{ "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": { "execution": { "iopub.execute_input": "2020-11-06T18:27:01.263214Z", "iopub.status.busy": "2020-11-06T18:27:01.262241Z", "iopub.status.idle": "2020-11-06T18:27:03.363561Z", "shell.execute_reply": "2020-11-06T18:27:03.363020Z" } }, "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": { "execution": { "iopub.execute_input": "2020-11-06T18:27:03.375749Z", "iopub.status.busy": "2020-11-06T18:27:03.375262Z", "iopub.status.idle": "2020-11-06T18:27:07.077906Z", "shell.execute_reply": "2020-11-06T18:27:07.078301Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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