Discrete-valued time series analysis by parsimonious high-order Markov chains

Problems of statistical analysis of discrete-valued time series are considered. A family of parsimonious (small-parametric) models for observed data are proposed based on high-order Markov chains. Consistent statistical estimators for parameters of the proposed 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 approach is also applied for statistical analysis of spatio-temporal data. Theoretical results are illustrated by results of computer experiments on real statistical data