A note on stationary bootstrap variance estimator under long-range dependence

Taegyu Kang, Young Min Kim and Jongho Im

Statistics & Probability Letters, 2021, vol. 169, issue C

Abstract: The stationary bootstrap method is popularly used to compute the standard errors or confidence regions of estimators, generated from time processes exhibiting weakly dependent stationarity. Most previous stationary bootstrap methods have focused on studying large-sample properties of stationary bootstrap inference about a sample mean under short-range dependence. For long-range dependence, recent studies have investigated the properties of block bootstrap methods using overlapping and non-overlapping blocking techniques with fixed block lengths. However, the characteristics of a stationary bootstrap with random block lengths are less well-known under long-range dependence. We investigate the asymptotic property of a stationary bootstrap variance estimator for a sample mean under long-range dependence. Our theoretical and simulation results indicate that the stationary bootstrap method does not have n−consistency for stationary and long-range dependent time processes.

Keywords: Bootstrap variance estimation; Long-range dependence; Stationary bootstrap (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2020.108971

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