On the validity of resampling methods under long memory
The Annals of Statistics · 2017 · Volume 45 · Issue 6
Abstract
For long-memory time series, inference based on resampling is of crucial importance, since the asymptotic distribution can often be non-Gaussian and is difficult to determine statistically. However, due to the strong dependence, establishing the asymptotic validity of resampling methods is nontrivial. In this paper, we derive an efficient bound for the canonical correlation between two finite blocks of a long-memory time series. We show how this bound can be applied to establish the asymptotic consistency of subsampling procedures for general statistics under long memory. It allows the subsample size $b$ to be $o(n)$, where $n$ is the sample size, irrespective of the strength of the memory. We are then able to improve many results found in the literature. We also consider applications of subsampling procedures under long memory to the sample covariance, M-estimation and empirical processes.
Keywords
62G09, 62M10, block sampling, Canonical correlation, long memory, long-range dependence, noncentral limit theorems, Resampling, sampling window, subsampling
Enable JavaScript for citation tools and additional paper interactions.