June 2021 Bootstrap long memory processes in the frequency domain
Javier Hidalgo
Author Affiliations +
Ann. Statist. 49(3): 1407-1435 (June 2021). DOI: 10.1214/20-AOS2006


The aim of the paper is to describe a bootstrap, contrary to the sieve bootstrap, valid under either long memory (LM) or short memory (SM) dependence. One of the reasons of the failure of the sieve bootstrap in our context is that under LM dependence, the sieve bootstrap may not be able to capture the true covariance structure of the original data. We also describe and examine the validity of the bootstrap scheme for the least squares estimator of the parameter in a regression model and for model specification. The motivation for the latter example comes from the observation that the asymptotic distribution of the test is intractable.


I thank the Associate Editor and three referees for helpful comments which led to a much improved and clearer version of the article. Also, I thank Hao Dong and Chen Qiu for their excellent Monte Carlo computations. Of course, all remaining errors are my sole responsibility.


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Javier Hidalgo. "Bootstrap long memory processes in the frequency domain." Ann. Statist. 49 (3) 1407 - 1435, June 2021. https://doi.org/10.1214/20-AOS2006


Received: 1 February 2017; Revised: 1 March 2020; Published: June 2021
First available in Project Euclid: 9 August 2021

MathSciNet: MR4298869
zbMATH: 1473.62141
Digital Object Identifier: 10.1214/20-AOS2006

Primary: 62F40 , 62G10
Secondary: 62G30 , 62J20

Keywords: Bootstrap methods , Frequency domain , long memory

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.49 • No. 3 • June 2021
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