Journal of Statistical Theory and Practice

, Volume 5, Issue 2, pp 261–284 | Cite as

A Characterization of Categorical Markov Chains

  • Reza HosseiniEmail author
  • Nhu Le
  • Jim Zidek


We prove a representation theorem for {Xt} (t denotes time), an rth order categorical Markov chain. We prove that the conditional probability P(Xt|Xt − 1, …, Xt−r) can be written as a linear combination of the monomials of past process responses Xt − 1, …, Xt−r. Simulations show that the “partial likelihood estimation” and the representation together give us satisfactory results. We also check the performance of “BIC” criterion for selecting optimal models and find that to be quite satisfactory. An advantage of this model over existing models is its capacity to admit covariates as linear terms by extension. For example, we can add some seasonal processes to get a non-stationary chain for daily precipitation values.

AMS Subject Classification

62M05 62M09 60J10 


Categorical stochastic processes Markov chains Characterization Estimation BIC 


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Copyright information

© Grace Scientific Publishing 2011

Authors and Affiliations

  1. 1.University of British ColumbiaVancouverCanada
  2. 2.BC Cancer Agency Research CenterVancouverCanada

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