Mixture of Forward-Directed and Backward-Directed Autoregressive Hidden Markov Models for Time Series Modeling

Hidden Markov models (HMM) are a ubiquitous tool for modeling time series data. The HMM can be poor at capturing dependency between observations because of the statistical assumptions it makes. Therefore, the extension of the HMM called forward-directed Autoregressive HMM (ARHMM) is considered to handle the dependencies between observations. It is also  more appropriate to use an Autoregressive Hidden Markov Model directed backward in time. In this paper, we present a sequence-level mixture of these two forms of ARHMM (called MARHMM), effectively allowing the model to choose for itself whether a forward-directed or backward-directed model or a soft combination of the two models are most appropriate for a given data set. For this purpose, we use the conditional independence relations in the context of a Bayesian network which is a probabilistic graphical model. The performance of the MARHMM is discussed by applying it to the simulated and real data sets. We show that the proposed model has greater modeling power than the conventional forward-directed ARHMM.