There are different types of models which allow for some type of "switching" behavior. A popular/trendy choice is the Markov Switching Model (MSM). However, the MSM is only one, and it is (probably by a wide margin) the most complicated and most likely to fail to produce reasonable results. To be more specific, consider three models which are all based upon the following two "regime" linear model:

\begin{equation} y_t = \left\{ {\begin{array}{*{20}c}{X_t \beta _1 + u_t } & {{\rm{if}}\,S_t = 1} \\{X_t \beta _2 + u_t } & {{\rm{if}}\,S_t = 2} \\\end{array}} \right. \label{eq:break_genericregimes} \end{equation}

The simplest possibility is the structural break model, which defines

\begin{equation} S_t = \left\{ {\begin{array}{*{20}c}1 & {{\rm{if}}\,\,t \le T_0 } \\2 & {{\rm{if}}\,\,t > T_0 } \\\end{array}} \right. \label{eq:break_generalswitch} \end{equation}

In most cases where the MSM is the wrong tool, this is what is actually needed. This is designed to look at a one-time change at a particular date (such as relaxation of currency controls, adoption of the Euro, etc.) Now, if you want to test for a change at a specific date, this is just a standard textbook "Chow test". If you want to check more carefully whether a shift occurs at the date of interest (rather than some other date), then this becomes (for a linear model) an application of the @APBreakTest or @BaiPerron procedures. The "General Structure" page describes the process for looking for one or more breaks at an unknown location in a model.

 

Another model type has a threshold break

\begin{equation} S_t = \left\{ {\begin{array}{*{20}c}1 & {{\rm{if}}\,\,Z_{t - d} \le \gamma } \\2 & {{\rm{if}}\,\,Z_{t - d} > \gamma } \\\end{array}} \right. \label{eq:break_genericthreshold} \end{equation}

where \(Z\) is an observable series, but the trigger value \(\gamma\) and possibly the delay \(d\) are unknown and must be estimated (typically by some form of grid search). This gives you different models for "high" and "low" values of the \(Z\) variable. The Threshold Autoregression is the most common form of this, but there is little difference between the handling of threshold autoregressions and a threshold effect on any other type of model.
 

So how does an MSM compare with these? First, in the MSM, \(S_t\) is unobservable—in fact, a more descriptive title for these is Hidden (Regime) Markov Model. Second, and perhaps more important, \(S_t\) is (in most cases) uncontrollable. If more than one parameter is changing between the two regimes, it may be difficult to produce the desired separation between regimes. For instance, a common setup is to allow the \(\beta\)’s (or at least a subset) to change between regimes, with that being the intended interpretation, but to also allow the variances to change as well. Though the intent is that the variance is passively changing to follow the switches in the coefficients, far too often, with that model, the maximum likelihood estimates produce regimes which are best described as low- and high-variance and it's the coefficients that are just what they are in that regime breakdown. By contrast, with the other two types of regime models, you can observe the regimes (given the estimates) and in the case of the threshold model, can describe the conditions which separate the regimes.
 

Copyright © 2026 Thomas A. Doan