Specification testing in Markov-switching time-series models

This paper develops a series of specification tests of Markov-switching time-series models. Tests for omitted autocorrelation, omitted ARCH, misspecification of the Markovian dynamics, and omitted explanatory variables are proposed. All of the tests can be constructed as a natural byproduct of the routine used to calculate the ‘smoothed’ probability that a given observation came from a particular regime, and do not require estimation of additional parameters. The paper performs Monte Carlo analysis of the tests and briefly illustrates their use with an empirical application.