On the relation between Global VAR Models and Matrix Time Series Models with Multiple Terms

TL;DR

This paper explores the connections between Global VAR and Matrix Time Series models, revealing how restrictions in both can unify them into a joint framework for better understanding multidimensional time series.

Contribution

It demonstrates the theoretical relationship between GVAR and MaTS models, providing a unified perspective under certain restrictions.

Findings

Identifies conditions linking GVAR and MaTS models

Provides a joint framework for analyzing multidimensional time series

Enhances understanding of model restrictions and their implications

Abstract

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.