{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimating or specifying parameters in state space models\n", "\n", "In this notebook we show how to fix specific values of certain parameters in statsmodels' state space models while estimating others.\n", "\n", "In general, state space models allow users to:\n", "\n", "1. Estimate all parameters by maximum likelihood\n", "2. Fix some parameters and estimate the rest\n", "3. Fix all parameters (so that no parameters are estimated)\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "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", "\n", "from importlib import reload\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "\n", "from pandas_datareader.data import DataReader" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To illustrate, we will use the Consumer Price Index for Apparel, which has a time-varying level and a strong seasonal component." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "endog = DataReader('CPIAPPNS', 'fred', start='1980').asfreq('MS')\n", "endog.plot(figsize=(15, 3));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is well known (e.g. Harvey and Jaeger [1993]) that the HP filter output can be generated by an unobserved components model given certain restrictions on the parameters.\n", "\n", "The unobserved components model is:\n", "\n", "$$\n", "\\begin{aligned}\n", "y_t & = \\mu_t + \\varepsilon_t & \\varepsilon_t \\sim N(0, \\sigma_\\varepsilon^2) \\\\\n", "\\mu_t &= \\mu_{t-1} + \\beta_{t-1} + \\eta_t & \\eta_t \\sim N(0, \\sigma_\\eta^2) \\\\\n", "\\beta_t &= \\beta_{t-1} + \\zeta_t & \\zeta_t \\sim N(0, \\sigma_\\zeta^2) \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "For the trend to match the output of the HP filter, the parameters must be set as follows:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\frac{\\sigma_\\varepsilon^2}{\\sigma_\\zeta^2} & = \\lambda \\\\\n", "\\sigma_\\eta^2 & = 0\n", "\\end{aligned}\n", "$$\n", "\n", "where $\\lambda$ is the parameter of the associated HP filter. For the monthly data that we use here, it is usually recommended that $\\lambda = 129600$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['sigma2.irregular', 'sigma2.level', 'sigma2.trend']\n" ] } ], "source": [ "# Run the HP filter with lambda = 129600\n", "hp_cycle, hp_trend = sm.tsa.filters.hpfilter(endog, lamb=129600)\n", "\n", "# The unobserved components model above is the local linear trend, or \"lltrend\", specification\n", "mod = sm.tsa.UnobservedComponents(endog, 'lltrend')\n", "print(mod.param_names)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The parameters of the unobserved components model (UCM) are written as:\n", "\n", "- $\\sigma_\\varepsilon^2 = \\text{sigma2.irregular}$\n", "- $\\sigma_\\eta^2 = \\text{sigma2.level}$\n", "- $\\sigma_\\zeta^2 = \\text{sigma2.trend}$\n", "\n", "To satisfy the above restrictions, we will set $(\\sigma_\\varepsilon^2, \\sigma_\\eta^2, \\sigma_\\zeta^2) = (1, 0, 1 / 129600)$.\n", "\n", "Since we are fixing all parameters here, we do not need to use the `fit` method at all, since that method is used to perform maximum likelihood estimation. Instead, we can directly run the Kalman filter and smoother at our chosen parameters using the `smooth` method." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Unobserved Components Results \n", "==============================================================================\n", "Dep. Variable: CPIAPPNS No. Observations: 481\n", "Model: local linear trend Log Likelihood -2395.749\n", "Date: Fri, 21 Feb 2020 AIC 4797.498\n", "Time: 13:54:07 BIC 4810.013\n", "Sample: 01-01-1980 HQIC 4802.418\n", " - 01-01-2020 \n", "Covariance Type: opg \n", "====================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------------\n", "sigma2.irregular 1.0000 0.010 96.595 0.000 0.980 1.020\n", "sigma2.level 0 0.000 0 1.000 -0.000 0.000\n", "sigma2.trend 7.716e-06 2.29e-07 33.765 0.000 7.27e-06 8.16e-06\n", "===================================================================================\n", "Ljung-Box (Q): 4138.44 Jarque-Bera (JB): 3.76\n", "Prob(Q): 0.00 Prob(JB): 0.15\n", "Heteroskedasticity (H): 2.01 Skew: -0.01\n", "Prob(H) (two-sided): 0.00 Kurtosis: 2.57\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n" ] } ], "source": [ "res = mod.smooth([1., 0, 1. / 129600])\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The estimate that corresponds to the HP filter's trend estimate is given by the smoothed estimate of the `level` (which is $\\mu_t$ in the notation above):" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "ucm_trend = pd.Series(res.level.smoothed, index=endog.index)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is easy to see that the estimate of the smoothed level from the UCM is equal to the output of the HP filter:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(15, 3))\n", "\n", "ax.plot(hp_trend, label='HP estimate')\n", "ax.plot(ucm_trend, label='UCM estimate')\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a seasonal component" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, unobserved components models are more flexible than the HP filter. For example, the data shown above is clearly seasonal, but with time-varying seasonal effects (the seasonality is much weaker at the beginning than at the end). One of the benefits of the unobserved components framework is that we can add a stochastic seasonal component. In this case, we will estimate the variance of the seasonal component by maximum likelihood while still including the restriction on the parameters implied above so that the trend corresponds to the HP filter concept.