Simultaneous Decorrelation of Matrix Time Series

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