{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Recursive least squares\n", "\n", "Recursive least squares is an expanding window version of ordinary least squares. In addition to availability of regression coefficients computed recursively, the recursively computed residuals the construction of statistics to investigate parameter instability.\n", "\n", "The `RecursiveLS` class allows computation of recursive residuals and computes CUSUM and CUSUM of squares statistics. Plotting these statistics along with reference lines denoting statistically significant deviations from the null hypothesis of stable parameters allows an easy visual indication of parameter stability.\n", "\n", "Finally, the `RecursiveLS` model allows imposing linear restrictions on the parameter vectors, and can be constructed using the formula interface." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "from pandas_datareader.data import DataReader\n", "\n", "np.set_printoptions(suppress=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 1: Copper\n", "\n", "We first consider parameter stability in the copper dataset (description below)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This data describes the world copper market from 1951 through 1975. In an\n", "example, in Gill, the outcome variable (of a 2 stage estimation) is the world\n", "consumption of copper for the 25 years. The explanatory variables are the\n", "world consumption of copper in 1000 metric tons, the constant dollar adjusted\n", "price of copper, the price of a substitute, aluminum, an index of real per\n", "capita income base 1970, an annual measure of manufacturer inventory change,\n", "and a time trend.\n", "\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/travis/miniconda/envs/statsmodels-test/lib/python3.7/site-packages/numpy/core/fromnumeric.py:2495: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n", " return ptp(axis=axis, out=out, **kwargs)\n" ] } ], "source": [ "print(sm.datasets.copper.DESCRLONG)\n", "\n", "dta = sm.datasets.copper.load_pandas().data\n", "dta.index = pd.date_range('1951-01-01', '1975-01-01', freq='AS')\n", "endog = dta['WORLDCONSUMPTION']\n", "\n", "# To the regressors in the dataset, we add a column of ones for an intercept\n", "exog = sm.add_constant(dta[['COPPERPRICE', 'INCOMEINDEX', 'ALUMPRICE', 'INVENTORYINDEX']])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, construct and fit the model, and print a summary. Although the `RLS` model computes the regression parameters recursively, so there are as many estimates as there are datapoints, the summary table only presents the regression parameters estimated on the entire sample; except for small effects from initialization of the recursions, these estimates are equivalent to OLS estimates." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Statespace Model Results \n", "==============================================================================\n", "Dep. Variable: WORLDCONSUMPTION No. Observations: 25\n", "Model: RecursiveLS Log Likelihood -154.720\n", "Date: Tue, 17 Dec 2019 R-squared: 0.965\n", "Time: 23:37:57 AIC 319.441\n", "Sample: 01-01-1951 BIC 325.535\n", " - 01-01-1975 HQIC 321.131\n", "Covariance Type: nonrobust Scale 117717.127\n", "==================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "----------------------------------------------------------------------------------\n", "const -6562.3719 2378.939 -2.759 0.006 -1.12e+04 -1899.737\n", "COPPERPRICE -13.8132 15.041 -0.918 0.358 -43.292 15.666\n", "INCOMEINDEX 1.21e+04 763.401 15.853 0.000 1.06e+04 1.36e+04\n", "ALUMPRICE 70.4146 32.678 2.155 0.031 6.367 134.462\n", "INVENTORYINDEX 311.7330 2130.084 0.146 0.884 -3863.155 4486.621\n", "===================================================================================\n", "Ljung-Box (Q): 15.65 Jarque-Bera (JB): 1.70\n", "Prob(Q): 0.68 Prob(JB): 0.43\n", "Heteroskedasticity (H): 3.38 Skew: -0.67\n", "Prob(H) (two-sided): 0.13 Kurtosis: 2.53\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Parameters and covariance matrix estimates are RLS estimates conditional on the entire sample.\n" ] } ], "source": [ "mod = sm.RecursiveLS(endog, exog)\n", "res = mod.fit()\n", "\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The recursive coefficients are available in the `recursive_coefficients` attribute. Alternatively, plots can generated using the `plot_recursive_coefficient` method." