Estimation and inference in multivariate Markov chains

The literature of Markov chains has recently focused on modeling multiple categorical data sequences. The usual procedure for handling these multivariate Markov chains (MMC), with $m categorical data and s states, consists of expanding the state space by considering m^{s} new states. This model rapidly becomes intractable even with moderate values of m and s due to the excessive number of parameters to estimate. Ching and Fung...