Matrix-variate integer-valued autoregressive processes

In the fields of sociology and economics, the modeling of matrix-variate integervalued time series is urgent. However, no prior studies have addressed the modeling of such data. To address this topic, this paper proposes a novel matrix-variate integer-valued autoregressive model. The key techniques lie in defining two leftand right-matricial thinning operators. The probabilistic and statistical properties of the proposed model are investigated. Furthermore, two estimation methods are developed: projection estimation and iterative least squares estimation. The corresponding asymptotic properties of these estimators are established. Additionally, the order-determination problem is addressed. In the simulation studies, the estimation results are given and the theoretical properties are verified. Finally, it is shown that the matrix-variate integer-valued autoregressive model is superior to the continuous matrix-variate autoregressive and multivariate integer-valued autoregressive models for matrix-variate integer-valued time series data.