Skip-sampling: subsampling in the frequency domain

TL;DR

This paper introduces a new method for subsampling the Discrete Fourier Transform (DFT) in the frequency domain, providing theoretical insights and expanding the toolkit for bootstrap methods in time series analysis.

Contribution

It proposes a novel frequency-domain subsampling technique for DFT ordinates and explores its theoretical properties and potential applications.

Findings

The new method has desirable asymptotic properties.

It extends the applicability of bootstrap methods in frequency domain.

Theoretical analysis supports its validity for time series inference.

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, etc.; subsampling for time series is also available, and is closely related to the block-bootstrap. `Frequency-domain' bootstrap has been performed either by resampling the periodogram ordinates or by resampling the ordinates of the Discrete Fourier Transform (DFT). The paper at hand proposes a novel construction of subsampling the DFT ordinates, and investigates its theoretical properties and realm of applicability.