Bootstrapping long memory time series: Application in low frequency estimators

Abstract

Bootstrapping time series requires dealing with the dependence that may exist within the sample. Several strategies have been proposed, but their validity has only been proven for short memory series and there has been little progress in their theoretical properties under long memory, where strong persistence may invalidate conventional techniques. The first contribution is to review all these recent advances, paying particular attention to those approaches that do not rely on parametric models and offering a guide for practitioners who wish to use them in semiparametric or nonparametric contexts. The second contribution is a Monte Carlo analysis of the applicability of these bootstrap techniques for approximating the distribution of low frequency estimators of the memory parameter based on spectral behaviour at frequencies close to the origin.