{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Detrending, Stylized Facts and the Business Cycle\n", "\n", "In an influential article, Harvey and Jaeger (1993) described the use of unobserved components models (also known as \"structural time series models\") to derive stylized facts of the business cycle.\n", "\n", "Their paper begins:\n", "\n", " \"Establishing the 'stylized facts' associated with a set of time series is widely considered a crucial step\n", " in macroeconomic research ... For such facts to be useful they should (1) be consistent with the stochastic\n", " properties of the data and (2) present meaningful information.\"\n", " \n", "In particular, they make the argument that these goals are often better met using the unobserved components approach rather than the popular Hodrick-Prescott filter or Box-Jenkins ARIMA modeling techniques.\n", "\n", "statsmodels has the ability to perform all three types of analysis, and below we follow the steps of their paper, using a slightly updated dataset." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "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", "\n", "from IPython.display import display, Latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Unobserved Components\n", "\n", "The unobserved components model available in statsmodels can be written as:\n", "\n", "$$\n", "y_t = \\underbrace{\\mu_{t}}_{\\text{trend}} + \\underbrace{\\gamma_{t}}_{\\text{seasonal}} + \\underbrace{c_{t}}_{\\text{cycle}} + \\sum_{j=1}^k \\underbrace{\\beta_j x_{jt}}_{\\text{explanatory}} + \\underbrace{\\varepsilon_t}_{\\text{irregular}}\n", "$$\n", "\n", "see Durbin and Koopman 2012, Chapter 3 for notation and additional details. Notice that different specifications for the different individual components can support a wide range of models. The specific models considered in the paper and below are specializations of this general equation.\n", "\n", "### Trend\n", "\n", "The trend component is a dynamic extension of a regression model that includes an intercept and linear time-trend.\n", "\n", "\n", "\\begin{align}\n", "\\underbrace{\\mu_{t+1}}_{\\text{level}} & = \\mu_t + \\nu_t + \\eta_{t+1} \\qquad & \\eta_{t+1} \\sim N(0, \\sigma_\\eta^2) \\\\\\\\\n", "\\underbrace{\\nu_{t+1}}_{\\text{trend}} & = \\nu_t + \\zeta_{t+1} & \\zeta_{t+1} \\sim N(0, \\sigma_\\zeta^2) \\\\\n", "\\end{align}\n", "\n", "\n", "where the level is a generalization of the intercept term that can dynamically vary across time, and the trend is a generalization of the time-trend such that the slope can dynamically vary across time.\n", "\n", "For both elements (level and trend), we can consider models in which:\n", "\n", "- The element is included vs excluded (if the trend is included, there must also be a level included).\n", "- The element is deterministic vs stochastic (i.e. whether or not the variance on the error term is confined to be zero or not)\n", "\n", "The only additional parameters to be estimated via MLE are the variances of any included stochastic components.\n", "\n", "This leads to the following specifications:\n", "\n", "| | Level | Trend | Stochastic Level | Stochastic Trend |\n", "|----------------------------------------------------------------------|-------|-------|------------------|------------------|\n", "| Constant | ✓ | | | |\n", "| Local Level
(random walk) | ✓ | | ✓ | |\n", "| Deterministic trend | ✓ | ✓ | | |\n", "| Local level with deterministic trend
(random walk with drift) | ✓ | ✓ | ✓ | |\n", "| Local linear trend | ✓ | ✓ | ✓ | ✓ |\n", "| Smooth trend
(integrated random walk) | ✓ | ✓ | | ✓ |\n", "\n", "### Seasonal\n", "\n", "The seasonal component is written as:\n", "\n", "$$\n", "\\gamma_t = - \\sum_{j=1}^{s-1} \\gamma_{t+1-j} + \\omega_t \\qquad \\omega_t \\sim N(0, \\sigma_\\omega^2)\n", "$$\n", "\n", "The periodicity (number of seasons) is s, and the defining character is that (without the error term), the seasonal components sum to zero across one complete cycle. The inclusion of an error term allows the seasonal effects to vary over time.\n", "\n", "The variants of this model are:\n", "\n", "- The periodicity s\n", "- Whether or not to make the seasonal effects stochastic.\n", "\n", "If the seasonal effect is stochastic, then there is one additional parameter to estimate via MLE (the variance of the error term).