Matrix valued time series (MaTS) and global vector autoregressive (GVAR) models both impose restrictions on the general VAR for multidimensional data sets, in order to bring down the number of parameters. Both models are motivated from a different viewpoint such that on first sight they do not have much in common. When investigating the models more closely, however, one notices many connections between the two model sets. This paper investigates the relations between the restrictions imposed by the two models. We show that under appropriate restrictions in both models we obtain a joint framework allowing to gain insight into the nature of GVARs from the viewpoint of MaTS.

翻译：矩阵值时间序列（MaTS）与全局向量自回归（GVAR）模型均对多维数据集的一般VAR模型施加约束，以降低参数数量。两种模型虽从不同视角出发，初看之下似无太多共同之处。然而，通过深入考察可发现两类模型体系间存在诸多关联。本文研究两种模型所施加约束之间的内在联系。我们证明，在适当的约束条件下，两类模型可形成一个统一框架，从而能够从MaTS的视角深入理解GVAR模型的性质。