Bootstrapping locally stationary processes

Abstract

We propose a non-parametric method to bootstrap locally stationary processes which combines a time domain wild bootstrap approach with a non-parametric frequency domain approach. The method generates pseudotime series which mimic (asymptotically) correct, the local second- and to the necessary extent the fourth-order moment structure of the underlying process. Thus it can be applied to approximate the distribution of several statistics that are based on observations of the locally stationary process. We prove a bootstrap central limit theorem for a general class of statistics that can be expressed as functionals of the preperiodogram, the latter being a useful tool for inferring properties of locally stationary processes. Some simulations and a real data example shed light on the finite sample properties and illustrate the ability of the bootstrap method proposed. © 2014 Royal Statistical Society.