{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Markov switching autoregression models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook provides an example of the use of Markov switching models in statsmodels to replicate a number of results presented in Kim and Nelson (1999). It applies the Hamilton (1989) filter the Kim (1994) smoother.\n", "\n", "This is tested against the Markov-switching models from E-views 8, which can be found at http://www.eviews.com/EViews8/ev8ecswitch_n.html#MarkovAR or the Markov-switching models of Stata 14 which can be found at http://www.stata.com/manuals14/tsmswitch.pdf." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "import requests\n", "from io import BytesIO\n", "\n", "# NBER recessions\n", "from pandas_datareader.data import DataReader\n", "from datetime import datetime\n", "usrec = DataReader('USREC', 'fred', start=datetime(1947, 1, 1), end=datetime(2013, 4, 1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hamilton (1989) switching model of GNP\n", "\n", "This replicates Hamilton's (1989) seminal paper introducing Markov-switching models. The model is an autoregressive model of order 4 in which the mean of the process switches between two regimes. It can be written:\n", "\n", "$$\n", "y_t = \\mu_{S_t} + \\phi_1 (y_{t-1} - \\mu_{S_{t-1}}) + \\phi_2 (y_{t-2} - \\mu_{S_{t-2}}) + \\phi_3 (y_{t-3} - \\mu_{S_{t-3}}) + \\phi_4 (y_{t-4} - \\mu_{S_{t-4}}) + \\varepsilon_t\n", "$$\n", "\n", "Each period, the regime transitions according to the following matrix of transition probabilities:\n", "\n", "$$ P(S_t = s_t | S_{t-1} = s_{t-1}) =\n", "\\begin{bmatrix}\n", "p_{00} & p_{10} \\\\\n", "p_{01} & p_{11}\n", "\\end{bmatrix}\n", "$$\n", "\n", "where $p_{ij}$ is the probability of transitioning *from* regime $i$, *to* regime $j$.\n", "\n", "The model class is `MarkovAutoregression` in the time-series part of `statsmodels`. In order to create the model, we must specify the number of regimes with `k_regimes=2`, and the order of the autoregression with `order=4`. The default model also includes switching autoregressive coefficients, so here we also need to specify `switching_ar=False` to avoid that.\n", "\n", "After creation, the model is `fit` via maximum likelihood estimation. Under the hood, good starting parameters are found using a number of steps of the expectation maximization (EM) algorithm, and a quasi-Newton (BFGS) algorithm is applied to quickly find the maximum." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Get the RGNP data to replicate Hamilton\n", "dta = pd.read_stata('https://www.stata-press.com/data/r14/rgnp.dta').iloc[1:]\n", "dta.index = pd.DatetimeIndex(dta.date, freq='QS')\n", "dta_hamilton = dta.rgnp\n", "\n", "# Plot the data\n", "dta_hamilton.plot(title='Growth rate of Real GNP', figsize=(12,3))\n", "\n", "# Fit the model\n", "mod_hamilton = sm.tsa.MarkovAutoregression(dta_hamilton, k_regimes=2, order=4, switching_ar=False)\n", "res_hamilton = mod_hamilton.fit()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Markov Switching Model Results
Dep. Variable: rgnp No. Observations: 131
Model: MarkovAutoregression Log Likelihood -181.263
Date: Tue, 17 Dec 2019 AIC 380.527
Time: 23:42:08 BIC 406.404
Sample: 04-01-1951 HQIC 391.042
- 10-01-1984
Covariance Type: approx
\n", "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Regime 0 parameters
coef std err z P>|z| [0.025 0.975]
const -0.3588 0.265 -1.356 0.175 -0.877 0.160
\n", "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Regime 1 parameters
coef std err z P>|z| [0.025 0.975]
const 1.1635 0.075 15.614 0.000 1.017 1.310
\n", "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Non-switching parameters
coef std err z P>|z| [0.025 0.975]
sigma2 0.5914 0.103 5.761 0.000 0.390 0.793
ar.L1 0.0135 0.120 0.112 0.911 -0.222 0.249
ar.L2 -0.0575 0.138 -0.418 0.676 -0.327 0.212
ar.L3 -0.2470 0.107 -2.310 0.021 -0.457 -0.037
ar.L4 -0.2129 0.111 -1.926 0.054 -0.430 0.004
\n", "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Regime transition parameters
coef std err z P>|z| [0.025 0.975]
p[0->0] 0.7547 0.097 7.819 0.000 0.565 0.944
