{ "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": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/travis/miniconda/envs/statsmodels-test/lib/python3.7/site-packages/pandas_datareader/compat/__init__.py:7: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n", " from pandas.util.testing import assert_frame_equal\n" ] } ], "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" ] } ], "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: Fri, 21 Feb 2020 R-squared: 0.965\n", "Time: 13:53:52 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 1558.41803044 1958.43326657\n", " -51474.95388788 -4168.9514887 -2252.613551 -446.55914623\n", " -5288.39795721 -6942.31935658 -7846.08902828 -6643.15121767\n", " -6274.1101604 -7272.01696738 -6319.02648989 -5822.23929583\n", " -6256.30903253 -6737.40446584 -6477.42842164 -5995.90747758\n", " -6450.80678724 -6022.92167288 -5258.35153529 -5320.8913717\n", " -6562.37194573]\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": [ "[ 0.69971507 0.65841239 1.2462967 2.05476027 2.39888914 3.17861975\n", " 2.67244668 2.01783211 2.46131743 2.05268634 0.95054332 -1.04505551\n", " -2.5546529 -2.29908156 -1.45289497 -1.95353998 -1.35046625 0.15789825\n", " 0.63286526 -1.4818459 ]\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 692.784\n", "Date: Fri, 21 Feb 2020 R-squared: 0.813\n", "Time: 13:53:55 AIC -1381.568\n", "Sample: 01-01-1970 BIC -1375.671\n", " - 01-01-2005 HQIC -1379.172\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 -5.930 0.000 -0.004 -0.002\n", "M2 0.9097 0.037 24.582 0.000 0.837 0.982\n", "===================================================================================\n", "Ljung-Box (Q): 1858.97 Jarque-Bera (JB): 18.33\n", "Prob(Q): 0.00 Prob(JB): 0.00\n", "Heteroskedasticity (H): 5.30 Skew: -0.82\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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\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: Fri, 21 Feb 2020 R-squared: 0.989\n", "Time: 13:53:55 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: Fri, 21 Feb 2020 R-squared: 0.989\n", "Time: 13:53:55 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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 1 }