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Selecting the number of regimes in Hidden Markov models is an importantproblem. There are many criteria that are used to select this number, such asAkaike information criterion (AIC), Bayesian information criterion (BIC),integrated completed likelihood (ICL), deviance information criterion (DIC),and Watanabe-Akaike information criterion (WAIC), to name a few. In thisarticle, we introduced goodness-of-fit tests for general Hidden Markov modelswith covariates, where the distribution of the observations is arbitrary, i.e.,continuous, discrete, or a mixture of both. Then, a selection procedure isproposed based on this goodness-of-fit test. The main aim of this article is tocompare the classical information criterion with the new criterion, when theoutcome is either continuous, discrete or zero-inflated. Numerical experimentsassess the finite sample performance of the goodness-of-fit tests, andcomparisons between the different criteria are made.

Are Information criteria good enough to choose the right the number of regimes in Hidden Markov Models?