Bootstrap long memory processes in the frequency domain

Abstract

The aim of the paper is to describe a bootstrap, contrary to the sieve bootstrap, valid under either long memory ($\mathit{LM}$) or short memory ($\mathit{SM}$) dependence. One of the reasons of the failure of the sieve bootstrap in our context is that under $\mathit{LM}$ dependence, the sieve bootstrap may not be able to capture the true covariance structure of the original data. We also describe and examine the validity of the bootstrap scheme for the least squares estimator of the parameter in a regression model and for model specification. The motivation for the latter example comes from the observation that the asymptotic distribution of the test is intractable.