Frequency Domain Statistical Inference for High-Dimensional Time Series

• 成果类型: Article; Early Access
• 署名作者: Krampe, Jonas; Paparoditis, Efstathios
• 署名单位: Cornell University; University of Cyprus
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2025.2479244
• 发表日期: 2025
• 关键词: false discovery rate; confidence-intervals; spectral-analysis; covariance; models; shrinkage; tests

摘要

Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence or the partial coherence, encode comprehensively the complex linear relations between the component processes of the multivariate system. In this article, we develop inference procedures for such parameters in a high-dimensional, time series setup. Toward this goal, we first focus on the derivation of consistent estimators of the coherence and, more importantly, of the partial coherence which possess manageable limiting distributions that are suitable for testing purposes. Statistical tests of the hypothesis that the maximum over frequencies of the coherence, respectively, of the partial coherence, do not exceed a prespecified threshold value are developed. Our approach allows for testing hypotheses for individual coherences and/or partial coherences as well as for multiple testing of large sets of such parameters. In the latter case, a consistent procedure to control the false discovery rate is developed. The finite sample performance of the inference procedures introduced is investigated by means of simulations and applications to the construction of graphical interaction models for brain connectivity based on EEG data are presented.Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.