Subsampling for General Statistics under Long Range Dependence with application to change point analysis

Abstract: In the statistical inference for long range dependent time series the shape of the limit distribution typically depends on unknown parameters. Therefore, we propose to use subsampling. We show the validity of subsampling for general statistics and long range dependent subordinated Gaussian processes which satisfy mild regularity conditions. We apply our method to a self-normalized change-point test statistic so that we can test for structural breaks in long range dependent time series without having to estimate any nuisance parameter. The finite sample properties are investigated in a simulation study. We analyze three data sets and compare our results to the conclusions of other authors.