p[1->0] 0.0959 0.038 2.542 0.011 0.022 0.170


Warnings:
[1] Covariance matrix calculated using numerical (complex-step) differentiation." ], "text/plain": [ "\n", "\"\"\"\n", " Markov Switching Model Results \n", "================================================================================\n", "Dep. Variable: rgnp No. Observations: 131\n", "Model: MarkovAutoregression Log Likelihood -181.263\n", "Date: Tue, 17 Dec 2019 AIC 380.527\n", "Time: 23:42:08 BIC 406.404\n", "Sample: 04-01-1951 HQIC 391.042\n", " - 10-01-1984 \n", "Covariance Type: approx \n", " Regime 0 parameters \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const -0.3588 0.265 -1.356 0.175 -0.877 0.160\n", " Regime 1 parameters \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const 1.1635 0.075 15.614 0.000 1.017 1.310\n", " Non-switching parameters \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "sigma2 0.5914 0.103 5.761 0.000 0.390 0.793\n", "ar.L1 0.0135 0.120 0.112 0.911 -0.222 0.249\n", "ar.L2 -0.0575 0.138 -0.418 0.676 -0.327 0.212\n", "ar.L3 -0.2470 0.107 -2.310 0.021 -0.457 -0.037\n", "ar.L4 -0.2129 0.111 -1.926 0.054 -0.430 0.004\n", " Regime transition parameters \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "p[0->0] 0.7547 0.097 7.819 0.000 0.565 0.944\n", "p[1->0] 0.0959 0.038 2.542 0.011 0.022 0.170\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using numerical (complex-step) differentiation.\n", "\"\"\"" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res_hamilton.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We plot the filtered and smoothed probabilities of a recession. Filtered refers to an estimate of the probability at time $t$ based on data up to and including time $t$ (but excluding time $t+1, ..., T$). Smoothed refers to an estimate of the probability at time $t$ using all the data in the sample.\n", "\n", "For reference, the shaded periods represent the NBER recessions." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(2, figsize=(7,7))\n", "ax = axes[0]\n", "ax.plot(res_hamilton.filtered_marginal_probabilities[0])\n", "ax.fill_between(usrec.index, 0, 1, where=usrec['USREC'].values, color='k', alpha=0.1)\n", "ax.set_xlim(dta_hamilton.index[4], dta_hamilton.index[-1])\n", "ax.set(title='Filtered probability of recession')\n", "\n", "ax = axes[1]\n", "ax.plot(res_hamilton.smoothed_marginal_probabilities[0])\n", "ax.fill_between(usrec.index, 0, 1, where=usrec['USREC'].values, color='k', alpha=0.1)\n", "ax.set_xlim(dta_hamilton.index[4], dta_hamilton.index[-1])\n", "ax.set(title='Smoothed probability of recession')\n", "\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the estimated transition matrix we can calculate the expected duration of a recession versus an expansion." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 4.07604746 10.42589384]\n" ] } ], "source": [ "print(res_hamilton.expected_durations)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, it is expected that a recession will last about one year (4 quarters) and an expansion about two and a half years." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Kim, Nelson, and Startz (1998) Three-state Variance Switching\n", "\n", "This model demonstrates estimation with regime heteroskedasticity (switching of variances) and no mean effect. The dataset can be reached at http://econ.korea.ac.kr/~cjkim/MARKOV/data/ew_excs.prn.\n", "\n", "The model in question is:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\varepsilon_t \\\\\n", "\\varepsilon_t & \\sim N(0, \\sigma_{S_t}^2)\n", "\\end{align}\n", "$$\n", "\n", "Since there is no autoregressive component, this model can be fit using the `MarkovRegression` class. Since there is no mean effect, we specify `trend='nc'`. There are hypothesized to be three regimes for the switching variances, so we specify `k_regimes=3` and `switching_variance=True` (by default, the variance is assumed to be the same across regimes)." ] }, { "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": [ "# Get the dataset\n", "ew_excs = requests.get('http://econ.korea.ac.kr/~cjkim/MARKOV/data/ew_excs.prn').content\n", "raw = pd.read_table(BytesIO(ew_excs), header=None, skipfooter=1, engine='python')\n", "raw.index = pd.date_range('1926-01-01', '1995-12-01', freq='MS')\n", "\n", "dta_kns = raw.loc[:'1986'] - raw.loc[:'1986'].mean()\n", "\n", "# Plot the dataset\n", "dta_kns[0].plot(title='Excess returns', figsize=(12, 3))\n", "\n", "# Fit the model\n", "mod_kns = sm.tsa.MarkovRegression(dta_kns, k_regimes=3, trend='nc', switching_variance=True)\n", "res_kns = mod_kns.fit()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/travis/build/statsmodels/statsmodels/statsmodels/base/model.py:1354: RuntimeWarning: invalid value encountered in sqrt\n", " bse_ = np.sqrt(np.diag(self.cov_params()))\n", "/home/travis/miniconda/envs/statsmodels-test/lib/python3.7/site-packages/scipy/stats/_distn_infrastructure.py:901: RuntimeWarning: invalid value encountered in greater\n", " return (a < x) & (x < b)\n", "/home/travis/miniconda/envs/statsmodels-test/lib/python3.7/site-packages/scipy/stats/_distn_infrastructure.py:901: RuntimeWarning: invalid value encountered in less\n", " return (a < x) & (x < b)\n", "/home/travis/miniconda/envs/statsmodels-test/lib/python3.7/site-packages/scipy/stats/_distn_infrastructure.py:1892: RuntimeWarning: invalid value encountered in less_equal\n", " cond2 = cond0 & (x <= _a)\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Markov Switching Model Results
Dep. Variable: 0 No. Observations: 732
Model: MarkovRegression Log Likelihood 1001.895
Date: Tue, 17 Dec 2019 AIC -1985.790
Time: 23:42:13 BIC -1944.428
Sample: 01-01-1926 HQIC -1969.834
- 12-01-1986
Covariance Type: approx
\n", "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Regime 0 parameters
coef std err z P>|z| [0.025 0.975]
sigma2 0.0012 0.000 7.136 0.000 0.001 0.002
\n", "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Regime 1 parameters
coef std err z P>|z| [0.025 0.975]
sigma2 0.0040 0.000 8.489 0.000 0.003 0.005
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Regime 2 parameters
coef std err z P>|z| [0.025 0.975]
sigma2 0.0311 0.006 5.461 0.000 0.020 0.042
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Regime transition parameters
coef std err z P>|z| [0.025 0.975]
p[0->0] 0.9747 0.000 7857.416 0.000 0.974 0.975
p[1->0] 0.0195 0.010 1.949 0.051 -0.000 0.039
p[2->0] 2.354e-08 nan nan nan nan nan
p[0->1] 0.0253 3.97e-05 637.835 0.000 0.025 0.025
p[1->1] 0.9688 0.013 75.528 0.000 0.944 0.994
p[2->1] 0.0493 0.032 1.551 0.121 -0.013 0.112


Warnings:
[1] Covariance matrix calculated using numerical (complex-step) differentiation." ], "text/plain": [ "\n", "\"\"\"\n", " Markov Switching Model Results \n", "==============================================================================\n", "Dep. Variable: 0 No. Observations: 732\n", "Model: MarkovRegression Log Likelihood 1001.895\n", "Date: Tue, 17 Dec 2019 AIC -1985.790\n", "Time: 23:42:13 BIC -1944.428\n", "Sample: 01-01-1926 HQIC -1969.834\n", " - 12-01-1986 \n", "Covariance Type: approx \n", " Regime 0 parameters \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "sigma2 0.0012 0.000 7.136 0.000 0.001 0.002\n", " Regime 1 parameters \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "sigma2 0.0040 0.000 8.489 0.000 0.003 0.005\n", " Regime 2 parameters \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "sigma2 0.0311 0.006 5.461 0.000 0.020 0.042\n", " Regime transition parameters \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "p[0->0] 0.9747 0.000 7857.416 0.000 0.974 0.975\n", "p[1->0] 0.0195 0.010 1.949 0.051 -0.000 0.039\n", "p[2->0] 2.354e-08 nan nan nan nan nan\n", "p[0->1] 0.0253 3.97e-05 637.835 0.000 0.025 0.025\n", "p[1->1] 0.9688 0.013 75.528 0.000 0.944 0.994\n", "p[2->1] 0.0493 0.032 1.551 0.121 -0.013 0.112\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using numerical (complex-step) differentiation.\n", "\"\"\"" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res_kns.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we plot the probabilities of being in each of the regimes; only in a few periods is a high-variance regime probable." