Structural Analysis of a Dynamic Multilayer Network via Matrix Autoregressive Models: A Case Study of International Interactions between Countries

Abstract

Dynamic and multilayer networks have been widely studied separately, but their joint analysis remains comparatively underdeveloped. Because the relational information of a dynamic multilayer network can be represented as a tensor at each time point $t$, each layer can be summarized through a set of structural statistics, yielding a matrix-valued observation and, consequently, a matrix-valued time series. To exploit this structure, we propose the use of matrix autoregressive (MAR) models, which simultaneously characterize temporal dependence across relational layers and structural statistics. We apply this framework to the ICEWS dataset, which records international interactions among countries under four relational domains and therefore naturally defines a dynamic multilayer network. The results indicate that negative verbal interactions (\textit{Verbal-}) play a prominent role in the subsequent structural reconfiguration of the material-interaction layers, while mean strength exhibits the strongest temporal persistence and reciprocity the broadest cross-statistic influence. These findings illustrate the usefulness of MAR models for providing a parsimonious and interpretable characterization of temporal and cross-layer dependence in dynamic multilayer networks.