Skip-sampling: subsampling in the frequency domain

Abstract

Over the last 35 years, several bootstrap methods for time series have been proposed. Popular time domain methods include the block-bootstrap, the stationary bootstrap, the linear process bootstrap, among others; subsampling for time series is also available, and is closely related to the block-bootstrap. The frequency domain bootstrap has been performed either by resampling the periodogram ordinates or by resampling the ordinates of the discrete Fourier transform. The paper at hand proposes a novel construction of subsampling the discrete Fourier transform ordinates, and investigates its theoretical properties and realm of applicability. Numerical studies show that the new method performs comparably to the frequency domain bootstrap for linear spectral means and ratio statistics, while at the same time yielding significant computational savings as well as numerical stability.