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(3, figsize=(10,7))\n", "\n", "ax = axes[0]\n", "ax.plot(res_kns.smoothed_marginal_probabilities[0])\n", "ax.set(title='Smoothed probability of a low-variance regime for stock returns')\n", "\n", "ax = axes[1]\n", "ax.plot(res_kns.smoothed_marginal_probabilities[1])\n", "ax.set(title='Smoothed probability of a medium-variance regime for stock returns')\n", "\n", "ax = axes[2]\n", "ax.plot(res_kns.smoothed_marginal_probabilities[2])\n", "ax.set(title='Smoothed probability of a high-variance regime for stock returns')\n", "\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Filardo (1994) Time-Varying Transition Probabilities\n", "\n", "This model demonstrates estimation with time-varying transition probabilities. The dataset can be reached at http://econ.korea.ac.kr/~cjkim/MARKOV/data/filardo.prn.\n", "\n", "In the above models we have assumed that the transition probabilities are constant across time. Here we allow the probabilities to change with the state of the economy. Otherwise, the model is the same Markov autoregression of Hamilton (1989).\n", "\n", "Each period, the regime now transitions according to the following matrix of time-varying transition probabilities:\n", "\n", "$$ P(S_t = s_t | S_{t-1} = s_{t-1}) =\n", "\\begin{bmatrix}\n", "p_{00,t} & p_{10,t} \\\\\n", "p_{01,t} & p_{11,t}\n", "\\end{bmatrix}\n", "$$\n", "\n", "where $p_{ij,t}$ is the probability of transitioning *from* regime $i$, *to* regime $j$ in period $t$, and is defined to be:\n", "\n", "$$\n", "p_{ij,t} = \\frac{\\exp\\{ x_{t-1}' \\beta_{ij} \\}}{1 + \\exp\\{ x_{t-1}' \\beta_{ij} \\}}\n", "$$\n", "\n", "Instead of estimating the transition probabilities as part of maximum likelihood, the regression coefficients $\\beta_{ij}$ are estimated. These coefficients relate the transition probabilities to a vector of pre-determined or exogenous regressors $x_{t-1}$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Get the dataset\n", "filardo = requests.get('http://econ.korea.ac.kr/~cjkim/MARKOV/data/filardo.prn').content\n", "dta_filardo = pd.read_table(BytesIO(filardo), sep=' +', header=None, skipfooter=1, engine='python')\n", "dta_filardo.columns = ['month', 'ip', 'leading']\n", "dta_filardo.index = pd.date_range('1948-01-01', '1991-04-01', freq='MS')\n", "\n", "dta_filardo['dlip'] = np.log(dta_filardo['ip']).diff()*100\n", "# Deflated pre-1960 observations by ratio of std. devs.\n", "# See hmt_tvp.opt or Filardo (1994) p. 302\n", "std_ratio = dta_filardo['dlip']['1960-01-01':].std() / dta_filardo['dlip'][:'1959-12-01'].std()\n", "dta_filardo['dlip'][:'1959-12-01'] = dta_filardo['dlip'][:'1959-12-01'] * std_ratio\n", "\n", "dta_filardo['dlleading'] = np.log(dta_filardo['leading']).diff()*100\n", "dta_filardo['dmdlleading'] = dta_filardo['dlleading'] - dta_filardo['dlleading'].mean()\n", "\n", "# Plot the data\n", "dta_filardo['dlip'].plot(title='Standardized growth rate of industrial production', figsize=(13,3))\n", "plt.figure()\n", "dta_filardo['dmdlleading'].plot(title='Leading indicator', figsize=(13,3));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The time-varying transition probabilities are specified by the `exog_tvtp` parameter.\n", "\n", "Here we demonstrate another feature of model fitting - the use of a random search for MLE starting parameters. Because Markov switching models are often characterized by many local maxima of the likelihood function, performing an initial optimization step can be helpful to find the best parameters.\n", "\n", "Below, we specify that 20 random perturbations from the starting parameter vector are examined and the best one used as the actual starting parameters. Because of the random nature of the search, we seed the random number generator beforehand to allow replication of the result." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "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": [ "mod_filardo = sm.tsa.MarkovAutoregression(\n", " dta_filardo.iloc[2:]['dlip'], k_regimes=2, order=4, switching_ar=False,\n", " exog_tvtp=sm.add_constant(dta_filardo.iloc[1:-1]['dmdlleading']))\n", "\n", "np.random.seed(12345)\n", "res_filardo = mod_filardo.fit(search_reps=20)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Markov Switching Model Results
