## The Annals of Statistics

### On the validity of resampling methods under long memory

#### 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.

#### Article information

Source
Ann. Statist., Volume 45, Number 6 (2017), 2365-2399.

Dates
Revised: August 2016
First available in Project Euclid: 15 December 2017

https://projecteuclid.org/euclid.aos/1513328576

Digital Object Identifier
doi:10.1214/16-AOS1524

Mathematical Reviews number (MathSciNet)
MR3737895

Zentralblatt MATH identifier
06838136

#### Citation

Bai, Shuyang; Taqqu, Murad S. On the validity of resampling methods under long memory. Ann. Statist. 45 (2017), no. 6, 2365--2399. doi:10.1214/16-AOS1524. https://projecteuclid.org/euclid.aos/1513328576

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