In this paper, we introduce a new generalized negative binomial thinning operator with dependent counting series. Some properties of the thinning operator are derived. A new stationary integer-valued autoregressive model based on the thinning operator is constructed. In addition various properties of the process are determined, unknown parameters are estimated by several methods and the behavior of the estimators is described through the numerical results. Also, the model is applied on a real data set and compared to some relevant INAR(1) models.

中文翻译：

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基于相关零膨胀计数序列的时间序列模型

在本文中，我们介绍了一种新的具有相关计数序列的广义负二项式稀疏算子。导出了稀疏运算符的某些属性。建立了基于稀疏算子的平稳整数值自回归模型。另外，确定过程的各种属性，通过几种方法估计未知参数，并通过数值结果描述估计器的行为。此外，该模型还应用于实际数据集，并与一些相关的INAR（1）模型进行了比较。