Dep. Variable: dlip No. Observations: 514
Model: MarkovAutoregression Log Likelihood -586.572
Date: Tue, 17 Dec 2019 AIC 1195.144
Time: 23:42:29 BIC 1241.808
Sample: 03-01-1948 HQIC 1213.433
- 04-01-1991
Covariance Type: approx
\n", "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Regime 0 parameters
coef std err z P>|z| [0.025 0.975]
const -0.8659 0.153 -5.658 0.000 -1.166 -0.566
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Regime 1 parameters
coef std err z P>|z| [0.025 0.975]
const 0.5173 0.077 6.706 0.000 0.366 0.668
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Non-switching parameters
coef std err z P>|z| [0.025 0.975]
sigma2 0.4844 0.037 13.172 0.000 0.412 0.556
ar.L1 0.1895 0.050 3.761 0.000 0.091 0.288
ar.L2 0.0793 0.051 1.552 0.121 -0.021 0.180
ar.L3 0.1109 0.052 2.136 0.033 0.009 0.213
ar.L4 0.1223 0.051 2.418 0.016 0.023 0.221
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Regime transition parameters
coef std err z P>|z| [0.025 0.975]
p[0->0].tvtp0 1.6494 0.446 3.702 0.000 0.776 2.523
p[1->0].tvtp0 -4.3595 0.747 -5.833 0.000 -5.824 -2.895
p[0->0].tvtp1 -0.9945 0.566 -1.758 0.079 -2.103 0.114
p[1->0].tvtp1 -1.7702 0.508 -3.484 0.000 -2.766 -0.775


Warnings:
[1] Covariance matrix calculated using numerical (complex-step) differentiation." ], "text/plain": [ "\n", "\"\"\"\n", " Markov Switching Model Results \n", "================================================================================\n", "Dep. Variable: dlip No. Observations: 514\n", "Model: MarkovAutoregression Log Likelihood -586.572\n", "Date: Tue, 17 Dec 2019 AIC 1195.144\n", "Time: 23:42:29 BIC 1241.808\n", "Sample: 03-01-1948 HQIC 1213.433\n", " - 04-01-1991 \n", "Covariance Type: approx \n", " Regime 0 parameters \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const -0.8659 0.153 -5.658 0.000 -1.166 -0.566\n", " Regime 1 parameters \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const 0.5173 0.077 6.706 0.000 0.366 0.668\n", " Non-switching parameters \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "sigma2 0.4844 0.037 13.172 0.000 0.412 0.556\n", "ar.L1 0.1895 0.050 3.761 0.000 0.091 0.288\n", "ar.L2 0.0793 0.051 1.552 0.121 -0.021 0.180\n", "ar.L3 0.1109 0.052 2.136 0.033 0.009 0.213\n", "ar.L4 0.1223 0.051 2.418 0.016 0.023 0.221\n", " Regime transition parameters \n", "=================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "---------------------------------------------------------------------------------\n", "p[0->0].tvtp0 1.6494 0.446 3.702 0.000 0.776 2.523\n", "p[1->0].tvtp0 -4.3595 0.747 -5.833 0.000 -5.824 -2.895\n", "p[0->0].tvtp1 -0.9945 0.566 -1.758 0.079 -2.103 0.114\n", "p[1->0].tvtp1 -1.7702 0.508 -3.484 0.000 -2.766 -0.775\n", "=================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using numerical (complex-step) differentiation.\n", "\"\"\"" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res_filardo.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we plot the smoothed probability of the economy operating in a low-production state, and again include the NBER recessions for comparison." ] }, { "cell_type": "code", "execution_count": 12, "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=(12,3))\n", "\n", "ax.plot(res_filardo.smoothed_marginal_probabilities[0])\n", "ax.fill_between(usrec.index, 0, 1, where=usrec['USREC'].values, color='gray', alpha=0.2)\n", "ax.set_xlim(dta_filardo.index[6], dta_filardo.index[-1])\n", "ax.set(title='Smoothed probability of a low-production state');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the time-varying transition probabilities, we can see how the expected duration of a low-production state changes over time:\n" ] }, { "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": [ "res_filardo.expected_durations[0].plot(\n", " title='Expected duration of a low-production state', figsize=(12,3));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "During recessions, the expected duration of a low-production state is much higher than in an expansion." ] } ], "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 }