Graphical Principal Component Analysis of Multivariate Functional Time Series

• 成果类型: Article
• 署名作者: Tan, Jianbin; Liang, Decai; Guan, Yongtao; Huang, Hui
• 署名单位: Sun Yat Sen University; Nankai University; Shenzhen Research Institute of Big Data; The Chinese University of Hong Kong, Shenzhen; Renmin University of China; Renmin University of China
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2302198
• 发表日期: 2024
• 页码: 3073-3085
• 关键词: models; THEOREM; Lasso

摘要

In this article, we consider multivariate functional time series with a two-way dependence structure: a serial dependence across time points and a graphical interaction among the multiple functions within each time point. We develop the notion of dynamic weak separability, a more general condition than those assumed in literature, and use it to characterize the two-way structure in multivariate functional time series. Based on the proposed weak separability, we develop a unified framework for functional graphical models and dynamic principal component analysis, and further extend it to optimally reconstruct signals from contaminated functional data using graphical-level information. We investigate asymptotic properties of the resulting estimators and illustrate the effectiveness of our proposed approach through extensive simulations. We apply our method to hourly air pollution data that were collected from a monitoring network in China. Supplementary materials for this article are available online.