The threshold bootstrap and threshold jackknife

Abstract

We propose two new resampling schemes for weakly dependent time series: the threshold bootstrap (TB) and the threshold jackknife (TJ). The TB works by resampling random length chunks which are some multiple of a cycle. A cycle consists of alternating high and low runs that are created when the time series wanders back and forth across a threshold. Similarly, TJ replicates are created by sequentially deleting chunks. Monte Carlo simulations show that, for various ARMA models, the TB performs better than the moving blocks bootstrap and stationary bootstrap with respect to the mean squared error of the standard error estimate of the sample mean, when each resampling scheme uses its optimal chunk/block size. The TB and stationary bootstrap are comparable when approximating the sampling distribution of the sample mean, while the moving blocks bootstrap has relatively poor performance. The TB is simpler than the matched-block bootstrap, though less accurate for short AR(1) series. Simulations also show that the TB and TJ have similar performance when estimating the standard error of the sample mean.