2017•Austrian Journal of StatisticsOpen access

High-order Vector Markov Chain with Partial Connections in Data Analysis

Yu. S. Kharin, M. V. Maltsew

Abstract

A new mathematical model for discrete time series is proposed: homogenous vector Markov chain of the order s with partial connections. Conditional probability distribution for this model is determined only by a few components of previous vector states. Probabilistic properties of the model are given: ergodicity conditions and conditions under which the stationary probability distribution is uniform. Consistent statistical estimators for model parameters are constructed.

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Key concepts: Markov chain, Ergodicity, Mathematics, Discrete phase-type distribution, Continuous-time Markov chain, Additive Markov chain, Applied mathematics, Markov property