Matrix time series, which consist of matrix-valued data observed over time, are prevalent in various fields such as economics, finance, and engineering. Such matrix time series data are often observed in high dimensions. Matrix factor models are employed to reduce the dimensionality of such data, but they lack the capability to make predictions without specified dynamics in the latent factor process. To address this issue, we propose a two-component dynamic matrix factor model that extends the standard matrix factor model by incorporating a matrix autoregressive structure for the low-dimensional latent factor process. This two-component model injects prediction capability to the matrix factor model and provides deeper insights into the dynamics of high-dimensional matrix time series. We present the estimation procedures of the model and their theoretical properties, as well as empirical analysis of the estimation procedures via simulations, and a case study of New York city taxi data, demonstrating the performance and usefulness of the model.

翻译：矩阵时间序列，即随时间观测的矩阵值数据，在经济学、金融学和工程学等多个领域普遍存在。此类矩阵时间序列数据通常具有高维特性。矩阵因子模型被用于降低此类数据的维度，但若潜在因子过程未设定动态结构，则模型缺乏预测能力。为解决这一问题，我们提出了一种双分量动态矩阵因子模型，该模型通过为低维潜在因子过程引入矩阵自回归结构，扩展了标准矩阵因子模型。此双分量模型为矩阵因子模型注入了预测能力，并提供了对高维矩阵时间序列动态的更深入洞察。我们阐述了模型的估计方法及其理论性质，并通过模拟对估计方法进行了实证分析，同时以纽约市出租车数据为例进行了案例研究，验证了模型的性能与实用性。