Second-order autoregressive Hidden Markov Model

Abstract

We propose an extension of Hidden Markov Model (HMM) to support second-order Markov dependence in the observable random process. We propose a Bayesian method to estimate the parameters of the model and the non-observable sequence of states. We compare and select the best model, including the dependence order and number of states, using model selection criteria like Bayes factor and deviance information criterion (DIC). We apply the procedure to several simulated datasets and verify the good performance of the estimation procedure. Tests with a real dataset show an improved fitting when compared with usual first order HMMs demonstrating the usefulness of the proposed model.