Locally Stationary Processes and the Local Block Bootstrap

Abstract

This chapter describes locally stationary processes and the local block bootstrap. For time series that are not stationary, the block bootstrap is not directly applicable. It is found that because of the nonstationarity, the block bootstrap method is not directly applicable, and neither are its different variations such as the stationary bootstrap. Rather, a modification that takes into account the changing stochastic structure should be constructed. Such a modification has been proposed in the Local Block Bootstrap (LBB) procedure. The basic premise of the LBB is to only resample blocks that are close to each other. It is found that doing a block bootstrap within the local window would require a block size b that is big but small with respect to the local window size. An approximation to the sampling distribution of the sample mean is presented. It is observed that to investigate the consistency of the LBB, one requires some conditions on the block size, as well as the window size indicating the local neighborhood. © 2003 Elsevier B.V. All rights reserved.