\n", "\n", "Adding the stochastic seasonal component adds one new parameter, `sigma2.seasonal`." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['sigma2.irregular', 'sigma2.level', 'sigma2.trend', 'sigma2.seasonal']\n" ] } ], "source": [ "# Construct a local linear trend model with a stochastic seasonal component of period 1 year\n", "mod = sm.tsa.UnobservedComponents(endog, 'lltrend', seasonal=12, stochastic_seasonal=True)\n", "print(mod.param_names)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, we will continue to restrict the first three parameters as described above, but we want to estimate the value of `sigma2.seasonal` by maximum likelihood. Therefore, we will use the `fit` method along with the `fix_params` context manager.\n", "\n", "The `fix_params` method takes a dictionary of parameters names and associated values. Within the generated context, those parameters will be used in all cases. In the case of the `fit` method, only the parameters that were not fixed will be estimated." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# Here we restrict the first three parameters to specific values\n", "with mod.fix_params({'sigma2.irregular': 1, 'sigma2.level': 0, 'sigma2.trend': 1. / 129600}):\n", " # Now we fit any remaining parameters, which in this case\n", " # is just `sigma2.seasonal`\n", " res_restricted = mod.fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alternatively, we could have simply used the `fit_constrained` method, which also accepts a dictionary of constraints:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "res_restricted = mod.fit_constrained({'sigma2.irregular': 1, 'sigma2.level': 0, 'sigma2.trend': 1. / 129600})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The summary output includes all parameters, but indicates that the first three were fixed (and so were not estimated)." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Unobserved Components Results \n", "=====================================================================================\n", "Dep. Variable: CPIAPPNS No. Observations: 481\n", "Model: local linear trend Log Likelihood -1208.728\n", " + stochastic seasonal(12) AIC 2419.456\n", "Date: Fri, 21 Feb 2020 BIC 2423.604\n", "Time: 13:54:07 HQIC 2421.088\n", "Sample: 01-01-1980 \n", " - 01-01-2020 \n", "Covariance Type: opg \n", "============================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "--------------------------------------------------------------------------------------------\n", "sigma2.irregular (fixed) 1.0000 nan nan nan nan nan\n", "sigma2.level (fixed) 0 nan nan nan nan nan\n", "sigma2.trend (fixed) 7.716e-06 nan nan nan nan nan\n", "sigma2.seasonal 0.0662 0.010 6.589 0.000 0.047 0.086\n", "===================================================================================\n", "Ljung-Box (Q): 3539.80 Jarque-Bera (JB): 0.55\n", "Prob(Q): 0.00 Prob(JB): 0.76\n", "Heteroskedasticity (H): 1.40 Skew: 0.00\n", "Prob(H) (two-sided): 0.04 Kurtosis: 2.83\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n" ] } ], "source": [ "print(res_restricted.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For comparison, we construct the unrestricted maximum likelihood estimates (MLE). In this case, the estimate of the level will no longer correspond to the HP filter concept." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "res_unrestricted = mod.fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can retrieve the smoothed estimates of the trend and seasonal components." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# Construct the smoothed level estimates\n", "unrestricted_trend = pd.Series(res_unrestricted.level.smoothed, index=endog.index)\n", "restricted_trend = pd.Series(res_restricted.level.smoothed, index=endog.index)\n", "\n", "# Construct the smoothed estimates of the seasonal pattern\n", "unrestricted_seasonal = pd.Series(res_unrestricted.seasonal.smoothed, index=endog.index)\n", "restricted_seasonal = pd.Series(res_restricted.seasonal.smoothed, index=endog.index)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Comparing the estimated level, it is clear that the seasonal UCM with fixed parameters still produces a trend that corresponds very closely (although no longer exactly) to the HP filter output.\n", "\n", "Meanwhile, the estimated level from the model with no parameter restrictions (the MLE model) is much less smooth than these." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(15, 3))\n", "\n", "ax.plot(unrestricted_trend, label='MLE, with seasonal')\n", "ax.plot(restricted_trend, label='Fixed parameters, with seasonal')\n", "ax.plot(hp_trend, label='HP filter, no seasonal')\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, the UCM with the parameter restrictions is still able to pick up the time-varying seasonal component quite well." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(15, 3))\n", "\n", "ax.plot(unrestricted_seasonal, label='MLE')\n", "ax.plot(restricted_seasonal, label='Fixed parameters')\n", "ax.legend();" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 2 }