Structural Breaks and Switching Models |
On another page, we discuss basic stability tests (tests for the lack of a structural break). Here, we’ll look at more advanced ways of testing for breaks, and consider models that incorporate one or more structural breaks. In most cases, we are actually testing a proposed model for specification errors. Does a single specification seem to work across the entire data set? Are the errors homoscedastic, or are they higher in one part of the data set? If the model fails to pass the test, it’s very rare that the alternative model with the break is actually what we would think is “correct.” Instead, it simply points us in the direction of a better model. Most of the newer techniques are likewise specification tests on a simpler model. Let’s look more closely at what we’ve seen earlier:
Why would we be interested in the estimates from a subset (particularly a very small subset) of the data if we were convinced that the data were accurately described with a time-invariant model? With recursive least squares, the alternative to the null hypothesis of a time-invariant model with i.i.d. residuals is the vague alternative that they aren’t. The CUSUM test looks for breaks in the model itself, while CUSUMSQ examines breaks in the variance.
For least squares, RLS can do the calculations of the sequential estimates very quickly using the Kalman filter. The same types of calculation can be done (less efficiently) for other types of models with direct sequential estimation.
This computes a set of linear regressions with a complete break at a relatively arbitrary location (to test for stability of the variance). Clearly, the sample split used is not intended as an alternative “model”; it’s chosen to maximize the power of the test in case the variance does indeed change systematically with the variable which controls the split.
Similar to tests based upon the recursive residuals, these use the fact that under the null of a correct and time-invariant model, various subsample statistics should “fluctuate” in a particular way. If they don’t, that is taken as evidence against the model, without necessarily suggesting a specific alternative. See the GARCHFLUX.RPF program for an example of the use of the general @FLUX procedure for testing stability in a non-linear model. (@STABTEST is for linear models only).
A standard Chow test uses a sample split at a known location, testing for a complete break in the specification at that point. A full structural break is unlikely to be of much use—are there no coefficients that we think are the same across the sample?
Other Topics in this Section
Rolling Sample Estimation describes how to estimate a model (linear or non-linear) with rolling samples, typically either adding entries to the end (which is what recursive least squares does) or moving a window of fixed size through the data set.
A General Structure for Analyzing Breaks looks at how to organize a calculation of a model with unknown break points.
Unit Roots and Breaks looks at tests for unit roots allowing for breaks.
Switching Models is an overview of the different types of "switching" models to help you choose the appropriate form.
Threshold Autoregression discusses various forms of "threshold" models where the model switches form depending upon the observed value of some series.
Markov Switching Models describes how to estimate models which switch under the control of an unobserved Markov chain.
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