\n", "\n", "### Cycle\n", "\n", "The cyclical component is intended to capture cyclical effects at time frames much longer than captured by the seasonal component. For example, in economics the cyclical term is often intended to capture the business cycle, and is then expected to have a period between \"1.5 and 12 years\" (see Durbin and Koopman).\n", "\n", "The cycle is written as:\n", "\n", "\n", "\\begin{align}\n", "c_{t+1} & = c_t \\cos \\lambda_c + c_t^* \\sin \\lambda_c + \\tilde \\omega_t \\qquad & \\tilde \\omega_t \\sim N(0, \\sigma_{\\tilde \\omega}^2) \\\\\\\\\n", "c_{t+1}^* & = -c_t \\sin \\lambda_c + c_t^* \\cos \\lambda_c + \\tilde \\omega_t^* & \\tilde \\omega_t^* \\sim N(0, \\sigma_{\\tilde \\omega}^2)\n", "\\end{align}\n", "\n", "\n", "The parameter $\\lambda_c$ (the frequency of the cycle) is an additional parameter to be estimated by MLE. If the seasonal effect is stochastic, then there is one another parameter to estimate (the variance of the error term - note that both of the error terms here share the same variance, but are assumed to have independent draws).\n", "\n", "### Irregular\n", "\n", "The irregular component is assumed to be a white noise error term. Its variance is a parameter to be estimated by MLE; i.e.\n", "\n", "$$\n", "\\varepsilon_t \\sim N(0, \\sigma_\\varepsilon^2)\n", "$$\n", "\n", "In some cases, we may want to generalize the irregular component to allow for autoregressive effects:\n", "\n", "$$\n", "\\varepsilon_t = \\rho(L) \\varepsilon_{t-1} + \\epsilon_t, \\qquad \\epsilon_t \\sim N(0, \\sigma_\\epsilon^2)\n", "$$\n", "\n", "In this case, the autoregressive parameters would also be estimated via MLE.\n", "\n", "### Regression effects\n", "\n", "We may want to allow for explanatory variables by including additional terms\n", "\n", "$$\n", "\\sum_{j=1}^k \\beta_j x_{jt}\n", "$$\n", "\n", "or for intervention effects by including\n", "\n", "\n", "\\begin{align}\n", "\\delta w_t \\qquad \\text{where} \\qquad w_t & = 0, \\qquad t < \\tau, \\\\\\\\\n", "& = 1, \\qquad t \\ge \\tau\n", "\\end{align}\n", "\n", "\n", "These additional parameters could be estimated via MLE or by including them as components of the state space formulation.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data\n", "\n", "Following Harvey and Jaeger, we will consider the following time series:\n", "\n", "- US real GNP, \"output\", ([GNPC96](https://research.stlouisfed.org/fred2/series/GNPC96))\n", "- US GNP implicit price deflator, \"prices\", ([GNPDEF](https://research.stlouisfed.org/fred2/series/GNPDEF))\n", "- US monetary base, \"money\", ([AMBSL](https://research.stlouisfed.org/fred2/series/AMBSL))\n", "\n", "The time frame in the original paper varied across series, but was broadly 1954-1989. Below we use data from the period 1948-2008 for all series. Although the unobserved components approach allows isolating a seasonal component within the model, the series considered in the paper, and here, are already seasonally adjusted.\n", "\n", "All data series considered here are taken from [Federal Reserve Economic Data (FRED)](https://research.stlouisfed.org/fred2/). Conveniently, the Python library [Pandas](https://pandas.pydata.org/) has the ability to download data from FRED directly." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "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": [ "# Datasets\n", "from pandas_datareader.data import DataReader\n", "\n", "# Get the raw data\n", "start = '1948-01'\n", "end = '2008-01'\n", "us_gnp = DataReader('GNPC96', 'fred', start=start, end=end)\n", "us_gnp_deflator = DataReader('GNPDEF', 'fred', start=start, end=end)\n", "us_monetary_base = DataReader('AMBSL', 'fred', start=start, end=end).resample('QS').mean()\n", "recessions = DataReader('USRECQ', 'fred', start=start, end=end).resample('QS').last().values[:,0]\n", "\n", "# Construct the dataframe\n", "dta = pd.concat(map(np.log, (us_gnp, us_gnp_deflator, us_monetary_base)), axis=1)\n", "dta.columns = ['US GNP','US Prices','US monetary base']\n", "dates = dta.index._mpl_repr()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To get a sense of these three variables over the timeframe, we can plot them:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", 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