{"ID":2872852,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.07347","arxiv_id":"2509.07347","title":"Matrix-variate integer-valued autoregressive processes","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2509.07347","url_pdf":"https://arxiv.org/pdf/2509.07347v1","authors":"[\"Nuo Xu\",\"Kai Yang\",\"Fukang Zhu\"]","published":"2025-09-09T02:52:29Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}