Statistical estimation of high-order dependencies in discrete-valued time series

Abstract

Any digital society generates a lot of discrete-valued data. If this discrete-valued data are considered in dynamics (in dependence on time t ∈ Z) we get discrete-valued time series x t ∈ A, where A is some discrete set. This paper is devoted to probabilistic modeling and statistical analysis of high order stochastic dependencies of x t on its prehistory {x τ : τ < t}. The outline of the paper is as follows: Markov chain of order s and its parsimonious (small-parametric) models; approaches to construction of parsimonious models; FBE-method for statistical estimation of parameters in parsimonious models; robustness in statistical estimation of parameters for parsimonious models; application to computer data analysis