Modeling multivariate integer-valued time series with appropriate methods is currently a popular research topic. In this paper, we propose a multivariate integer-valued autoregressive time series model based on a fixed network community structure. We use the negative binomial distribution as the conditional marginal distribution and a copula to construct the conditional joint distribution. The newly proposed model introduces the heterogeneity of nodes. Stability conditions are provided for both fixed and increasing dimensions. We estimate the parameters of the proposed model by maximizing the quasi-likelihood function with known and unknown community membership matrices, respectively. Corresponding asymptotic properties of parameter estimates are also provided. A simulation study is conducted to demonstrate the asymptotic behavior of the proposed model, and two real datasets are employed to compare the proposed model with other competitive models.

中文翻译：

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多元整数值时间序列的负二项社区网络向量自回归


使用适当的方法对多元整数值时间序列进行建模是当前的热门研究课题。在本文中，我们提出了一种基于固定网络社区结构的多元整数值自回归时间序列模型。我们使用负二项式分布作为条件边际分布和连接函数来构造条件联合分布。新提出的模型引入了节点的异构性。为固定尺寸和增加尺寸提供了稳定性条件。我们通过分别使用已知和未知的社区成员矩阵最大化拟似然函数来估计所提出模型的参数。还提供了参数估计的相应渐近性质。进行了仿真研究来证明所提出模型的渐近行为，并使用两个真实数据集将所提出的模型与其他竞争模型进行比较。