Sieve bootstrap with variable length Markov chains for stationary categorical time series

Peter Bühlmann

October 1999

Abstract

We study a bootstrap for stationary categorical time series based on the method of sieves. The data generating process is approximated by so-called variable length Markov chains [VLMC], a flexible but still parsimoniously parameterized class of Markov models. Then, the resampling is given by simulating from the fitted model. We show that in the `niche' of categorical time series, the VLMC-sieve outperforms the more general block bootstrap. Moreover, the VLMC-sieve scheme enjoys the implementational advantage of using the plug-in rule for bootstrapping a statistical procedure, which is generally not the case for the block method. Our results are illustrated from a theoretical and empirical perspective. For the latter, we also present a real data application about (in-) homogeneity classification of a DNA strand.

Download:

Compressed Postscript (146 Kb)
PDF (319 Kb)

Go back to the Research Reports from Seminar für Statistik.