Statistical analysis of high-order Markov dependencies

Abstract

The paper deals with parsimonious models of integer valued time series. Such models are special cases of high-order Markov chain with a small number of parameters. Two new parsimonious models are presented. The first is Markov chain of order s with r partial connections, and the second model is called Markov chain of conditional order. Theoretical results on probabilistic properties and statistical inferences for these models are given.