We propose a contemporaneous bilinear transformation for matrix time series to alleviate the difficulties in modelling and forecasting large number of time series together. More precisely the transformed matrix splits into several small matrices, and those small matrix series are uncorrelated across all times. Hence an effective dimension-reduction is achieved by modelling each of those small matrix series separately without the loss of information on the overall linear dynamics. We adopt the bilinear transformation such that the rows and the columns of the matrix do not mix together, as they typically represent radically different features. As the targeted transformation is not unique, we identify an ideal version through a new normalization, which facilitates the no-cancellation accumulation of the information from different time lags. The non-asymptotic error bounds of the estimated transformation are derived, leading to the uniform convergence rates of the estimation. The proposed method is illustrated numerically via both simulated and real data examples.
翻译:我们建议同时对矩阵时间序列进行双线转换,以缓解建模和预测大量时间序列的困难。更确切地说,变换矩阵分为几个小矩阵,这些小矩阵序列在任何时候都不相干。因此,通过在不丢失关于总体线性动态的信息的情况下分别建模这些小矩阵序列,可以有效地减少尺寸。我们采用双线转换,使矩阵的行和列不相混合,因为它们通常代表完全不同的特征。由于目标变换并非独一无二,我们通过新的正常化找到理想的版本,从而便利不同时间滞后的信息的不清除积累。估计变换的非被动错误界限是产生的,导致估算的统一趋同率。拟议方法通过模拟和真实数据示例以数字方式加以说明。