Glossary

Stationary Bootstrap

A resampling method for stationary time series that constructs pseudo-time series by concatenating blocks of random length drawn from a geometric distribution. The resulting pseudo-series is itself stationary, yielding better finite-sample performance.

Definition

Why It Matters

Standard bootstrap methods assume independent and identically distributed observations, an assumption violated by time-series data where autocorrelation structure carries essential information. The stationary bootstrap, introduced by Politis and Romano (1994), preserves the dependence structure while maintaining stationarity of the resampled series. This makes it suitable for constructing confidence intervals, computing standard errors, and conducting hypothesis tests for time-series statistics where analytical distributions are unavailable.

Example

A researcher estimating the Sharpe ratio of the BIST-100 index needs a confidence interval but no analytical formula exists for the estimator's distribution. Using the stationary bootstrap with an average block length of 10 trading days, 1,000 pseudo-series are generated, the Sharpe ratio is computed for each, and the 2.5th and 97.5th percentiles yield a 95% confidence interval. The random block lengths ensure that the resampled series preserves the volatility clustering present in the original data.

Related Terms

Software Notes

SPSS: Not natively supported; use R integration for stationary bootstrap resampling.
R: Use the sb() function from the np package or the stationary_bootstrap() function from the boot package with custom statistics. The meboot package offers an alternative maximum-entropy bootstrap for stationary series.
Stata: No built-in command; implement the stationary bootstrap using simulate with a custom program that draws geometric-length blocks. The boottest package supports wild bootstrap but not stationary bootstrap directly.