Block Bootstrap (Moving Block and Stationary)
Block Bootstrap (Moving Block and Stationary Bootstrap) · Also known as: moving block bootstrap, stationary bootstrap, blok bootstrap (moving block / stationary)
Block bootstrap is a resampling method for dependent, autocorrelated time-series data: instead of resampling single observations, it resamples whole blocks of consecutive observations so the serial-correlation structure is preserved. The moving block variant was introduced by Künsch (1989) and the stationary variant by Politis and Romano (1994).
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When to use it
Use block bootstrap when you need standard errors or confidence intervals for a statistic computed on autocorrelated time-series data and you do not want to assume a parametric error model. It expects a genuine time-series structure and a reasonable length — at least about 50 observations — because the block length must be chosen to match the autocorrelation. With short series (n below 30) too few blocks are available and the dependence cannot be reproduced; below 20 observations the block-length choice becomes unreliable and a plain bootstrap is preferable.
Strengths & limitations
- Preserves the serial-correlation structure of the data, so inference stays valid under dependence where the ordinary bootstrap fails.
- Distribution-free: it does not require normality or a parametric model for the errors.
- Offers both fixed-length (moving block) and stationarity-preserving (stationary) variants to suit the series at hand.
- Results are sensitive to the block length, which must be tuned to the autocorrelation structure and has no universally optimal choice.
- Needs a reasonably long series (around 50+ observations); short series leave too few blocks to capture the dependence.
- Assumes (approximate) stationarity of the series; strong trends or structural breaks undermine the resampling.
Frequently asked
How is block bootstrap different from the ordinary bootstrap?
The ordinary bootstrap resamples individual observations independently, which destroys any time dependence. Block bootstrap resamples consecutive blocks of observations, keeping the within-block correlation intact so inference remains valid for autocorrelated data.
What is the difference between the moving block and stationary versions?
The moving block bootstrap uses fixed-length overlapping blocks. The stationary bootstrap of Politis and Romano draws blocks of random, geometrically distributed length, which makes the resampled series itself stationary and reduces sensitivity to a single block-length choice.
How do I choose the block length?
The block length should match the autocorrelation structure: long enough to capture the meaningful dependence but short enough to leave many distinct blocks. There is no single optimal value, so it is the key tuning decision and should be guided by the autocorrelation of the series.
What if my time series is short?
With fewer than about 30 observations there are too few blocks to preserve the dependence, and below 20 the block-length choice is unreliable. In those cases a standard bootstrap or a permutation test is the safer alternative.
Sources
- Künsch, H. R. (1989). The Jackknife and the Bootstrap for General Stationary Observations. Annals of Statistics, 17(3), 1217-1241. DOI: 10.1214/aos/1176347265 ↗
- Politis, D. N., & Romano, J. P. (1994). The Stationary Bootstrap. Journal of the American Statistical Association, 89(428), 1303-1313. DOI: 10.1080/01621459.1994.10476870 ↗
How to cite this page
ScholarGate. (2026, June 1). Block Bootstrap (Moving Block and Stationary Bootstrap). ScholarGate. https://scholargate.app/en/statistics/block-bootstrap
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