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 modelling 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, i.e. 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.

摘要

我们提出了 p × q 矩阵时间序列的同期双线性变换，以减轻 p 和/或 q 较大时矩阵时间序列建模和预测的困难。生成的变换矩阵采用由多个小矩阵组成的块结构，并且这些小矩阵系列在所有时间都是不相关的。因此，通过在不丢失线性动力学信息的情况下分别对这些小矩阵系列中的每一个进行建模，可以实现整体简约模型。这种简约模型通常具有更好的预测性能，即使潜在的真实动态在转换后偏离假定的不相关块结构时也是如此。导出了估计变换的均匀收敛率，证明了所提出的双线性变换的一个重要优点，即 它在技术上等同于维度为 max(p, q) 而不是 p × q 的向量时间序列的去相关。所提出的方法通过模拟和真实数据示例进行了数值说明。