Simultaneous Decorrelation of Matrix Time Series
提出一种双线性变换方法，将高维矩阵时间序列转化为块状结构，使各子序列互不相关，从而可分别建模，提升预测性能，并证明了变换的收敛速度。
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.