Simulation output analysis using the threshold bootstrap

The threshold bootstrap extends the bootstrap method of inference to autocorrelated data series, such as the outputs of discrete event simulations. The method works by resampling random chunks that 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. Monte Carlo simulations show that the threshold bootstrap performs well in estimating the standard error of the sample mean and constructing confidence intervals with appropriate coverage and compact half-widths. We establish the asymptotic unbiasedness and consistency of threshold bootstrap estimates in the case of the sample mean. Comparison with the method of batch means and the moving blocks bootstrap shows that the threshold bootstrap is an attractive alternative for simulation output analysis.