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Simultaneous decorrelation of matrix time series

Hana, Yuefeng, Chenb, Rong, Zhangb, Cun-Hui and Yao, Qiwei ORCID: 0000-0003-2065-8486 (2023) Simultaneous decorrelation of matrix time series. Journal of the American Statistical Association. ISSN 0162-1459

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Identification Number: 10.1080/01621459.2022.2151448


We propose a contemporaneous bilinear transformation for a p × 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 × q. The proposed method is illustrated numerically via both simulated and real data examples. Supplementary materials for this article are available online.

Item Type: Article
Official URL:
Additional Information: © 2023 The Authors
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 21 Nov 2022 12:48
Last Modified: 09 Jun 2024 07:00

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