{ "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": { "execution": { "iopub.execute_input": "2021-02-02T06:54:36.084725Z", "iopub.status.busy": "2021-02-02T06:54:36.083992Z", "iopub.status.idle": "2021-02-02T06:54:37.285148Z", "shell.execute_reply": "2021-02-02T06:54:37.284198Z" } }, "outputs": [], "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": { "execution": { "iopub.execute_input": "2021-02-02T06:54:37.292003Z", "iopub.status.busy": "2021-02-02T06:54:37.290985Z", "iopub.status.idle": "2021-02-02T06:54:38.072035Z", "shell.execute_reply": "2021-02-02T06:54:38.072617Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "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": { "execution": { "iopub.execute_input": "2021-02-02T06:54:38.076690Z", "iopub.status.busy": "2021-02-02T06:54:38.075466Z", "iopub.status.idle": "2021-02-02T06:54:38.087996Z", "shell.execute_reply": "2021-02-02T06:54:38.088869Z" } }, "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": { "execution": { "iopub.execute_input": "2021-02-02T06:54:38.093045Z", "iopub.status.busy": "2021-02-02T06:54:38.091809Z", "iopub.status.idle": "2021-02-02T06:54:38.149772Z", "shell.execute_reply": "2021-02-02T06:54:38.150762Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Unobserved Components Results \n", "==============================================================================\n", "Dep. Variable: CPIAPPNS No. Observations: 492\n", "Model: local linear trend Log Likelihood -2540.046\n", "Date: Tue, 02 Feb 2021 AIC 5086.093\n", "Time: 06:54:38 BIC 5098.676\n", "Sample: 01-01-1980 HQIC 5091.035\n", " - 12-01-2020 \n", "Covariance Type: opg \n", "====================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------------\n", "sigma2.irregular 1.0000 0.010 102.345 0.000 0.981 1.019\n", "sigma2.level 0 0.000 0 1.000 -0.000 0.000\n", "sigma2.trend 7.716e-06 2.23e-07 34.625 0.000 7.28e-06 8.15e-06\n", "===================================================================================\n", "Ljung-Box (L1) (Q): 202.10 Jarque-Bera (JB): 3.07\n", "Prob(Q): 0.00 Prob(JB): 0.22\n", "Heteroskedasticity (H): 2.07 Skew: -0.06\n", "Prob(H) (two-sided): 0.00 Kurtosis: 2.63\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": { "execution": { "iopub.execute_input": "2021-02-02T06:54:38.155342Z", "iopub.status.busy": "2021-02-02T06:54:38.154027Z", "iopub.status.idle": "2021-02-02T06:54:38.159673Z", "shell.execute_reply": "2021-02-02T06:54:38.160590Z" } }, "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": { "execution": { "iopub.execute_input": "2021-02-02T06:54:38.164621Z", "iopub.status.busy": "2021-02-02T06:54:38.163345Z", "iopub.status.idle": "2021-02-02T06:54:38.407202Z", "shell.execute_reply": "2021-02-02T06:54:38.406481Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "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(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": { "execution": { "iopub.execute_input": "2021-02-02T06:54:38.412408Z", "iopub.status.busy": "2021-02-02T06:54:38.411688Z", "iopub.status.idle": "2021-02-02T06:54:38.414664Z", "shell.execute_reply": "2021-02-02T06:54:38.414988Z" } }, "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": { "execution": { "iopub.execute_input": "2021-02-02T06:54:38.420734Z", "iopub.status.busy": "2021-02-02T06:54:38.418719Z", "iopub.status.idle": "2021-02-02T06:54:38.546346Z", "shell.execute_reply": "2021-02-02T06:54:38.545531Z" } }, "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": { "execution": { "iopub.execute_input": "2021-02-02T06:54:38.551500Z", "iopub.status.busy": "2021-02-02T06:54:38.549957Z", "iopub.status.idle": "2021-02-02T06:54:38.677178Z", "shell.execute_reply": "2021-02-02T06:54:38.677820Z" } }, "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": { "execution": { "iopub.execute_input": "2021-02-02T06:54:38.684137Z", "iopub.status.busy": "2021-02-02T06:54:38.683543Z", "iopub.status.idle": "2021-02-02T06:54:38.694221Z", "shell.execute_reply": "2021-02-02T06:54:38.694672Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Unobserved Components Results \n", "=====================================================================================\n", "Dep. Variable: CPIAPPNS No. Observations: 492\n", "Model: local linear trend Log Likelihood -1345.686\n", " + stochastic seasonal(12) AIC 2693.372\n", "Date: Tue, 02 Feb 2021 BIC 2697.544\n", "Time: 06:54:38 HQIC 2695.012\n", "Sample: 01-01-1980 \n", " - 12-01-2020 \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 0.0809 0.009 9.239 0.000 0.064 0.098\n", "===================================================================================\n", "Ljung-Box (L1) (Q): 399.47 Jarque-Bera (JB): 23.87\n", "Prob(Q): 0.00 Prob(JB): 0.00\n", "Heteroskedasticity (H): 1.99 Skew: -0.34\n", "Prob(H) (two-sided): 0.00 Kurtosis: 3.85\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": { "execution": { "iopub.execute_input": "2021-02-02T06:54:38.697531Z", "iopub.status.busy": "2021-02-02T06:54:38.696860Z", "iopub.status.idle": "2021-02-02T06:54:40.445523Z", "shell.execute_reply": "2021-02-02T06:54:40.446648Z" } }, "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": { "execution": { "iopub.execute_input": "2021-02-02T06:54:40.451133Z", "iopub.status.busy": "2021-02-02T06:54:40.449769Z", "iopub.status.idle": "2021-02-02T06:54:40.457597Z", "shell.execute_reply": "2021-02-02T06:54:40.458546Z" } }, "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": { "execution": { "iopub.execute_input": "2021-02-02T06:54:40.463043Z", "iopub.status.busy": "2021-02-02T06:54:40.461663Z", "iopub.status.idle": "2021-02-02T06:54:40.750787Z", "shell.execute_reply": "2021-02-02T06:54:40.751854Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "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": { "execution": { "iopub.execute_input": "2021-02-02T06:54:40.756151Z", "iopub.status.busy": "2021-02-02T06:54:40.754896Z", "iopub.status.idle": "2021-02-02T06:54:41.049653Z", "shell.execute_reply": "2021-02-02T06:54:41.048701Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "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(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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 2 }