Block Bootstrap

Definition

Block bootstrap is a resampling technique designed for dependent (time-series) data. Instead of resampling individual observations, the block bootstrap resamples contiguous blocks to preserve the serial dependence structure within each block. Variants include the non-overlapping block bootstrap, the moving (overlapping) block bootstrap, and the stationary bootstrap of Politis and Romano (1994), which uses random-length blocks drawn from a geometric distribution. Patton, Politis, and White (2009) provide an automatic method for selecting the optimal block length.

Why It Matters

Standard (i.i.d.) bootstrap methods assume observations are independent, an assumption violated in virtually all time-series data. Resampling individual observations from a dependent series destroys the correlation structure and yields invalid inference. Block bootstrap methods preserve within-block dependence, making them essential for constructing valid confidence intervals and standard errors in time-series econometrics.

Example

A researcher studying daily BIST-100 returns wants to bootstrap the Sharpe ratio. Because daily returns exhibit autocorrelation and volatility clustering, an i.i.d. bootstrap would underestimate the standard error. Instead, the researcher uses a block bootstrap with blocks of 10 trading days, preserving the short-run dependence structure within each resampled block.

Related Terms

• Bootstrap
• Stationary Bootstrap
• Autocorrelation
• GARCH

Software Notes

• SPSS: Not natively available; use R integration via STATS R extension or Python programmability.
• R: Use the boot package with custom block-resampling functions, or the npboot package. The tsbootstrap function in tseries provides basic time-series bootstrap.
• Stata: No built-in block bootstrap; implement manually using bootstrap with a program that resamples blocks, or use the bsamp command from SSC for moving block bootstrap.