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.

翻译：在社会学和经济学领域，矩阵值整数值时间序列的建模需求日益迫切。然而，现有研究尚未涉及此类数据的建模问题。针对这一主题，本文提出了一种新颖的矩阵值整数值自回归模型。其关键技术在于定义了两个左矩阵稀释算子和右矩阵稀释算子。本文深入研究了所提出模型的概率论与统计学性质。此外，开发了两种估计方法：投影估计法和迭代最小二乘估计法，并建立了相应估计量的渐近性质。同时，解决了模型阶数确定问题。在仿真研究中，给出了估计结果并验证了理论性质。最后，研究表明对于矩阵值整数值时间序列数据，矩阵值整数值自回归模型优于连续型矩阵值自回归模型和多变量整数值自回归模型。