Statistical Analysis of Discrete-valued Time Series by Parsimonious High-order Markov Chains

Abstract

Problems of statistical analysis of discrete-valued time series are considered. Two approaches for construction of parsimonious (small-parametric) models for observed discrete data are proposed based on high-order Markov chains.Consistent statistical estimators for parameters of the developed models and some known models, and also statistical tests on the values of parameters are constructed. Probabilistic properties of the constructed statistical inferences are given. The developed theory is also applied for statistical analysis of spatio-temporal data. Theoretical results are illustrated by computer experiments on real statistical data.