Open Access
December 2017 On the validity of resampling methods under long memory
Shuyang Bai, Murad S. Taqqu
Ann. Statist. 45(6): 2365-2399 (December 2017). DOI: 10.1214/16-AOS1524


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.


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Shuyang Bai. Murad S. Taqqu. "On the validity of resampling methods under long memory." Ann. Statist. 45 (6) 2365 - 2399, December 2017.


Received: 1 February 2016; Revised: 1 August 2016; Published: December 2017
First available in Project Euclid: 15 December 2017

zbMATH: 06838136
MathSciNet: MR3737895
Digital Object Identifier: 10.1214/16-AOS1524

Primary: 62G09 , 62M10

Keywords: block sampling , Canonical correlation , long memory , long-range dependence , noncentral limit theorems , Resampling , sampling window , subsampling

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 6 • December 2017
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