Simultaneous Decorrelation of Matrix Time Series

• 成果类型: Article
• 署名作者: Han, Yuefeng; Chen, Rong; Zhang, Cun-Hui; Yao, Qiwei
• 署名单位: University of Notre Dame; Rutgers University System; Rutgers University New Brunswick; University of London; London School Economics & Political Science
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2151448
• 发表日期: 2024
• 页码: 957-969
• 关键词: regularized estimation; component analysis; tensor regression; linear-models; number

摘要

We propose a contemporaneous bilinear transformation for a p x q matrix time series to alleviate the difficulties in modeling and forecasting matrix time series when p and/or q are large. The resulting transformed matrix assumes a block structure consisting of several small matrices, and those small matrix series are uncorrelated across all times. Hence, an overall parsimonious model is achieved by modeling each of those small matrix series separately without the loss of information on the linear dynamics. Such a parsimonious model often has better forecasting performance, even when the underlying true dynamics deviates from the assumed uncorrelated block structure after transformation. The uniform convergence rates of the estimated transformation are derived, which vindicate an important virtue of the proposed bilinear transformation, that is, it is technically equivalent to the decorrelation of a vector time series of dimension max(p, q) instead of p x q. The proposed method is illustrated numerically via both simulated and real data examples. for this article are available online.