Abstract The existing bivariate integer-valued autoregressive process of order 1 (BINAR(1)) with negative binomial (NB) innovations is developed under stationary moment conditions and in particular under same level of over-dispersion index. In this paper, we propose a flexible BINAR(1) under NB innovations where the counting series are subject to two different levels of over-dispersion under same stationary moment condition. The unknown parameters of the new model are estimated using a generalized quasi-likelihood (QL) estimating equation. The performance of this estimation method is assessed through some numerical experiments under different time dimensions.

中文翻译：

---

具有非均匀水平过度分散的灵活的观测驱动平稳二元负二项式INAR（1）

摘要在稳态矩条件下，特别是在相同水平的超分散指数下，开发了现有的具有负二项式（NB）创新的1阶双变量整数值自回归过程（BINAR（1））。在本文中，我们提出了一种在NB创新下的灵活BINAR（1），其中在相同的静止力矩条件下，计数序列受到两个不同级别的过度分散的影响。新模型的未知参数是使用广义拟似然（QL）估计方程估算的。该估计方法的性能通过在不同时间范围内的一些数值实验进行评估。