The Sieve Bootstrap

Ordinary bootstrap resampling assumes observations are independent, which is exactly what time series aren't — today's return is correlated with yesterday's. The sieve bootstrap handles dependence by first fitting an autoregressive model to the data (a model that predicts each value from a number of its own past values), which captures most of the time-dependence in a manageable form. It then bootstraps the model's residuals, which by construction are close to independent, and uses the fitted autoregressive structure to simulate new time series from those resampled residuals — new series that share the original data's dependence structure without ever needing to resample overlapping blocks of raw data.

The "sieve" in the name refers to the fact that the order of the fitted autoregressive model is allowed to grow slowly as the sample size increases, so the approximation becomes arbitrarily accurate for a very broad class of stationary processes, not just ones that are literally autoregressive.

A worked example

Given 2,000 days of daily returns, a sieve bootstrap might fit an AR(5) model (using the last five days to predict the next), producing a set of roughly independent residuals. Resampling those residuals with replacement and running them back through the fitted AR(5) equation generates a new synthetic 2,000-day return series that preserves the original data's short-term autocorrelation structure, giving a more realistic assessment of a strategy's Sharpe ratio uncertainty than a naive bootstrap that shuffled daily returns independently and destroyed the autocorrelation entirely.