Model selection in hidden Markov models : a simulation study

A review of model selection procedures in hidden Markov models reveals contrasting evidence about the reliability and the precision of the most commonly used methods. In order to evaluate and compare existing proposals, we develop a Monte Carlo experiment which allows a powerful insight on the behaviour of the most widespread model selection methods. We find that the number of observations, the conditional state-dependent probabilities, and the latent transition matrix are the main factors influencing information criteria and likelihood ratio test results. We also find evidence that, for shorter univariate time series, AIC strongly outperforms BIC.