Number of hidden states and memory: a joint order estimation problem for Markov chains with Markov regime
This paper deals with order identification for Markov chains with Markov regime (MCMR) in the context of finite alphabets. We define the joint order of a MCMR process in terms of the number k of states of the hidden Markov chain and the memory m of the conditional Markov chain. We study the properties of penalized maximum likelihood estimators for the unknown order (k, m) of an observed MCMR process, relying on information theoretic arguments. The novelty of our work relies in the joint...