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.

Statistical analysis of multivariate discrete-valued time series

“…To avoid this ''curse of dimensionality'' it is appropriate to use parsimonious models of high-order Markov chains that are determined by small number of parameters, say M ≪ D MC(s) [72]. We review three main approaches [74] for construction of convenient parametrization of the matrix P characterizing the MDV time series by (12).…”