In this paper, a new bivariate random coefficient integer-valued autoregressive process based on modified negative binomial operator with dependent innovations is proposed. Basic probabilistic and statistical properties of this model are derived. To estimate unknown parameters, Yule-Walker, conditional least squares and conditional maximum likelihood methods are considered and evaluated by Monte Carlo simulations. Asymptotic properties of the estimators are derived. Moreover, coherent forecasting and possible extension of the proposed model is provided. Finally, the proposed model is applied to the monthly crime datasets and compared with other models.

翻译：本文提出了一种基于修正负二项算子且具有相依新息的新型双变量随机系数整数值自回归过程。推导了该模型的基本概率与统计性质。为估计未知参数，考虑了Yule-Walker法、条件最小二乘法及条件极大似然法，并通过蒙特卡洛模拟评估其性能。推导了估计量的渐近性质。此外，给出了该模型的一致性预测及其可能的扩展。最后，将该模型应用于月度犯罪数据集，并与其他模型进行了比较。