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@ChadFulton
Created May 16, 2019 21:19
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Estimating and specifying parameters in state space models
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{
"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": [],
"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": [
"<Figure size 1080x216 with 1 Axes>"
]
},
"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: 472\n",
"Model: local linear trend Log Likelihood -2357.655\n",
"Date: Thu, 16 May 2019 AIC 4721.309\n",
"Time: 17:14:36 BIC 4733.767\n",
"Sample: 01-01-1980 HQIC 4726.211\n",
" - 04-01-2019 \n",
"Covariance Type: opg \n",
"====================================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"------------------------------------------------------------------------------------\n",
"sigma2.irregular 1.0000 0.010 95.774 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 2.3e-07 33.498 0.000 7.26e-06 8.17e-06\n",
"===================================================================================\n",
"Ljung-Box (Q): 4043.50 Jarque-Bera (JB): 3.77\n",
"Prob(Q): 0.00 Prob(JB): 0.15\n",
"Heteroskedasticity (H): 2.11 Skew: -0.02\n",
"Prob(H) (two-sided): 0.00 Kurtosis: 2.56\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",
"text/plain": [
"<Figure size 1080x216 with 1 Axes>"
]
},
"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 `fixed_params` context manager.\n",
"\n",
"The `fixed_params` 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.fixed_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": [
"The summary output includes all parameters, but indicates that the first three were fixed (and so were not estimated)."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Unobserved Components Results \n",
"=====================================================================================\n",
"Dep. Variable: CPIAPPNS No. Observations: 472\n",
"Model: local linear trend Log Likelihood -1188.307\n",
" + stochastic seasonal(12) AIC 2384.614\n",
"Date: Thu, 16 May 2019 BIC 2401.130\n",
"Time: 17:14:36 HQIC 2391.118\n",
"Sample: 01-01-1980 \n",
" - 04-01-2019 \n",
"Covariance Type: opg \n",
"============================================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"--------------------------------------------------------------------------------------------\n",
"sigma2.irregular (fixed) 1.0000 0.046 21.945 0.000 0.911 1.089\n",
"sigma2.level (fixed) 0 0.000 0 1.000 -0.001 0.001\n",
"sigma2.trend (fixed) 7.716e-06 4.46e-07 17.316 0.000 6.84e-06 8.59e-06\n",
"sigma2.seasonal 0.0608 0.010 6.323 0.000 0.042 0.080\n",
"===================================================================================\n",
"Ljung-Box (Q): 3507.23 Jarque-Bera (JB): 0.52\n",
"Prob(Q): 0.00 Prob(JB): 0.77\n",
"Heteroskedasticity (H): 1.51 Skew: -0.01\n",
"Prob(H) (two-sided): 0.01 Kurtosis: 2.84\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": 10,
"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": 11,
"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": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1080x216 with 1 Axes>"
]
},
"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": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1080x216 with 1 Axes>"
]
},
"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": "3.7.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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