Sieve Bootstrap With Variable-Length Markov Chains for Stationary Categorical Time Series

Abstract

A bootstrap for stationary categorical time series based on the method of sieves is studied here. The data-generating process is approximated by the so-called variable-length Markov chain (VLMC), a flexible class of Markov models that allows for parsimonious structure. Then the resampling is given by simulating from the fitted model. It is shown that for a whole class of stationary categorical time series that is more general than VLMC, the VLMC sieve has faster rate of convergence for variance estimation than the more general block bootstrap. Results are illustrated from a theoretical and empirical perspective. For the latter, a real data application about (in-) homogeneity classification of a DNA strand is also presented. Finally, the VLMC sieve scheme enjoys an implementational advantage of using the plug-in rule for bootstrapping a statistical procedure, which generally is not the case for the block method.