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Simultaneous decorrelation of matrix time series

Yuefeng Hana, Rong Chenb, Cun-Hui Zhangb and Qiwei Yao

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: 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.

Keywords: decorrelation transformation; eigenanalysis; matrix time series; forecasting; uniform convergence rates; grant IIS-1741390. Chen was supported in part by National Science Foundation grants DMS-1503409; DMS-1737857 and IIS-1741390. Zhang was supported in part by NSF grants DMS-1721495; IIS-1741390 and CCF-1934924.; EP/V007556/1; T&F deal (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 13 pages
Date: 2023-01-11
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Published in Journal of the American Statistical Association, 11, January, 2023. ISSN: 0162-1459

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