Finding the number of latent states in hidden Markov models using information criteria

Hidden Markov models (HMMs) are often used to model time series data and are applied in many fields of research. However, estimating the unknown number of hidden states in the Markov chain is a non-trivial component of HMM model selection and an area of active research. Currently, AIC and BIC are commonly used for this purpose, despite theoretical issues and some evidence of poor performance in the literature. Here, motivated by the HMMs developed to model seismic tremor data, we use simulation studies to compare the performance of a number of model selection information criteria when used to select the number of hidden states in HMMs, including an adjusted BIC not previously used with HMMs. We find that AIC and BIC are not always reliable tools for selecting the number of hidden states in HMMs and that other information criteria such as adjusted BIC can actually perform better, depending on factors such as sample size and sojourn times in each state. We apply the information criteria to a set of HMMs fitted to seismic tremor data and compare the models selected by the different criteria.