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 2.88890087 4.94795049 1558.41803037 1958.43326647\n", " -51474.95653949 -4168.95010015 -2252.61351252 -446.55910053\n", " -5288.3979429 -6942.31935003 -7846.08902378 -6643.15120355\n", " -6274.11014673 -7272.01695475 -6319.02647946 -5822.239286\n", " -6256.30902239 -6737.40445526 -6477.42840909 -5995.90746352\n", " -6450.80677247 -6022.92165976 -5258.35152305 -5320.89135907\n", " -6562.37193091]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/travis/miniconda/envs/statsmodels-test/lib/python3.7/site-packages/pandas/plotting/_matplotlib/converter.py:103: FutureWarning: Using an implicitly registered datetime converter for a matplotlib plotting method. The converter was registered by pandas on import. Future versions of pandas will require you to explicitly register matplotlib converters.\n", "\n", "To register the converters:\n", "\t>>> from pandas.plotting import register_matplotlib_converters\n", "\t>>> register_matplotlib_converters()\n", " warnings.warn(msg, FutureWarning)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "print(res.recursive_coefficients.filtered[0])\n", "res.plot_recursive_coefficient(range(mod.k_exog), alpha=None, figsize=(10,6));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The CUSUM statistic is available in the `cusum` attribute, but usually it is more convenient to visually check for parameter stability using the `plot_cusum` method. In the plot below, the CUSUM statistic does not move outside of the 5% significance bands, so we fail to reject the null hypothesis of stable parameters at the 5% level." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.69971508 0.65841243 1.24629673 2.05476031 2.39888918 3.17861979\n", " 2.67244671 2.01783214 2.46131746 2.05268637 0.95054335 -1.04505547\n", " -2.55465287 -2.29908152 -1.45289493 -1.95353994 -1.35046621 0.15789828\n", " 0.63286529 -1.48184587]\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "print(res.cusum)\n", "fig = res.plot_cusum();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another related statistic is the CUSUM of squares. It is available in the `cusum_squares` attribute, but it is similarly more convenient to check it visually, using the `plot_cusum_squares` method. In the plot below, the CUSUM of squares statistic does not move outside of the 5% significance bands, so we fail to reject the null hypothesis of stable parameters at the 5% level." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "res.plot_cusum_squares();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Example 2: Quantity theory of money\n", "\n", "The quantity theory of money suggests that \"a given change in the rate of change in the quantity of money induces ... an equal change in the rate of price inflation\" (Lucas, 1980). Following Lucas, we examine the relationship between double-sided exponentially weighted moving averages of money growth and CPI inflation. Although Lucas found the relationship between these variables to be stable, more recently it appears that the relationship is unstable; see e.g. Sargent and Surico (2010)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "start = '1959-12-01'\n", "end = '2015-01-01'\n", "m2 = DataReader('M2SL', 'fred', start=start, end=end)\n", "cpi = DataReader('CPIAUCSL', 'fred', start=start, end=end)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def ewma(series, beta, n_window):\n", " nobs = len(series)\n", " scalar = (1 - beta) / (1 + beta)\n", " ma = []\n", " k = np.arange(n_window, 0, -1)\n", " weights = np.r_[beta**k, 1, beta**k[::-1]]\n", " for t in range(n_window, nobs - n_window):\n", " window = series.iloc[t - n_window:t + n_window+1].values\n", " ma.append(scalar * np.sum(weights * window))\n", " return pd.Series(ma, name=series.name, index=series.iloc[n_window:-n_window].index)\n", "\n", "m2_ewma = ewma(np.log(m2['M2SL'].resample('QS').mean()).diff().iloc[1:], 0.95, 10*4)\n", "cpi_ewma = ewma(np.log(cpi['CPIAUCSL'].resample('QS').mean()).diff().iloc[1:], 0.95, 10*4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After constructing the moving averages using the $\\beta = 0.95$ filter of Lucas (with a window of 10 years on either side), we plot each of the series below. Although they appear to move together prior for part of the sample, after 1990 they appear to diverge." