Multiplier subsample bootstrap for statistics of time series

Abstract

Block-based bootstrap, block-based subsampling and multiplier bootstrap are three common nonparametric tools for statistical inference under dependent observations. Combining the ideas of those three, a novel resampling approach, the multiplier subsample bootstrap (MSB), is proposed. Instead of generating a resample from the observations, the MSB imitates the statistic by weighting the block-based subsample statistics with independent standard Gaussian random variables. Given the asymptotic normality of the statistic, the bootstrap validity is established under some mild moment conditions. Involving the idea of MSB, the other resampling approach, the hybrid multiplier subsampling periodogram bootstrap (HMP), is developed for mimicking frequency-domain spectral mean statistics in the paper. A simulation study demonstrates that both the MSB and HMP achieve good performance.