Multiple hidden Markov models for categorical time series

Abstract

We introduce multiple hidden Markov models (MHMMs) where an observed multivariate categorical time series depends on an unobservable multivariate Markov chain. MHMMs provide an elegant framework for specifying various independence relationships between multiple discrete time processes. These independencies are interpreted as Markov properties of a mixed graph and a chain graph associated to the latent and observable components of the MHMM, respectively. These Markov properties are also translated into zero restrictions on the parameters of marginal models for the transition probabilities and the distributions of the observable variables given the latent states.

Hidden Markov Models for Longitudinal Rating Data with Dynamic Response Styles

“…Point (ii) above can be based on the approach of graphical HMMs by Colombi and Giordano (2015). Regarding point (iii), Assumption B4 on the observation model can be relaxed by modelling the observation probabilities as function of individual covariates as an alternative to the presence of covariate effects on the latent component.…”

“…is analogous to the Granger non causality assumption A1. This model, according to which each latent variable does not Granger cause the other one, is a special case of the graphical multiple HMMs introduced by Colombi and Giordano (2015). The drawback of this model is that, under the two non Granger causality conditions, the transition probabilities π it (u, l|ū, l) do not have a closed expression and must be computed numerically as a function of the probabilities π U it (u|ū), π L it (l| l) and a set of k − 1 odds ratios defined on the bivariate transition probabilities.…”

“…The drawback of this model is that, under the two non Granger causality conditions, the transition probabilities π it (u, l|ū, l) do not have a closed expression and must be computed numerically as a function of the probabilities π U it (u|ū), π L it (l| l) and a set of k − 1 odds ratios defined on the bivariate transition probabilities. See Colombi and Giordano (2015) for more details on these Granger non causality conditions and on a marginal parametrization that can be used in this context.…”

Hidden Markov Model for Exchange Rate with EWMA Control Chart

“…In time series cases, there are many researches which studied about hidden Markov model. One of them discussed robust classification of multivariate time series as explained in [6], categorical time series which introduced in [7], and time series modeling for risk also obtained in [8]. Moreover, to predict a trend in financial time series using hidden Markov model was also as discussed in [9].…”