May 2022 Model-free bootstrap for a general class of stationary time series
Yiren Wang, Dimitris N. Politis
Author Affiliations +
Bernoulli 28(2): 744-770 (May 2022). DOI: 10.3150/21-BEJ1352


A model-free bootstrap procedure for a general class of stationary time series is introduced. The theoretical framework is established, showing asymptotic validity of bootstrap confidence intervals for many statistics of interest. In addition, asymptotic validity of one-step ahead bootstrap prediction intervals is also demonstrated. Finite-sample experiments are conducted to empirically confirm the performance of the new method, and to compare with popular methods such as the block bootstrap and the autoregressive (AR)-sieve bootstrap.

Funding Statement

This research was partially supported by NSF grants DMS 16-13026 and DMS 19-14556.


Many thanks are due to Jens-Peter Kreiss, Stathis Paparoditis, and the participants of the August 2015 Workshop on Recent Developments in Statistics for Complex Dependent Data, Loccum (Germany), where the seeds of this work were first presented. We are also grateful to three anonymous reviewers for their constructive comments.


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Yiren Wang. Dimitris N. Politis. "Model-free bootstrap for a general class of stationary time series." Bernoulli 28 (2) 744 - 770, May 2022.


Received: 1 January 2020; Revised: 1 April 2021; Published: May 2022
First available in Project Euclid: 3 March 2022

MathSciNet: MR4388918
zbMATH: 07526564
Digital Object Identifier: 10.3150/21-BEJ1352

Keywords: bootstrap validity , confidence intervals , m-approximation , Transformation function

Rights: Copyright © 2022 ISI/BS


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Vol.28 • No. 2 • May 2022
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