5pZ3PJUnqQt7Nt4BKPcGq0cOsGj3MNZvXt7scSZK0ADwzJUmSVIBhSpIkqQDDlCRJUgGGKUmSpAIMU5IkSQUYpiRJkgpoKkxFxLURMRARhyLinTMs84aIOBAR+yPi460tU5IkqTPNOs5URJSADwGvAYaAByJid2YeaFjmcuDXgO/NzKcjwmG+JUnSOaGZM1NXA4cy83BmloG7gBumLPMW4EOZ+TRAZo60tkxJkqTO1EyYuggYbJgeqrc1+i7guyLivoi4PyKunW5DEXFzROyLiH1HjhyZX8WSJEkdpJkwNd3D5HLK9DLgcmAHsBP4bxHRd8ZKmbdn5rbM3LZ27dq51ipJktRxmglTQ8DGhumLgeFplvmLzDyVmV8HBqiFK0mSpK7WTJh6ALg8Il4cEb3AjcDuKcv8OfBDABFxIbXLfodbWagkSVInmjVMZeY4cAvwWeBh4O7M3B8Rt0bE9fXFPgs8GREHgC8A/zYzn1yooiVJkjrFrEMjAGTmvcC9U9re0/A6gbfXvyRJks4ZjoAuSZJUgGFKkiSpAMOUJElSAYYpSZKkAgxTkiRJBTR1N5/ao1JN9gyMsH/4KFdsWMOOTeso9Uw3IL0kSWoXw1SHqlSTm+7YS//gKGPlCit7S2zd2Medu7YbqCRJ6iBe5utQewZG6B8c5Xi5QgLHyxX6B0fZMzDS7tIkSVIDw1SH2j98lLFyZVLbWLnCgeGjbapIkiRNxzDVoa7YsIaVvaVJbSt7S2zZsKZNFUmSpOkYpjrUjk3r2Lqxj6iUIausqveZ2rFpXbtLkyRJDQxTHarUE9y5aztrD95D39B93LbzSjufS5LUgbybr4OVeoJVo4dZNXqYazavb3c5kiRpGp6ZkiRJKsAwJUmSVIBhSpIkqQDDlCRJUgGGKUmSpAIMU5IkSQUYpiRJkgowTEmSJBVgmJIkSSrAMCVJklSAYUqSJKkAw5QkSVIBhilJkqQCDFOSJEkFGKYkSZIKWNbuArSwKtVkz8AI+4ePcsWGNezYtI5ST7S7LEmSuoZhqotVqslNd+ylf3CUsXKFlb0ltm7s485d2w1UkiS1iJf5utiegRH6B0c5Xq6QwPFyhf7BUfYMjLS7NEmSuoZhqovtHz7KWLkyqW2sXOHA8NE2VSRJUvcxTHWxKzasYWVvaVLbyt4SWzasaVNFkiR1H8NUF9uxaR1bN/YRlTJklVX1PlM7Nq1rd2mSJHUNw1QXK/UEd+7aztqD99A3dB+37bzSzueSJLWYd/N1uVJPsGr0MKtGD3PN5vXtLkeSpK7jmSlJkqQCmgpTEXFtRAxExKGIeOdZlnt9RGREbGtdiZIkSZ1r1jAVESXgQ8B1wBZgZ0RsmWa5C4BfAPa2ukhJkqRO1cyZqauBQ5l5ODPLwF3ADdMs9++B3wZOtLA+SZKkjtZMmLoIGGyYHqq3nRYRVwIbM/MzLaxNkiSp4zUTpqa7jz5Pz4zoAX4XeMesG4q4OSL2RcS+I0eONF+lJElSh2omTA0BGxumLwaGG6YvAL4b2BMRjwCvAHZP1wk9M2/PzG2ZuW3t2rXzr1qSJKlDNBOmHgAuj4gXR0QvcCOwe2JmZn47My/MzMsy8zLgfuD6zNy3IBVLkiR1kFnDVGaOA7cAnwUeBu7OzP0RcWtEXL/QBUqSJHWypkZAz8x7gXuntL1nhmV3FC9LkiRpafBxMppVpZrsGRhh//BRrtiwhh2b1vl8P0mS6gxTOqtKNbnpjr30D44yVq6wsrfE1o19PjBZkqQ6n82ns9ozMEL/4CjHyxUSOF6u0D84yp6BkXaXJklSRzBM6az2Dx9lrFyZ1DZWrnBg+GibKpIkqbMYpnRWV2xYw8re0qS2lb0ltmxY06aKJEnqLIYpndWOTevYurGPqJQhq6yq95nasWldu0uTJKkjGKZ0VqWe4M5d21l78B76hu7jtp1X2vlckqQG3s2nWZV6glWjh1k1ephrNq9vdzmSJHUUz0xJkiQVYJiSJEkqwDAlSZJUgGFKkiSpAMOUJElSAYYpSZKkAhwaQQuuUk32DIywf/goV2xYw45N6xynSpLUNQxTWlCVanLTHXvpHxxlrFxhZX0EdQf+lCR1Cy/zaUHtGRihf3CU4+UKCRwvV+gfHGXPwEi7S5MkqSUMU1pQ+4ePMlauTGobK1c4MHy0TRVJktRahiktqCs2rGFlb2lS28reEls2rGlTRZIktZZhSgtqx6Z1bN3YR1TKkFVW1ftM7di0rt2lSZLUEoYpLahST3Dnru2sPXgPfUP3cdvOK+18LknqKt7NpwVX6glWjR5m1ehhrtm8vt3lSJLUUp6ZkiRJKsAwJUmSVIBhSpIkqQDDlCRJUgF2QNeS4PP9JEmdyjCljufz/SRJnczLfOp4Pt9PktTJDFPqeD7fT5LUyQxT6ng+30+S1MkMU+p4Pt9PktTJDFPqeD7fT5LUybybT0uCz/eTJHUqz0xJkiQVYJiSJEkqwMt8Oic4grokaaEYptT1HEFdkrSQmrrMFxHXRsRARByKiHdOM//tEXEgIr4SEZ+LiEtbX6o0P46gLklaSLOGqYgoAR8CrgO2ADsjYsuUxb4EbMvMlwGfAn671YVK8+UI6pKkhdTMmamrgUOZeTgzy8BdwA2NC2TmFzLzeH3yfuDi1pYpzZ8jqEuSFlIzYeoiYLBheqjeNpNdwF8WKUpqJUdQlyQtpGY6oE/XQzenXTDip4FtwA/OMP9m4GaASy65pMkSpWImRlB/5et2UT5/Hb/z7l/2bj5JUss0c2ZqCNjYMH0xMDx1oYh4NfDrwPWZeXK6DWXm7Zm5LTO3rV27dj71SvMyMYJ63zfv55rN6w1SkqSWaSZMPQBcHhEvjohe4EZgd+MCEXEl8IfUgpS3SEmSpHPGrJf5MnM8Im4BPguUgI9k5v6IuBXYl5m7gf8MrAb+R0QAPJqZ1y9g3dKic+BPSdJ0mhq0MzPvBe6d0vaehtevbnFdUkdx4E9J0kx8Np/UBAf+lCTNxDAlNcGBPyVJMzFMSU1w4E9J0kwMU1ITHPhTkjQTw5TUhImBP9cevIe+ofu4beeVdj6XJAFN3s0n6bmBP1eNHuaazevbXY4kqUN4ZkqSJKkAz0xJi8iBPyWp+ximpEXiwJ+S1J28zCctEgf+lKTuZJiSFokDf0pSdzJMSYvEgT8lqTsZpqRF4sCfktSdDFPSInHgT0nqTt7NJy0iB/6UpO5jmJKWEMepkqTOY5iSlgjHqZKkzmSfKWmJcJwqSepMhilpiXCcKknqTIYpaYlwnCpJ6kyGKWmJcJwqSepMhilpiXCcKknqTN7NJy0hjlMlSZ3HMCWdYxyrSpJayzAlnUMcq0qSWs8+U9I5xLGqJKn1PDOlc0Jm1r5TOzvTOF2bX/9eb5mYZsr8av3F8fL4pGVy0rKTV548D8artZZvj52aPPP08mc2Nm5yvFKbeOrZ8pkrn7He5G098MhT045Vte+Rp9i6sW+6ctSkqceMpMXRW+rheauWt7UGw5RmVK0m1UwqmadDxLMnx6lmUk0ga+Eiod6W9bZaIKhmbRsAJ07VPsC//sSz5MT6JPVV6t/r0zO8PnZyHIAvPfr06XVoCD/PtdVCROM0wNGxUwD8/defmvc+OXaiVsOXB789720cr7+P+Q62ebxcW3/gsWfmvO4FK5bTu6yHk+PV0229y3pYvWI5X3v82LzqkaR26lu13DCl4jKTSjUZr079XqVSTU6OV8lMvv7Es7XQU62FmUo9LGVyOjBNzJtonzARIr4yNL8QUa5/eD/27RPzfp/PBbPqLEtqJls39vHSdavZ/+gTUFrGiuXLeOm61Wzd2Nfu0iRpyTJMdZjMWvg5ValSHq99JbUzOpVqlfFqMl55LjRVM09f9pnJyfpZoSJBRt2hpyd413WbeesvvoPK6vXc8rab2bqxjx47n0vSvBmmFklmcqqSlCtVTo1XKU+Epcpzwan2fXIwOmEQUov19AS9Tx6CJw9x1aW/2u5yJGnJM0y1UHm8yonxCidOVTh5qsrJ8Uq9jxHs/fpTdlBV16hWk/7BUR558lkue+H5nt2SdE4zTM3BxCW4E6cqnKiHpROnatMnx2v9k6aaaDNIqVtUq8lv/uXDHBo5Rnm8Su+yHl66bjXvum6zgUrSOckwNcV4pXo6ME103D4wfJQT45Va/yVDkc5x/YOjHBo5dvqOwJPjVQ6NHKN/cJSrLn1+m6uTpMV3Toepk+MVRo6enHSG6VRDZ+6Jjtvfrt9SLwkeefLZ03dnTiiPV3nkyWcNU5JaZil1Jzinw9SJU1WGnh5rdxnSknLZC8+fdqyqy154fhurktRNllp3Ah8nI2lOJsaqYrwMWWVF/Y+cY1VJapXG7gTJ5O4EnaipMBUR10bEQEQcioh3TjN/RUR8sj5/b0Rc1upCJXWGibGqVh/4c1Z+/Yv8wqsun/P/FqvV5KFvPM2nHxrioW88fXpAVkndo8jv+dm6E3SiWS/zRUQJ+BDwGmAIeCAidmfmgYbFdgFPZ+ZLI+JG4D8BP7kQBUtqvyJjVS210/eS5q7o7/lS607QzJmpq4FDmXk4M8vAXcANU5a5AfhY/fWngGsiwr+Kks6w1E7fS+eiomePi/6eL7XuBDH1qfJnLBDxeuDazPzZ+vRNwPbMvKVhma/WlxmqT/9jfZknZtruCy7dnK9510da8Bam1//lfgC2vnzrjMtUqsmz9YfGTufgga8CcPmW7553HUW30Qk1tGIb1tC6bXRCDUW2ceSZkzxxrHxG+9rVvVx4wYp516P2ykyOnawNWnze8hKrV5SYy/+pi67fqm10g1b8Wzz61BhjpypkQgSsXF7ikhesbHo7rfg9z0y+dugwlHrZsOFFM76PZT09rOotNbXNIu5+2z97MDO3TTevmTD1E8CPTAlTV2fmzzcss7++TGOYujozn5yyrZuBmwFWv+gl3/Pa9945/3fVArOFKUmt98yJcb45OjZpzLYIuKhvJRecN7cbjDshWHZDDc1+aJ1t/UefGuP4yVNAED0xpw/fouu3ahsT2v3vUWQbrdgPrfgdbeXv+Ww6IUw1846GgI0N0xcDwzMsMxQRy4DnAU9N3VBm3g7cDrBt27b85Ftf2cSPXzjfHjvFgeGjba1BOte0qs9UtZq89bN3UFm9nh/9pz887zFofu7jvwbAe35l95zXbcX6RbdRdD9M/HtUz+uD0jKOPHOS562c27/HQ994mg98/iBEredIZu0/qz/2souaGnus6Pqt2ga05rgqekwUqaEV++HTDw3xqQeHJjcmvPI7X8jrrrq46fewWH0j+1YtZ/OL1rR0m9O5+20zz2smTD0AXB4RLwa+CdwI/NSUZXYDbwL+Dng98Pmc7ZSXpHPSxN2ARQbjm/hDfWzLj0NpGR/4/MFzshN7K/bDRN8WlvUC8xvRvuhArq0YCLYV22jF/qxWk/ILX0pl9Xoe+sbTi35st2I/tKLzdyt+z5eSWTugZ+Y4cAvwWeBh4O7M3B8Rt0bE9fXF7gBeGBGHgLcDZwyfIEkTenqCqy59Pq+76mKuuvT5c/4DOykARM8524m9FfuhFbegT3z4NprLh2/R9Vu1jaL7szEIjb34+/nA5w/WzvrNofN20RpasR8mOn+vWNZDwLw7fxf9PV9KmrpwmZn3AvdOaXtPw+sTwE+0tjRJml6rHmlT9CxCu3XKWYiJD9+pl3Sa/fAtun6rtlF0f3bCWb5W7Idz7axSK5zTj5ORtDS1IgB0yqXCIoGuE4IQFP/wbcWHdyu2UXR/dkK4bVUQmjir5PM2m3NOh6kVy3pYv2YFJ05VOTleqY2HYU8vqeO1IgC04ixCu/vHdEIQatxOkQ/fVnx4F91G0f3ZSeHWILS4Zh0aYaFs27Yt9+3b15afPZPM5OR4lZOnqpwYr43RMRG0TpyqUvGRF1LHKPpE+Yk7lhp/qwN4/fdc3NQdSxNBaP+jT0BpGSuWL5vzma2JO68aP3xXLOvhF151+ZwCnZdjWqfI/mzlnar+mzZvse7mi4hCQyOcMyKC85aXOG95ieex/Iz55fFayDp5qsqJU5XTIevkeIXyuEFLWkxF//dd9CxCJ/SPAc9CtFqR/dkpZ/m0+AxTc9C7rKd2l8R5Z86rVLMesKr1M1rPvS6PV/GkltRZil5O6YT+Meo8BqFzk2GqRUo9wfkrlnH+DKPkn6pUOVWpUh6vUq5/P1XJ2nS97VTFPlvSYil6FqFT+sdIaj/D1CJZXupheamHVb0zL5OZtYBVqXJqUuiq9dcar2bD9yrjlfSMl1RAkbMIndT5W1J7GaY6SETQuyxqlxKbfN5r5pSQVUnGq5PD18TrzFr4qlSTak581aYb50manf1jJE0wTC1xEcHyUrC8hc94rFaTykTYqjIpeGUmmTw3TW16oi3r62d93sQ6tYw2MT15vYnXwBnrZb2NieVPT0+dLy0+g5AkMExpGj09Qe0hAkvLRNCDidCVp297nxraaGivLZ9Tpp/b5uTpxpUbXz43kTntIjQOQzJd/psuFOa0S86wgeZnn/VnLrYZ36N0juuE38+l4LxWnk2YJ8OUukZEEJMy4NILhJKkpWfWBx1LkiRpZoYpSZKkAgxTkiRJBRimJEmSCjBMSZIkFWCYkiRJKsAwJUmSVIBhSpIkqQDDlCRJUgGGKUmSpAIMU5IkSQVEtulJihFxBPjGAv+YC4EnFvhnnEvcn63jvmwd92XruC9bx33ZOp2yLy/NzLXTzWhbmFoMEbEvM7e1u45u4f5sHfdl67gvW8d92Truy9ZZCvvSy3ySJEkFGKYkSZIK6PYwdXu7C+gy7s/WcV+2jvuyddyXreO+bJ2O35dd3WdKkiRpoXX7mSlJkqQF1bVhKiKujYiBiDgUEe9sdz1LWUQ8EhH/EBH9EbGv3fUsNRHxkYgYiYivNrS9ICL+OiIO1r8/v501LhUz7Mv3RcQ368dnf0S8tp01LhURsTEivhARD0fE/oj4xXq7x+YcnWVfemzOUUScFxF/HxFfru/L36i3vzgi9taPy09GRG+7a23UlZf5IqIEfA14DTAEPADszMwDbS1siYqIR4BtmdkJ43wsORHxA8Ax4E8y87vrbb8NPJWZv1UP+8/PzF9tZ51LwQz78n3Ascz8L6hmqjwAAALFSURBVO2sbamJiBcBL8rMhyLiAuBB4MeBN+OxOSdn2ZdvwGNzTiIigPMz81hELAf+FvhF4O3ApzPzroj4A+DLmfnhdtbaqFvPTF0NHMrMw5lZBu4CbmhzTTpHZebfAE9Nab4B+Fj99ceo/eHVLGbYl5qHzPxWZj5Uf/0M8DBwER6bc3aWfak5yppj9cnl9a8EXgV8qt7eccdlt4api4DBhukhPLCLSOCvIuLBiLi53cV0ifWZ+S2o/SEG1rW5nqXuloj4Sv0yoJel5igiLgOuBPbisVnIlH0JHptzFhGliOgHRoC/Bv4RGM3M8foiHfeZ3q1hKqZp677rmYvnezPzKuA64Ofql1qkTvFh4CXAVuBbwO+0t5ylJSJWA38G/FJmHm13PUvZNPvSY3MeMrOSmVuBi6ldado83WKLW9XZdWuYGgI2NkxfDAy3qZYlLzOH699HgP9J7eBWMY/X+1lM9LcYaXM9S1ZmPl7/41sF/giPz6bV+6T8GfCnmfnperPH5jxMty89NovJzFFgD/AKoC8iltVnddxnereGqQeAy+u9/3uBG4Hdba5pSYqI8+sdKomI84EfBr569rXUhN3Am+qv3wT8RRtrWdImPvjr/gUen02pd/S9A3g4M/9rwyyPzTmaaV96bM5dRKyNiL7665XAq6n1QfsC8Pr6Yh13XHbl3XwA9VtQfw8oAR/JzPe3uaQlKSK+k9rZKIBlwMfdl3MTEZ8AdlB78vnjwHuBPwfuBi4BHgV+IjPtWD2LGfblDmqXURJ4BHjrRJ8fzSwivg/4IvAPQLXe/C5qfX08NufgLPtyJx6bcxIRL6PWwbxE7YTP3Zl5a/2z6C7gBcCXgJ/OzJPtq3Syrg1TkiRJi6FbL/NJkiQtCsOUJElSAYYpSZKkAgxTkiRJBRimJEmSCjBMSZIkFWCYkiRJKsAwJUmSVMD/B3K42oES4c5xAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from statsmodels.tsa.arima_process import ArmaProcess\n", "\n", "# build a list MA parameters\n", "ma = [0.8 ** i for i in range(30)]\n", "\n", "# Simulate the MA(30) model\n", "ar = np.array([1])\n", "AR_object = ArmaProcess(ar, ma)\n", "simulated_data = AR_object.generate_sample(nsample=5000)\n", "\n", "# Plot the ACF\n", "plot_acf(simulated_data, lags=30);\n", "plt.savefig('../images/arma_acf.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 }