Underdispersed and overdispersed phenomena are often observed in practice. To deal with these phenomena, we introduce a new thinning-based integer-valued autoregressive process. Some probabilistic and statistical properties of the process are obtained. The asymptotic normality of the estimators of the model parameters, using conditional least squares, weighted conditional least squares and modified quasi-likelihood methods, are presented. One overdispersed real-data example and one underdispersed real-data example are given to show the flexibility and superiority of the new model.

中文翻译：

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一种新的基于稀疏的INAR（1）处理，用于分散不足或过度分散的计数

在实践中经常观察到分散不足和分散过度的现象。为了解决这些现象，我们引入了一个新的基于细化的整数值自回归过程。获得了该过程的一些概率和统计性质。提出了使用条件最小二乘，加权条件最小二乘和改进的拟似然法的模型参数估计量的渐近正态性。给出了一个过度分散的实数据示例和一个欠分散的实数据示例，以显示新模型的灵活性和优越性。