Statistical Inference for High-Dimensional Spectral Density Matrix
成果类型：
Article; Early Access
署名作者：
Chang, Jinyuan; Jiang, Qing; Mcelroy, Tucker; Shao, Xiaofeng
署名单位：
Southwestern University of Finance & Economics - China; Southwestern University of Finance & Economics - China; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Beijing Normal University; Washington University (WUSTL); Washington University (WUSTL)
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1080/01621459.2025.2468013
发表日期：
2025
关键词：
CENTRAL LIMIT-THEOREMS
Gaussian Approximation
U-statistics
bootstrap approximations
functional connectivity
frequency-domain
covariance
shrinkage
MODEL
heteroskedasticity
摘要：
The spectral density matrix is a fundamental object of interest in time series analysis, and it encodes both contemporary and dynamic linear relationships between component processes of the multivariate system. In this article we develop novel inference procedures for the spectral density matrix in the high-dimensional setting. Specifically, we introduce a new global testing procedure to test the nullity of the cross-spectral density for a given set of frequencies and across pairs of component indices. For the first time, both Gaussian approximation and parametric bootstrap methodologies are employed to conduct inference for a high-dimensional parameter formulated in the frequency domain, and new technical tools are developed to provide asymptotic guarantees of the size accuracy and power for global testing. We further propose a multiple testing procedure for simultaneously testing the nullity of the cross-spectral density at a given set of frequencies. The method is shown to control the false discovery rate. Both numerical simulations and a real data illustration demonstrate the usefulness of the proposed testing methods. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.