A multivariate INAR(1) regression model based on the Sarmanov distribution is proposed for modelling claim counts from an automobile insurance contract with different types of coverage. The correlation between claims from different coverage types is considered jointly with the serial correlation between the observations of the same policyholder observed over time. Several models based on the multivariate Sarmanov distribution are analyzed. The new models offer some advantages since they have all the advantages of the MINAR(1) regression model but allow for a more flexible dependence structure by using the Sarmanov distribution. Driven by a real panel data set, these models are considered and fitted to the data to discuss their goodness of fit and computational efficiency.

中文翻译：

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基于Sarmanov分布的多元INAR（1）回归模型

提出了一种基于Sarmanov分布的多元INAR（1）回归模型，用于对具有不同承保范围的汽车保险合同的索赔计数进行建模。可以将不同承保类型的索赔之间的相关性与同一保单持有人的观察结果之间随时间变化的序列相关性一起考虑。分析了基于多元Sarmanov分布的几种模型。新模型具有一些优点，因为它们具有MINAR（1）回归模型的所有优点，但通过使用Sarmanov分布可以提供更灵活的依赖关系结构。在真实面板数据集的驱动下，考虑这些模型并将其拟合到数据中，以讨论它们的拟合优度和计算效率。