Journal of Statistical Planning and Inference

Available online 15 April 2024, 106183

Author links open overlay panelRuru Ma, Shibin Zhang

https://doi.org/10.1016/j.jspi.2024.106183

• • A resampling approach, MSB, is proposed for time series.

• • MSB is actually a Gaussian approximation.

• • The other resampling approach, HMP, is developed for frequency domain analysis.

• • MSB and HMP share the merits of several existing resampling methods.

• • MSB and HMP are applicable to extensive types 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.

https://doi.org/10.1016/j.jspi.2024.106183