We propose a contemporaneous bilinear transformation for a $p\times q$ 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 $p\times q$. The proposed method is illustrated numerically via both simulated and real data examples.
翻译:我们建议对美元和/或美元基质的基质时间序列同时进行双线转换,以缓解当美元和/或美元巨大时在建模和预测基质时间序列方面的困难。由此形成的转型矩阵假设了一个由若干小矩阵组成的块状结构,而这些小矩阵序列在任何时候都与气候无关。因此,通过在不失去线性动态信息的情况下分别建模这些小矩阵序列中的每一个,可以实现总体的相近模型。这种光谱模型往往能够更好地预测性能,即使基本真实动态在变换后偏离假设的与非碳有关的块状结构。估计变换的统一趋同率是推断出来的,这证明拟议的双线性变换的重要优点,即从技术上说它相当于一个矢量时间序列的最大值(p)$而不是$p/time q$。拟议的方法通过模拟和真实数据示例以数字方式加以说明。