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

Hidden markov models (hmm) are a ubiquitous tool for modeling timeseries data. the hmm can be poor at capturing dependency between observationsbecause of the statistical assumptions it makes. therefore, the extension of the hmmcalled forward-directed autoregressive hmm (arhmm) is considered to handle thedependencies between observations. it is also more appropriate to use an autoregres-sive hidden markov model directed backward in time. in this paper, we present a sequence-level mixture of these two forms of arhmm (called marhmm), eectively 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.