The Stationary Bootstrap
Abstract
This article introduces a resampling procedure called the stationary bootstrap as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on weakly dependent stationary observations. Previously, a technique based on resampling blocks of consecutive observations was introduced to construct confidence intervals for a parameter of the m-dimensional joint distribution of m consecutive observations, where m is fixed. This procedure has been generalized by constructing a “blocks of blocks” resampling scheme that yields asymptotically valid procedures even for a multivariate parameter of the whole (i.e., infinite-dimensional) joint distribution of the stationary sequence of observations. These methods share the construction of resampling blocks of observations to form a pseudo-time series, so that the statistic of interest may be recalculated based on the resampled data set. But in the context of applying this method to stationary data, it is natural to require the resampled pseudo-time series to be stationary (conditional on the original data) as well. Although the aforementioned procedures lack this property, the stationary procedure developed here is indeed stationary and possesses other desirable properties. The stationary procedure is based on resampling blocks of random length, where the length of each block has a geometric distribution. In this article, fundamental consistency and weak convergence properties of the stationary resampling scheme are developed.
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The paper uses stationary bootstrap resampling from Politis and Romano in its reality-check procedure.
“We resample G using the stationary bootstrap method of Politis and Romano (1994), with prespecified parameter set X, for B times, and label each resample as G b , b = 1, ⋯ , B.”
From Profitability and Data-Snooping Tests of Four Technical Trade Strategies for Cryptocurrency Pair BTC/USDT and ETH/USDT in Cryptocurrency Markets During 2022–2023 (2023) · cites this paper as Politis and Romano (1994)
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- Authors
- Politis, D. N., & Romano, J. P.
- Affiliations
- Purdue University West Lafayette (US)
- Stanford University (US)
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1994-12
- Volume
- 89
- Issue
- 428
- Pages
- 1303-1313
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2076396344
- Cited by
- 2,649
- References
- 27
- Citations by year
- 2026: 279 · 2025: 137 · 2024: 113 · 2023: 108 · 2022: 102 · 2021: 124 · 2020: 136 · 2019: 117 · 2018: 117 · 2017: 129 · 2016: 125 · 2015: 120 · 2014: 119 · 2013: 117 · 2012: 130
- FWCI
- 9.25
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- Helmholtz Centre for Ocean Research Kiel (GEOMAR) (acceptedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Keywords
- stationary bootstrap, resampling, standard errors, confidence regions, geometric distribution, consistency, weak convergence, infinite-dimensional parameters, block bootstrap
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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