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(13,3))\n", "\n", "ax.plot(m2_ewma, label='M2 Growth (EWMA)')\n", "ax.plot(cpi_ewma, label='CPI Inflation (EWMA)')\n", "ax.legend();" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Statespace Model Results \n", "==============================================================================\n", "Dep. Variable: CPIAUCSL No. Observations: 141\n", "Model: RecursiveLS Log Likelihood 692.796\n", "Date: Tue, 17 Dec 2019 R-squared: 0.813\n", "Time: 23:38:10 AIC -1381.592\n", "Sample: 01-01-1970 BIC -1375.694\n", " - 01-01-2005 HQIC -1379.195\n", "Covariance Type: nonrobust Scale 0.000\n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const -0.0033 0.001 -5.935 0.000 -0.004 -0.002\n", "M2 0.9098 0.037 24.584 0.000 0.837 0.982\n", "===================================================================================\n", "Ljung-Box (Q): 1859.31 Jarque-Bera (JB): 18.32\n", "Prob(Q): 0.00 Prob(JB): 0.00\n", "Heteroskedasticity (H): 5.30 Skew: -0.81\n", "Prob(H) (two-sided): 0.00 Kurtosis: 2.29\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Parameters and covariance matrix estimates are RLS estimates conditional on the entire sample.\n" ] } ], "source": [ "endog = cpi_ewma\n", "exog = sm.add_constant(m2_ewma)\n", "exog.columns = ['const', 'M2']\n", "\n", "mod = sm.RecursiveLS(endog, exog)\n", "res = mod.fit()\n", "\n", "print(res.summary())" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "res.plot_recursive_coefficient(1, alpha=None);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The CUSUM plot now shows substantial deviation at the 5% level, suggesting a rejection of the null hypothesis of parameter stability." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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/VvW7oFh9Ma23H7tOXOaN7w8S7euGoZ1Ma9WG2iw1/DTwuFLqKGVz9PNr8Vy1Jicnh6ysLNPvP/zwAyEhIZVe89xzz/HSSy9RVFRESUkJUDZn/9vpmJMnT+Lu7s60adO4//772bNnT6Xne/XqxcqVK8nPzyc7O5vVq1fXyHvo3r07mzZt4vjx4wCmaZbMzEzati27VFJRIfNmjjNkyBDef/9904dUxYdeY6e15vX/HuTpZQnc4teC5Q/2lAR/A5RS/PNOA+7Odjy8eC9X8ouuvZO4YTV6M5TWeiOwsfz3Y0B0TR7fHFJTU7n99tuBsjnxiRMncuutt5qe//bbb+natatptN+9e3dCQ0MxGAyEhYVVOtbGjRuZPXs21tbWODk58eWXX1Z6vmvXrowaNYqwsDC8vb2JiooyTZlUR6tWrZg7dy5jxoyhtLQUd3d3fvzxR5566ikmT57Mv/71L/r373/Tx3nuued47LHHMBgMaK3x8fH53XWBxqa4pJRnvklg6e4U7urmxYujgrGylPYMN6qZgw3vTQhn7Ce/8Py3+3lnfBdzh9ToSKnheiY7OxsnJydyc3OJiYlh7ty5REREmDusGtFY/i7zi0p4ePFe1h1I5dEBATw2MEAuHFbTu+uO8Pa6w3x0VwTDQqW71I2SUsMNyPTp00lKSiI/P5/Jkyc3mgTfWGTmFTHti13sPHmJF0cFM7mHj7lDahQe7OfPTwdTmbU8gSjv5tJwpAZJkq9nFi9ebO4QxB9Iy8pn8mc7OZqWxbvjuzAqzNPcITUa1pYWvDU2nOHvbeGZbxKYNzlKvh3VkAYxiVifppTEzWnof4cn03O48+PtnEzPYf7krpLga0EHdyeeHNKJ9QfTWGk8Z+5wGo16n+Tt7OxIT09v8EmiKdNak56ejp1dw/wKfuh8FnfO2U5WfhH/ntpN1sDXoik9fQlr58qLKxK5nCP1DGtCvZ+uadeuHSkpKVy4IAWNGjI7OzvatWtn7jBuWOLZTO6etwMbKwuWzuxOB/eG25qvIbC0ULx+h4GR72/l5dVJ/Gts+LV3EldV75O8tbW16Q5LIepSQkomd8/fgaONJYun3YJPI27wUZ8EtXFhZh9/PthwlNHhbekj35yqpd5P1whhDntOXWbivF9wtrMidkZ3SfB17OH+HfBr5cj/fZNAjhQxqxZJ8kL8xs4Tl7hnfhxujjbEzuhOezcHc4fU5NhZW/L6GANnMvJ464fD5g6nQZMkL8SvbE9OZ/Jncbi72BI7vTttm9mbO6QmK9rXjbtv8eLzn4+TkJJp7nBqRUlJCaWlpdd+YTVIkhei3JYjF5iyII62zexZMv0WWrs2zNVAjclTtwbi5mDDiysTG/wKu6ysLDZu3Mh7773H/fffT9euXXF2djb1cagt9f7CqxB1YbXxHH+J3YdfK0f+PbUbLZxsr72TqHUudtY8OaQTf/smgRXxZxkdXv97DxUVFXH48GHi4+MxGo2MGzeOLl26sHHjRkaNGgWUVcQNCwtj5syZtb60WJK8aPIWbj/B8ysSifRqzvzJXXF1qLqzlzCPP0W1Z9GOk7y25iCDOnvgYFN/0lZqaipaa1q3bs2pU6cYPXo0SUlJFBaWrfG3trYmKCiILl260KtXL9auXYvBYMDDw6PO7uitP/+1hKhjBcUlvLgyicU7TjEg0J0PJkZgb2Np7rDEb1haKF4YGcydc7bz6ebjPDow4No71YLS0lIWLVqE0WjEaDQSHx9PWloaTzzxBLNnz8bd3Z3WrVszePBgDAYDBoOBTp06YWNjA0Dz5s0ZPHhwncdd76tQClEbUq/kM3PRbvaeymBmH3+eHNIJSwuplVKfzVy4m61HL7Lpyb61Np2mtebs2bOmRG40GvHy8uK1115Da42HhwdXrlwhJCTElMj79OlDly7mLZFcq1UolVJ2wGbAtvx4X2ut/66U8qWsK5QbsAeYpLWW+5SF2e08cYkHFu0ht7CYDydGMNwgpW0bgieGdOKHpPN8uCGZ50d2rvbxcnNzSUpKIjU1leHDhwNlPaQ3b95seo2XlxejR48Gypqc7N69mzZt2mBl1XAmQWoi0gKgv9Y6WyllDWxVSv0XeBx4W2u9RCk1B7gf+LgGzifETSkp1Xy65Rhvrj1Eu+b2/HtqNzq1ljIFDUUHdyf+FNmeRb+c5L5ePrRrfn33L/y6bWVsbCzLli3DaDRy5MgRSktLcXNz4+LFiyilmDx5MmPHjsVgMBAaGkqzZpVbErZv377G31dtq4kerxrILn9oXf6jgf7AxPLtXwAvIElemMnxizk8uTSeXScvMzSkNa/fYcDVXi6wNjSPDQpg+b4zvP3jEd4aG/a757Ozs