Multiscale change point detection for dependent data

Abstract

In this article we study the theoretical properties of the simultaneous multiscale change point estimator (SMUCE) in piecewise-constant signal models with dependent error processes. Empirical studies suggest that in this case the change point estimate is inconsistent, but it is not known if alternatives suggested in the literature for correlated data are consistent. We propose a modification of SMUCE scaling the basic statistic by the long run variance of the error process, which is estimated by a difference-type variance estimator calculated from local means from different blocks. For this modification we prove model consistency for physical-dependent error processes and illustrate the finite sample performance by means of a simulation study.