This paper considers the determination of the order of hidden Markov models. Recently, a proposed predictive measure, the so-called widely applicable information criterion (WAIC), was derived. This criterion is a convenient alternative to the cross-validation approach due to its less computation processes and quick evaluation. We studied the properties of this criterion applied to hidden Markov models (HMMs) under the Bayesian principle. Such models include serial dependence and overdispersion of observed data. We investigated this criterion via simulation studies and a real data application. It is shown that the introduced criterion performs better with less complicated models, while it tends to over fit some more complicated models.