0lISKg03ZKYmEhKSgoODg7s27ePPXv2YDAYGD9+vGnKpcJ9991Xl2+nTtTIdw6llCWwG+gAfAgkAxla64r7kVOA+r/2STQ6+UUlfLQxmTkbk7G1tuDtcWHcFt5WapU3UG1c7bm3hw9zNx9lSHtN9rljGI1Gpk+fjqenJ5999hmPPvooAC4uLhgMBiZMmEBubi4ODg68+uqrvPbaa2Z+F3WrRpK81roECFdKNQOWA1X1eKvyCq9SajowHcrmv4SoKRsOpfH37xI5dSmX0eGezBoWJB2HGqCMjAwsLCxwcXFhz549LH/hAU7vMzLkjXwALCws6N69O56enowcORIfHx/CwsLw8vL63Yd5U/xwr+lG3hlKqY3ALUAzpZRV+Wi+HXD2D/aZC8yFstU1NRmPaJqOXcjmje8PsjYxFf9Wjiye2o0eHVqaOyxxHXJzc1m5cmWl6ZZTp07xwQcf8NBDD+Hq6oqTowMxI8eSkNeMf80cxZ0Du+PgUDY/7+vrK1Vrf6MmVte0AorKE7w9MBB4A9gA3EnZCpvJwHfVPZcQV3P6Ui5zNiWzZOdpbK0seHJIJ6b19sPGSqp31DcXL16slMijo6OZOXMmxcXFjB8/HisrKwIDA+nVqxcGg4GYmBgA/P392bBhA7mFxfSZvZFVZx2YZC/1ha6mJkbybYAvyuflLYD/aK1XKaWSgCVKqX8Ae4H5NXAuIX5n/5lMPtl8jDUJ51DAXd28+HP/AFo5S2kCcyssLOTQoUNkZ2fTvXt3ADp37syBAwdMr/Hw8KBt27JLdi4uLiQkJBAQEICt7R///TnYWPFI/w48910iW45clG5dV1ETq2uMwO/uBNBaHwOiq3t8IaqitWbzkYvM3ZzMtqPpONlacV9PH6b09MVTKkea1RdffMH69euJj4/nwIEDFBUVERERwe7duwGYOHEi9vb2ppUtHh4elfYPCQm5rvOM7dqeOZuO8dYPh+gd0LJJzrdfj4azol8IoLiklFXGc8zZlMzB81l4uNjyzNBAJnTzwsVOlkTWhfz8fA4cOGC6td9oNJKWlobRaARgzZo1bNu2DYPBwNChQzEYDISH/6+N37PPPlsjcdhaWfLogACeWmbkx6RUBge3rpHjNjaS5EWDUFxSyrf7zvLhhqMcv5hDRw8nZt9pYHR4W5lzryVaa86cOWNK5I8//ji2trY888wzvPPOO0BZ796QkBC6du1KYWEhNjY2LFq0CGvruvnAHRPRlo83JfOvHw8zMMgDCylN8TuS5EW9VlxSyjd7zvDBhqOcupRLsKcLn0yKZJD8g65ROTk5WFlZYWtry/r163n55ZcxGo1cvnzZ9JqRI0cSEhLCpEmT6NGjBwaDgQ4dOmBpWbmoW10leAArSwseGxjAo0v2sTrhHCPDPOvs3A2FJHlRL2mt+SEplX9+f5DkCzmEtnVl3j1RDAhyl7nXarpy5Qo//fRTpWqKycnJrFq1imHDhmFhYUFRURHjxo0zzZuHhITg6uoKQEREBBEREWZ+F/8z0uDJRxuSeXvdYYaGtMbKUr7Z/ZokeVHv7D55iVfXHGT3ycv4t3Lkk0mRDO5cd/W3G4srV65UusV/+PDhjBgxglOnTnH77bejlKJDhw6EhYUxadIk/P39AejXrx/btm0zc/TXz8JC8ZdBHZm5aDff7jvLnZHtzB1SvSJJXtQb5zPzeXl1EquN52jlbMurt4cyNqqdjMyuoaSkhOTkZEpKSggKCiI3N5fg4GBOnDhhek2zZs3o1KkTAJ06dWLHjh0EBwfj6Ohopqhr1pBgD0LauvDu+sOMCvOU6zS/IklemF1xSSkLfznJWz8cpqiklMcGBjA9xq9edQCqb+bOnUtcXBxGo5H9+/eTl5fHHXfcwddff42DgwNDhgzB29vbNN3Srl070zcha2troqMb1+pmpRR/HdyJKZ/vZOnu09zVzdvcIdUb0jREmNW+0xnMWp5A4tkr9OnYipdGB+PdonGMLqujok/or+8KtbW15ZtvvgGgW7duHDt2jLCwMFMi79q1K8HBwWaO3Hy01tw5ZztnLuex8cm+2Fk3nS5ftdo0RIibkZlXxJtrD7Fox0ncnW35cGIEw0JbN8l594o15kePHmXmzJkAjB8/3pTQK/qEVtwxCrB+/XocHR2b5H+vP6KU4onBnZjw6S/8e8cp7u8lNWxARvKijmmtWRF/lpdXHeBSTgGTe/jw+KCOODeBG5kKCgqwtrbGwsKC5cuX8/HHH2M0GklNTTW9JiMjA1dXV3744QfS0tIICwur1CdUXNtd837h0PksNj3ZD0fbpjGOlZG8qBdOpucwa/l+th69SFg7VxZM6UpIW1dzh1UrMjIy2L59e6XploMHD5KQkEBgYCAZGRmkp6czdOhQ05RLaGioaZmiORo+NxaPD+rEHR//zBfbT/Bg3w7mDsfsJMmLWqe1ZunuFF5ckYiFUrw8OpiJ3bwbRePsvLw8EhMTTYn8nnvuISIigi1btjBq1CigrE+CwWBg1KhRppK4U6ZMYcqUKeYMvdGK9G5O/0B3Ptl0jLtv8W7y5S4kyYtalVNQzNPLjKwynuMWPzf+NTa8QRYQ01pz6tQpLC0tadeuHcePH2fYsGEcPnyY0tJSABwcHIiOjiYiIoLevXuzadMmQkNDad68uZmjb3oeH9SREe9vZf6W4/xlUEdzh2NWkuRFrUm+kM2Mhbs5diGbJ4d0YmYf/wYzei8pKWH+/Pmmui1Go5ErV67wxBNPMHv2bFq3bk1gYKCp6XNYWBh+fn5YWJStz27WrJmpBrqoeyFtXRka0pr5W49zbw8fmjs23WsacuFV1Irv95/niaXx2FhZ8P6ELvSsh52ZSktLOXbsWKV5c39/f2bPno3WGnd3dwoKCkxLFMPCwujVq1eTXqbYkBxJzWLwO5uZEePP34YGmjucWiUXXkWdKS3VvPnDIT7amExYO1c+ujuStvVgeiYjI4OEhAQuXrzI7bffDkCPHj3YsWMHULb8rmPHjqZb+5VS7N+/H3d3qZXTUAV4ODPS4MnC7SeYEePXZEfz1R7JK6XaA18CrYFSYK7W+l2llBsQC/gAJ4CxWuvLf3QckJF8Q5dfVMLj/9nHmoTzTIhuzwujgrG1qtsbUkpLS01TJgsXLmTp0qUYjUZOnjwJgJubGxcvXkQpxcKFCyksLMRgMBAcHGy6KCoaj8OpWQx+ezOP9O/A44M7mTucWlPbI/li4K9a6z1KKWdgt1LqR+BeYL3W+nWl1N+AvwFP18D5RD2UmVvE/V/sZNfJyzw7PIipvf1q/ZwZGRns3bu3UvOKgwcPkpaWhoODA4cOHeLYsWP06NGDmTNnmqZdKkyaNKnWYxTm1dHDmVuDW/P5zyeYGuPXJFfa1PicvFLqO+CD8p++WutzSqk2wEat9VU/SmUk3zBdyink7nk7OJqWzdvjwhluaFOjxy8qKuLQoUOmZP7II4/Qtm1b3nvvPR599FEAWrVqZVpvPmvWLNzc3Go0BtFw7T+TyYj3t/LE4I483D/A3OHUijqbk1dK+VDW73UH4KG1PgdQnujda/Jcon5Iy8rn7nk7OJmey6eTo+hTjYbKWmvOnz+PnZ0dzZs3Z+fOnUybNo2kpCSKiooAsLGxYfDgwbRt25bRo0cTFBRUZZ9QISqEtHWlf6A787ceZ0pP3yZzF2yFGnu3SiknYBnwmNb6yvVerFJKTQemQ9lNI6LhOJ+Zz8RPf+FcZj6fT+lKD/8bW0GTk5NjmjOv+Llw4WxLcPoAACAASURBVAIffvghDz74IG5ubrRt29bUJ9RgMNCxY0dT5yFvb2+8vaXaoLi2h/t3YMxHP/PvHSeZHuNv7nDqVI1M1yilrIFVwFqt9b/Ktx1CpmsarZTLuUz8dAeXcgr5fEpXuvpUPT2itSYlJaVSIu/ZsycPP/wwV65cwdXVFXt7e0JCQkyJfPDgwQQGNu4lb6Lu3T1vBwfPZ7H16X6NrkJlrU7XqLIh+3zgQEWCL7cCmAy8Xv7nd9U9l6gfTqbnMPHTHWTlF7FoajfC2zcDykbmiYmJ5OXl0adPH7TW+Pr6mla2APj4+JjWmbu4uHD06FF8fHx+1ydUiJr25/4dGDf3F5bEneLenk2nQmVNTNf0BCYBCUqpfeXb/o+y5P4fpdT9wCngTzVwLmFmR9OymfjpdopKNIun3cLWlV/xj3XrTKVytdZERESwe/dulFI89NBDODk5/a5PaIWKdelC1LZufi2I9nFjzqZjTOzm3WS6R8kdr+Kqft0ndGvcbr77aTvFOVfYtz+RwNYujB8/nj179pimWiruDPX1bTojJdFwbDp8gcmfxfHPOw2MjWpv7nBqjNzxKq6pok9oxbz5rFmzsLW15fnnn+fdd98FwNLOCXsPX/40ehj+LcruYl28eLHp5iMh6ruYgJYEtXFh7uZj3BnRDosGUkupOiTJN0GXLl3CwcEBOzs7vv/+e55//nlTn1AACwsLJkyYQFBQEFOmTCGqRwwf7Csk27oZS6Z3r1QDXhK8aEiUUszs48ejS/bx08E0BnZu/Etv5V9oI3f58mWWLFnCM888w/Dhw2nfvj0tWrRgw4YNANjb2+Ps7MyMGTP47LPP2L17N9nZ2QQFBQHg1SGIL8+04IpVM764r1ujbfIhmo7hoW1o28yeOZuSzR1KnZCRfCNx4cKFSmVxb7/9dkaPHk1KSgoTJkzAysqKoKAg+vTpQ1hYGB07ltXY7tOnD+vXr6/ymFn5RUz+PI4T6bksuLcrkd5SF100fFaWFkzr7csLK5PYdeISUX+w/LexkCTfwBQWFnLgwAEsLCwIDQ0lJyeHDh06cP78edNrWrduTXR0NABBQUHEx8cTGBh4Q31CS0o1j3y1l8SzV5g7KZIe9bBUsBA3a2zX9ry7/ghzNh1jniR5YW7vvfcecXFxGI1GDhw4QHFxMXfeeSdLly7F0dGRsWPH4uPjY+oT6u7+vwoSVlZWlYpyXa/X1hxgw6EL/OO2EAYENf55S9G0ONhYcU93H95df4SjaVl0cHc2d0i1RpZQ1gN5eXkkJSWZplri4+NxdHRk5cqVAERHR3P+/PlKyxQjIyMJCKidYktLd53mya+N3NvDhxdGSYMM0TilZxfQ842fGGnwZPafwswdTrXIEsp6QmvN6dOniY+P59ixY6YKihMnTuTbb78FyvqEhoSEEBb2v//ptmzZgq2tbZ3EePD8FZ79dj89/Fvw7PCgOjmnEObQwsmWsVHt+SruFH8d3InWrnbmDqlWyEi+lmRnZ+Pg4ICFhQWxsbF8+OGHGI1GMjMzgbKlXJmZmTg7O/PTTz9x+fJlDAYDfn5+ZrvFP6egmFEfbOVKfjFrHulNK+e6+WARwlxOX8qlz+wNTOvtxzPDGu6gRkbytezixYts2bKlUhGu5ORkkpKSCAwMJD8/n9LSUiZOnGiabgkJCcHZuWwesH///mZ+B2XfMmYtT+D4xRwWTe0mCV40Ce3dHBga0obFcaf484AAnBphGeLG945qUWZmpukWf6PRyNSpU4mKiuLnn39mzJgxKKUICAggPDyce+65x5TEJ0+ezOTJk80c/dXF7jzNt/vO8vigjjdcMliIhmxqb19WJ5zjPztPc1+vxleOQ5J8FUpKSjh69Ch2dnZ4e3uTnJzMgAEDKlVTbN68Of379ycqKoo+ffoQFxdH586dcXR0NGPkN+fAuSv8fUUivQNa8lC/DuYOR4g61cWrOVHezfls23Hu6e6NlWXjuke0cb2bm1RcXMw777zDfffdR1RUFE5OTgQGBvLhhx8C4OnpSY8ePXjttddYvXo1p0+fJj09nbFjxwLg6upK165dG2SCzyss4aHFe3C1t+btceFYNoFaHkL81tTefqRczmNtYqq5Q6lxTebCa2FhoalPaMVPp06deOedd9Ba4+7ujoWFhalPqMFgoHv37rW2TLG++Pt3+/li+0kWT+0mNzyJJqukVNP/rY24Odqw/MGe5g7nhjWpC69aa1JTUzEajVy6dInx48cD0L17d/bs2QOU9Qnt3LkzUVFl/02UUhw5coRmzZqZLW5z2Hb0Il9sP8mUnj6S4EWTZmmhuK+nL39fkcjuk5eI9G48d8HWVPu/z4ARQJrWOqR8mxsQC/gAJ4CxWuvLVztOdUby8+bNY8mSJaY+oQBubm5cvHgRpRSxsbGUlJSY6rZU9Altqq7kF3Hr25uxs7FkzSO9G107NCFuVG5hMd1f+4nufi2YMynS3OHckLoYyS8APgC+/NW2vwHrtdavK6X+Vv746Ro63++kpKSQmZnJyJEjTVMuoaGhVDQUHzduXG2dukF6aWUSqVkFLHughyR4ISgrdXBXNy8+3pTMyfQcvFs0vGtsVamxOXmllA+w6lcjeWnkXU/9mJTKtC938ef+Hfjr4Kv+lQjRpKReyafXGz8xMdqLF0eHmDuc63a1kXxtrq7x0FqfAyj/0/0arxd1ID27gGe+MRLs6cKf+zfui8pC3CgPFztGhnnyn10pZOYWmTucGmH2JZRKqelKqV1KqV0Vc+midmitefJrI1fyi3lrbFiTaWQsxI2Y2suPvKIS/h138tovbgBq8195avk0DeV/plX1Iq31XK11lNY6qlWrVrUYjvhs2wl+OpjGrGFBBLZ2MXc4QtRLnT1d6NWhJV/8fILC4lJzh1NttZnkVwAV9/JPBr6rxXOJa0hIyeT1/x5gUGcP7unube5whKjXpvb2JfVKASvjz5o7lGqrkSSvlPoK2A50UkqlKKXuB14HBimljgCDyh8LM0jLymfGwl20crLln3cYTCuOhBBV69OxFQHuTny65Rj16YbRm1EjSyi11hP+4KkBNXF8cfPyi0qYsXA3l3OLWDqzO80dr78FoBBNlVKKqb19eXpZAj8np9OzAd8sKFfeGrHSUs3Ty4zsPZXBv8aGEdLW1dwhCdFgjA5vS0snGz7dcszcoVSLJPlGSmvNCysT+W7fWZ4c0omhoW3MHZIQDYqdtSX3dPdh46ELHEnNMnc4N02SfCOktWb22kN8uf0k02P8eLCvv7lDEqJBuvsWb+ysLZi35bi5Q7lpkuQbmdJSzYsrk/hoYzITotvzzNBAudAqxE1yc7Thjoh2LN93hgtZBeYO56ZIkm9E8otK+Mt/9rHg5xPc38uXV24LlQQvRDXd18uXwuJSFv7SMG+OkiTfSJxMz+GOj3/mu31neerWTjw7PAgLaQAiRLX5t3JiYJA7i345SX5RibnDuWGNrp58fZJyOZfdJy9z4FwW5zPzKNFgqaC1qz1tm9nh2cze9ONqf3Olj0tLNf/ZdZpX1hzAQinmT45iQJBHDb8TIZq2qb39GD/3F5btSeGubg3rZkJJ8jVMa836A2l8+ctJNh8uq8Vjbalo7WqHtYUFhSWlpF45R1FJ5RssnG2t8GrhQIC7EwEeznT0cCbA3Yn2bg5VtuQrKdVsPXqRf/14mPjTGUT7uPHW2DDauznUyfsUoinp5utGaFtX5m85zoSuXg3qW7Ik+Rq088QlXll9gH2nM2jtYsdjAwO4NaQ1/q2csP5Vc+DSUs3F7ALOZORxNiOfsxl5nMnI4/jFHOKOX+Lbff+7ldrWygL/Vk509ChL/oXFpZzNyGPzkQukXimglbMtb48L47bwtjL/LkQtqbg56tEl+9hwKK1BfVtuMj1ea1N6dgGvrD7AN3vP4OFiy18HdWJMRNub7vqelV/EkbRsjqZmczg1i8Np2RxJzeJcZj5KgbuzLaFtm3FHRFv6B7ljayVNP4SobUUlpcT8cwPeLRxYMr27ucOppEn1eK1LWmu+2XOGf6xOIiu/mIf7deChfh2wt6le0nW2sybCqzkRXs0rbc8pKMba0kJKBAthBtaWFkzp6cOraw6y/0xmg7mDXLLFTTqZnsOk+XH8dWk8vi0dWf1Ib54Y0qnaCf5qHG2tJMELYUbjo71wsrVqUKUOZCR/gwqKS5iz8RgfbjyKraUFL98Wwl3RDetCjBDi5rjYWTOua3sW/HyCp28NxLOZvblDuiYZFt6AbUcvMvSdLby97jCDO3uw7q99mHSLtyR4IZqQKT190Frzxc8nzB3KdZGR/HU4mpbNu+uPsDL+LD4tHPjyvmhiOkoXKyGaonbNHRga2obFcaf484AAnGzrdxqt39GZUVFJKVuPXiQ27jRrk85ja2XBowMCeKCvP3bWsppFiKZsWm8/VhvPEbvzNPf38jV3OFdV60leKXUr8C5gCczTWtfbDlFaa/acusx3+86y2niO9JxCXO2teahvB6b09KGFk625QxRC1APh7ZvR1ac5n209zuTu3je9XLou1GqSV0pZAh9S1v4vBdiplFqhtU6qzfNeL60156/kE386g81HLvLTgTTOX8nHztqCgUEejA5vS5+OrWRFixDid6b29mPGwt2sTUxluKH+9muo7ZF8NHBUa30MQCm1BBgN1GiSLy3VFJWWUlyiKS753+9FJaUUlZSSlV/M+Sv5pF3J5/yVfM5l5nMqPZfjF3NIzykEwNHGkpiOrRjU2YPBwa3r/TybEMK8BgZ54NPCgU+3HGNYaOt6e8d5bWeytsDpXz1OAbrV9ElWJ5zjz1/tva7XWihobqfwcLAktIUF3n72+Lla4eNqibVlAeSfwrj7VE2HKIRohPp6ahYkZLBg1RY6taheOu3Ro0cNRVVZbSf5qj7aKtVRUEpNB6YDeHl53dRJgto4MzbQDksLhZUFWCmwtFBYKrC0AHsrhZudBc3tLHCxVVjU009cIUTDEtPelqUH81mTnE+nFk7mDqdKtZ3kU4D2v3rcDjj76xdorecCc6Gsds3NnKSDuzP/vHfAzcYohBA37d68g3y0MRnPjmH4tHQ0dzi/U9tXFHcCAUopX6WUDTAeWFHL5xRCiDozubsP1hYWfL6tfvaBrdUkr7UuBh4G1gIHgP9orRNr85xCCFGX3F3sGBXuyX92pXC5fCFHfVLrawO11mu01h211v5a61dq+3xCCFHXpsf4kVdUwhfbT5g7lN+RBeBCCFFNHT2cGRjkzoKfT5BbWGzucCqRJC+EEDXggb4dyMgtYknc6Wu/uA5JkhdCiBoQ6d2caF835m05RmFxqbnDMZEkL4QQNeSBvv6czcznu31nzB2KiSR5IYSoIX07tiKwtTNzNiVTWlo/+mdLkhdCiBqilOKBvv4kX8jhxwOp5g4HkCQvhBA1anhoG9q72fPRxmS0Nv9oXpK8EELUICtLC6bH+BN/OoPtx9LNHY4keSGEqGl/imxHSydbPtxw1NyhSJIXQoiaZmdtyYwYP7YdTWf3yUtmjUWSvBBC1IK7bvHCzdGG99abdzQvSV4IIWqBg40V9/fyZdPhC8SfzjBbHJLkhRCiltzT3RtXe2ve/8l8o3lJ8kIIUUuc7ayZ0tOHdQdSSTp7xSwxSJIXQohaNKWHL862Vnyw4YhZzl+tJK+U+pNSKlEpVaqUivrNc88opY4qpQ4ppYZUL0whhGiYXB2smdzDhzUJ5zmcmlXn56/uSH4/MAbY/OuNSqnOlLX6CwZuBT5SSllW81xCCNEg3dfLFwcbSz4ww9x8tZK81vqA1vpQFU+NBpZorQu01seBo0B0dc4lhBANlZujDZNu8WaV8SzHLmTX6blra06+LfDryvkp5duEEKJJmtrbDxsrCz7ckFyn571mkldKrVNK7a/iZ/TVdqtiW5WVepRS05VSu5RSuy5cuHC9cQshRIPSytmWidHefLvvDKfSc+vsvNdM8lrrgVrrkCp+vrvKbilA+189bgec/YPjz9VaR2mto1q1anVj0QshRAMyo48flhaKjzfV3dx8bU3XrADGK6VslVK+QAAQV0vnAmDZsmW88MILfPPNNyQnJ1NaWn/abwkhBICHix3jotrz9e4UzmTk1ck5q7uE8nalVArQHVitlFoLoLVOBP4DJAHfAw9prUuqG+zVbN68mZdeeok77riDDh064OLiQv/+/U31nJOTk8nIMN+txUIIATCzrz8AczbWzdy8qg9F7StERUXpXbt23fT+ubm5JCYmYjQaMRqN5Ofn88knnwDQu3dvtm7dire3NwaDAYPBQI8ePRg2bFhNhS+EENflb8uMfLP3DFue6oeHi121j6eU2q21jqryucaU5K9m3bp17Nq1y/QBcPDgQYYNG8aKFSsAGD16NC1atCAsLMz0IdCiRYtaiUUI0bSdSs+l31sbmdzdh+dHdq728a6W5K2qffQGYuDAgQwcOND0uKCgwDR9U1xcTF5eHqtWreLzzz83veaJJ55g9uzZlJSUEBsbi8FgoFOnTlhbW9d5/EKIxsOrhQO3hbdlcdxJHuznT0sn21o7V5NJ8r9la2uLh4cHAFZWVvzwww8ApKammkb74eHhQNl8/l133QWAtbU1nTt3xmAw8MADD9C9e3e01ihV1apRIYSo2kP9/Fm+N4VPtxzjmaFBtXaeJpvk/4iHhweDBg1i0KBBpm1+fn4kJCSYkr/RaGT9+vWMGTMGgE2bNjFu3DjTNE/FT3BwMDY2NuZ6K0KIesyvlRMjDJ4s3H6SGTH+uDnWTq5oMnPytaFiBL9v3z7ef/99jEYj+/fvJz8/H4AdO3YQHR3Ntm3b2LJliyn5t23bVkb+QggOp2Yx+O3NPNyvA08M6XTTx5E5+VpSkajDw8OZP38+ACUlJRw9epT4+HhCQ0OBspH+rFmzTPs1b94cg8HAypUrcXZ2Ji0tDScnJxwcHOr+TQghzKajhzNDQ1rzxc8nmBbjh6t9zV/vk5F8HcnIyGD//v0YjUbi4+M5fvw4a9euRSnFPffcw6JFiwgICDCN9iMiIhg+fLi5wxZC1LLEs5kMf28rfxnYkUcHBtzUMWQJZT23YcMGNm/ebPoASE5OJiQkhISEBAD+8pe/UFBQYPoACA0NxdnZ2cxRCyFqyrvrjtAroAWR3m43tb8k+QYmOzub8+fP06FDBwBuv/12NmzYQGZmpuk1kyZN4ssvvwTg+++/x9/fHz8/PywtpWy/EE2NzMk3ME5OTqYED7B8+XK01pw6dcq0usfb2xuA/Px8hg8fTmlpKQ4ODoSEhGAwGBg3blyl+wKEEE2TJPkGQimFt7c33t7ejBw50rTd2tqauLg401SP0Wjkm2++oXPnzgwcOJCTJ0/Su3fvSks7w8LCCAgIwMpK/vqFaOzkX3kDZ2lpSWRkJJGRkaZtWmtKSsrqwRUXF9O7d2+MRiNr166luLgYgK+++orx48dz5MgRVq1aZfoAkHLPQjQukuQbIaWUaZTu7+/Pv//9b6CslMPBgwcxGo3ExMQAsGXLFh5//HHTvm3atMFgMDBnzhx8fHzIysrC1tZWbuoSooGSC6+C1NTUSnf0xsfHs2HDBpo1a8bzzz/Pa6+9RlBQUKXibQMHDpSLvELUE3LhVVyVh4cHHh4eVV6oHTRoEMXFxRiNRjZt2sSiRYtwcnIyrfR56623OH36tOkDoHPnztjb29f1WxBC/AFJ8uKqevfuTe/evU2PL1++zPHjx7GwKOs3k5iYSGxsLLm5ZT0rLSwsGDx4MP/973+BstIObdq0oX379lLKQQgzqNZ0jVJqNjASKASSgSla64zy554B7gdKgEe01muvdTyZrmmYSkpKOHbsmGm6x9HRkaeeegqAdu3acebMGVxdXU1TPbfeeisjRowwc9RCNB61djOUUmow8JPWulgp9QaA1vpppVRn4CsgGvAE1gEdr9UCUJJ846K1Zvv27ZWqdxqNRu69917ee+89ioqKCAsLIygoqNIST19fX9M3BSHEtdXanLzW+odfPfwFuLP899HAEq11AXBcKXWUsoS/vTrnEw2LUooePXrQo0cP0zatNXl5ZQ2MMzMzCQ4Oxmg0mm74AnjjjTd46qmnSE9PNzVrCQ0NxdXV1SzvQ4iGrCbn5O8DYst/b0tZ0q+QUr5NNHFKKVO1zZYtW7J06VIAcnJySEpKIj4+nu7duwOwZ88eHnroIdO+Ff15X3rpJcLDwykoKMDKykpW+QhxFddM8kqpdUDrKp6apbX+rvw1s4Bi4N8Vu1Xx+irnhZRS04HpAF5eXtcRsmiMHB0d6dq1K127djVtGzhwIKdPn6401RMfH2+aylm8eDEPPvigqZTDrxu029rWXjs1IRqSaq+TV0pNBmYCA7TWueXbngHQWr9W/ngt8ILW+qrTNTInL25EXFwcsbGxpuR/4cIFANLS0mjVqhWxsbHs3bvXlPylP69orGptTl4pdSvwNNCnIsGXWwEsVkr9i7ILrwFAXHXOJcRvRUdHEx0dDZTN9aemppKYmGgqzbBr1y7effddioqKALCxsSEiIoKff/4ZpRQHDx6kefPmpl6/QjRG1V1dcxSwBdLLN/2itZ5Z/twsyubpi4HHtNb/vdbxZCQvalpRURGHDh0yFW/Lycnhgw8+AMruAdi6dSvu7u6m0X7v3r257bbbzBy1EDdG6skLUYWtW7eye/du0wdAYmIigwYNYsWKFQAMHTrU1Kqxonqnp6en3NQl6h0payBEFXr16kWvXr1Mj4uLi03lGkpKSrCxsWHbtm189dVXptc88sgjvPvuu5SUlLBgwQIMBgPBwcHSn1fUW5LkhShnZWVFixYtgLISzt999x1Q1p+3ooBbcHAwAMeOHWPq1KlAWSmHiv68Dz/8MDExMZSWlqKUklG/MDtJ8kJcQ7NmzX5Xw8ff35+jR4+apnqMRiN79uzh8uXLQFkJ51GjRhEaGmqa6jEYDISHh0sBN1GnZE5eiFqwf/9+Pv74Y9MHwJUrV4Cygm3R0dFs2bKFdevWmT4A/Pz8pJSDuGkyJy9EHQsJCeHDDz8EqNSfNzQ0FIBffvmFf/zjH5SWlgLg4OBAaGgoa9euxdXVlTNnzuDg4EDz5s3N9h5E4yAjeSHMJDc3l6SkJNNoPzk5mRUrVqCU4p577mHhwoV4eXmZVvdERERwxx13mDtsUQ/JEkohGpiff/6ZrVu3mj4ADhw4QKdOndi/fz8ADz30ELm5uZXKOUh/3qZLpmuEaGB+W72zsLCQ1NRU0+PLly+zYcMGFixYYNo2duxYYmPLagR+++23+Pn5ERgYKP15mzhJ8kI0ADY2NrRv3970ePHixUBZnZ6K5Z2enp4A5Ofnc8cdd1BaWoqVlZWpXv9dd93F0KFDTSWdZXln0yBJXogGzN3dnQEDBjBgwADTNhsbm0qN2Sv680ZGRjJ06FBOnz5NZGRkpameipu67OzszPhuRG2QOXkhmojS0lIsLCw4ceIEr7zyCkajkYSEBFMTlyVLljBu3DgOHTrEsmXLTMlf+vPWfzInL4QwrcP38fHh008/Bf7Xnzc+Pt5U4iEuLo5Zs2aZ9qvoz/v555/j7+/P5cuXsbGxwdHRse7fhLhhMpIXQvzOlStX2L9/v+mO3vj4eNasWUOzZs34+9//zssvv4y/v3+l6Z6RI0diZSXjRnOQkbwQ4oa4uLj8boVPhWHDhmFlZWX6AFi+fDkODg6mu3rfeOMNjh8/bkr+0p/XvCTJCyFuSLdu3ejWrZvpcU5ODidOnDBNB504cYLY2Fg++eQT02v69u3Lhg0bgLK6Pu7u7nTo0EH689aB6jYNeRkYDZQCacC9WuuzquwqzbvAMCC3fPueax1PpmuEaBy01qSkpJhW99ja2vL4448D0K5dO86cOYO9vT3BwcGEhYUxbNgwxowZY+aoG65au+NVKeWitb5S/vsjQGet9Uyl1DDgz5Ql+W7Au1rrblc5FCBJXoimYM+ePb9rzj5+/Hjef/99ioqK6NSpE4GBgZWqd3bs2FH6815Frc3JVyT4co5AxSfGaOBLXfYJ8otSqplSqo3W+lx1zieEaPgiIiKIiIgwPdZam/rwZmVl0bNnT4xGI+vWrTNtf/XVV3nmmWdIT083NWsJCwvD3d3dLO+hIan2nLxS6hXgHiAT6Fe+uS1w+lcvSynfJkleCFGJUspUesHNzY2FCxcCZaUcDh06hNFoNH0oxMfH88QTT5j29fDwwGAw8OqrrxIVFUVeXh4WFhbY2trW/Rupp66Z5JVS64DWVTw1S2v9ndZ6FjBLKfUM8DDwd6CqOyeqnBdSSk0HpgN4eXldb9xCiEbOxsaG0NBQU3lmgP79+1cq5VDxU/EhERsby7Rp00zTPRU/ffv2bbLNWmpsnbxSyhtYrbUOUUp9AmzUWn9V/twhoO+1pmtkTl4IUR179+7l66+/NiX/U6dOAWU1flq1asXixYuJi4urVMqhMST/WpuTV0oFaK2PlD8cBRws/30F8LBSagllF14zZT5eCFHbunTpQpcuXUyPMzIySExMNJVhTkxM5NNPPyU3Nxcouws4NDSUvXv3opRi//79ODs74+Xl1WhKOVR3dc0yoBNlSyhPAjO11mfKl1B+ANxK2RLKKVrraw7RZSQvhKhtpaWlHDt2zDTaz8rK4q233gIgJiaGLVu24OLiYhrt9+7dm/Hjx5s56quTpiFCCHEddu3a9bslnr1792blypVA2TWBilo+FT/+/v5m788rZQ2EEOI6REVFERX1v1yptSYrKwso+wbg7u5OfHw8K1asMPXnfeCBB/joo48oKSlhzpw5povF9aU/ryR5IYT4A0opXFxcgLL5+yVLlgCQl5dHUlIS8fHxBAQEAHDs2DEefvhh077t27fHYDDwl7/8hQEDBlBcXAxQ50XcJMkLIcQNsre3JzIyksjINeetAAAABu9JREFUSNO2Dh06cObMmUp38hqNRnJycgDYtm0bQ4YMITg4uNJ0T7du3XBycqq1WGVOXggh6sDBgweZP3++6QOgomfvjh07iI6OrtaxZU5eCCHMLDAwkNmzZ5sep6amkpCQUOlmr9ogSV4IIczAw8MDDw+PWj+Pedf9CCGEqFWS5IUQohGTJC+EEI2YJHkhhGjEJMkLIUQjJkleCCEaMUnyQgjRiEmSF0KIRqxelTVQSl2grC59XWoJXKzjc/4RieWP1ad4JJaq1adYoH7FU9uxeGutW1X1RL1K8uaglNr1RzUf6prE8sfqUzwSS9XqUyxQv+IxZyz/3965hlhVRXH89zeb8pE5FoU1lQoVCFFqlEUPK7Kyh0FET7K0T/lB7YVSX6IgC4uSgoge2EvJHqT2tDIKTSktdXTMUYu0hiaysvKDmasPe0nH4Y42d86dI2fWDw5n37Uf53/3XbPO3vvsOzeWa4IgCEpMBPkgCIISE0Eeni5aQIbQ0j77k57QUpn9SQvsX3oK09Lt1+SDIAjKTIzkgyAISkzpgryk5yS1SmrM2E6W9Lmk1ZLmS+rn9hskfZ05dkk6RVJvSW9LWidpjaTpRWnxvDpJT0ta75qu6gI9B0qa5fYmSdMydS6W9I2kDZKmFqnF8w+Q9JWkBUVqkTTF/aVR0mxJB9dYS52k592+UtIot+fiv3npyeR1yoclHSNpkff7GkmT3D5A0kJJzX6ud7skzXQ/XSVpeKatcV6+WdK4IrV4fj9JP0h6oqNa9omZleoAzgGGA40Z2xfAuZ4eD9xfod5JwCZP9wbO83Qd8BlwSRFa/PV9wAOe7gEcXuu+Aa4H5mT64ztgEHAAsBEY4n2zEhhahJZMvduBV4AFBfbL0cC3QC/PexW4ucZaJgLPe/oIYLn7Ry7+m5eevHwYGAgM9/QhwHpgKPAwMNXtU4GHPD0GeBcQMBJY5vYBwCY/13u6vggtmfYedx9+oprPaW9H6UbyZvYpsLWN+UTgU08vBCqNIq4DZnsb281skad3ACuAhiK0OOOBB73NXWZW1ZcqOqjHgD6SegK9gB3ANuA0YIOZbfK+mQOMLUgLkhqAS4FnOqohby2kX1rr5Xm9gR9rrGUo8JHXawV+A07Ny3/z0uN5nfZhM2sxsxWe/gNoIt1cxwKzvNgs4EpPjwVesMRSoL+kgcBFwEIz22pmv/p7uLggLUgaARwJfNARDf+X0gX5dmgErvD01cAxFcpcw56BFQBJ/YHLceftai1+fYD7Ja2QNFdSnr8Z1p6e14C/gBbge2CGmW0lOfLmTP0tbitCC8BjwN3Arpw0VKXFzH4AZritBfjdzPL6o21Py0pgrKSekgYDI2jjTzXw3w7rqYUPSxoEDAOWAUeaWQuk4EuaRUD7vpqrD3dGi6QewCPAXdVef190lyA/HpgoaTlparUjmynpdGC7mTW2sfckBduZZrapIC09SaOwxWY2HPicFEzyoj09pwH/AEcBg4E7JA0hTTfbktcWrQ5pkXQZ0Gpmy3O6fme01JNGa4M9r4+kG2us5TlSsPiSdLNbAuzcXalG/luNnlx9WFJf4HVgsplt21vRCjbbi70ILbcB75jZ5gr5udAtfsjbzNYBowEknUCa3me5lgqjeNLe1mYze6xALb8A24E3/fVcYEIX6LkeeM/M/gZaJS0mTb03s+dosYEqliVy0jIMuELSGOBgoJ+kl8ys08G1Ci0GfGtmP3udN4AzgZdqpcXMdgJTdpeTtARozlTN3X+r1JObD0s6kBRUXzazN9z8k6SBZtbiSyCtbt9CZV/dAoxqY/+kIC1nAGdLug3oC9RJ+tPMqtrQUIluMZKXdISfewD3Ak9l8nqQppxz2tR5ADgUmFykFktPZebzn1NeAKztAj3fA+f7roA+pIdF60gP3Y6XNFhSHemmNK8ILWY2zcwazGyQ6/g4jwBfjRa3j1Ta2SLS59RUSy1+rT6evhDYaWZr/XVN/LcaPXn5sPfrs0CTmT2ayZoH7N4hMw54K2O/yT+rkaQltBbgfWC0pHqfgY12W5drMbMbzOxY9+E7Sev2uQV4oJS7a2aT1kT/Jt09JwCTSE+/1wPT8S+BeflRwNI2bTSQRmZNwNd+3FqEFrcfR3rQtYq0tnpsrfuGNKqYC6wh/UHelWlnjJffCNxTpJY2fVft7pq8+uU+UsBvBF4EDqqxlkHAN+6nH5L+E2Fu/puXnrx8GDjL39eqzPsaAxzmbTb7eYCXF/Ck++lq0kPp3W2NBzb4cUuRWjJt3kwNdtfEN16DIAhKTLdYrgmCIOiuRJAPgiAoMRHkgyAISkwE+SAIghITQT4IgqDERJAPgiAoMRHkgyAISkwE+SAIghLzL8wP0RTfZQgIAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "res.plot_cusum();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, the CUSUM of squares shows substantial deviation at the 5% level, also suggesting a rejection of the null hypothesis of parameter stability." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "res.plot_cusum_squares();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Example 3: Linear restrictions and formulas" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear restrictions\n", "\n", "It is not hard to implement linear restrictions, using the `constraints` parameter in constructing the model." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Statespace Model Results \n", "==============================================================================\n", "Dep. Variable: WORLDCONSUMPTION No. Observations: 25\n", "Model: RecursiveLS Log Likelihood -150.911\n", "Date: Tue, 17 Dec 2019 R-squared: 0.989\n", "Time: 23:38:11 AIC 309.822\n", "Sample: 01-01-1951 BIC 314.698\n", " - 01-01-1975 HQIC 311.174\n", "Covariance Type: nonrobust Scale 137155.014\n", "==================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "----------------------------------------------------------------------------------\n", "const -4839.4893 2412.410 -2.006 0.045 -9567.726 -111.253\n", "COPPERPRICE 5.9797 12.704 0.471 0.638 -18.921 30.880\n", "INCOMEINDEX 1.115e+04 666.308 16.738 0.000 9847.002 1.25e+04\n", "ALUMPRICE 5.9797 12.704 0.471 0.638 -18.921 30.880\n", "INVENTORYINDEX 241.3447 2298.951 0.105 0.916 -4264.516 4747.205\n", "===================================================================================\n", "Ljung-Box (Q): 22.60 Jarque-Bera (JB): 1.78\n", "Prob(Q): 0.31 Prob(JB): 0.41\n", "Heteroskedasticity (H): 1.75 Skew: -0.63\n", "Prob(H) (two-sided): 0.48 Kurtosis: 2.32\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Parameters and covariance matrix estimates are RLS estimates conditional on the entire sample.\n", "[2] Covariance matrix is singular or near-singular, with condition number 2.75e+17. Standard errors may be unstable.\n" ] } ], "source": [ "endog = dta['WORLDCONSUMPTION']\n", "exog = sm.add_constant(dta[['COPPERPRICE', 'INCOMEINDEX', 'ALUMPRICE', 'INVENTORYINDEX']])\n", "\n", "mod = sm.RecursiveLS(endog, exog, constraints='COPPERPRICE = ALUMPRICE')\n", "res = mod.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Formula\n", "\n", "One could fit the same model using the class method `from_formula`." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Statespace Model Results \n", "==============================================================================\n", "Dep. Variable: WORLDCONSUMPTION No. Observations: 25\n", "Model: RecursiveLS Log Likelihood -150.911\n", "Date: Tue, 17 Dec 2019 R-squared: 0.989\n", "Time: 23:38:11 AIC 309.822\n", "Sample: 01-01-1951 BIC 314.698\n", " - 01-01-1975 HQIC 311.174\n", "Covariance Type: nonrobust Scale 137155.014\n", "==================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "----------------------------------------------------------------------------------\n", "Intercept -4839.4893 2412.410 -2.006 0.045 -9567.726 -111.253\n", "COPPERPRICE 5.9797 12.704 0.471 0.638 -18.921 30.880\n", "INCOMEINDEX 1.115e+04 666.308 16.738 0.000 9847.002 1.25e+04\n", "ALUMPRICE 5.9797 12.704 0.471 0.638 -18.921 30.880\n", "INVENTORYINDEX 241.3447 2298.951 0.105 0.916 -4264.516 4747.205\n", "===================================================================================\n", "Ljung-Box (Q): 22.60 Jarque-Bera (JB): 1.78\n", "Prob(Q): 0.31 Prob(JB): 0.41\n", "Heteroskedasticity (H): 1.75 Skew: -0.63\n", "Prob(H) (two-sided): 0.48 Kurtosis: 2.32\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Parameters and covariance matrix estimates are RLS estimates conditional on the entire sample.\n", "[2] Covariance matrix is singular or near-singular, with condition number 2.75e+17. Standard errors may be unstable.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/travis/build/statsmodels/statsmodels/statsmodels/tsa/base/tsa_model.py:162: ValueWarning: No frequency information was provided, so inferred frequency AS-JAN will be used.\n", " % freq, ValueWarning)\n" ] } ], "source": [ "mod = sm.RecursiveLS.from_formula(\n", " 'WORLDCONSUMPTION ~ COPPERPRICE + INCOMEINDEX + ALUMPRICE + INVENTORYINDEX', dta,\n", " constraints='COPPERPRICE = ALUMPRICE')\n", "res = mod.fit()\n", "print(res.summary())" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 1 }