A Frequency Domain Bootstrap for General Multivariate Stationary Processes

TL;DR

This paper introduces the multivariate frequency domain hybrid bootstrap (MFHB), a new method for valid inference on multivariate stationary processes, addressing the lack of existing bootstrap procedures for frequency domain statistics.

Contribution

The paper develops and proves the asymptotic validity of the MFHB, a novel bootstrap method for multivariate frequency domain statistics under weak dependence conditions.

Findings

MFHB outperforms moving block bootstrap in simulations

Valid for general classes of periodogram-based statistics

Applicable to stationary multivariate processes with weak dependence

Abstract

For many relevant statistics of multivariate time series, no valid frequency domain bootstrap procedures exist. This is mainly due to the fact that the distribution of such statistics depends on the fourth-order moment structure of the underlying process in nearly every scenario, except for some special cases like Gaussian time series. In contrast to the univariate case, even additional structural assumptions such as linearity of the multivariate process or a standardization of the statistic of interest do not solve the problem. This paper focuses on integrated periodogram statistics as well as functions thereof and presents a new frequency domain bootstrap procedure for multivariate time series, the multivariate frequency domain hybrid bootstrap (MFHB), to fill this gap. Asymptotic validity of the MFHB procedure is established for general classes of periodogram-based statistics and for stationary multivariate processes satisfying rather weak dependence conditions. A simulation study is carried out which compares the finite sample performance of the MFHB with that of the moving block bootstrap.