This article considers a bivariate INAR(1) process based on an extension of the negative binomial thinning operator by prespecifying the distribution of the innovations. The dependence is introduced through the innovation components. The existence, uniqueness, strict stationarity, ergodicity, and some probabilistic properties of the process are derived. The estimation methods of conditional least squares and conditional maximum likelihood are considered. Some numerical results of the estimates are presented by simulation study. An application to crime data set is provided.

中文翻译：

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基于负二项式细化的二元INAR（1）过程

本文通过预先指定创新的分布，考虑了基于负二项式稀疏算子的扩展的二元INAR（1）过程。通过创新组件引入依赖性。推导了该过程的存在，唯一性，严格的平稳性，遍历性和一些概率性质。考虑了条件最小二乘和条件最大似然的估计方法。通过仿真研究给出了估计的一些数值结果。提供了犯罪数据集的应用程序。