In this paper, we propose the first-order stationary integer-valued autoregressive process with the cosine Poisson innovation, based on the negative binomial thinning operator. It can be equi-dispersed, under-dispersed and over-dispersed. Therefore, it is flexible for modelling integer-valued time series. Some statistical properties of the process are derived. The parameters of the process are estimated by two methods of estimation and the performances of the estimators are evaluated via some simulation studies. Finally, we demonstrate the usefulness of the proposed model by modelling and analyzing some practical count time series data on the daily deaths of COVID-19 and the drug calls data.

中文翻译：

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使用最近的细化算子和余弦泊松创新，通过 INAR(1) 流程对 COVID-19 和药物数据进行统计建模

在本文中，我们提出了基于负二项式细化算子的具有余弦泊松创新的一阶平稳整数值自回归过程。它可以是等分散、欠分散和过度分散。因此，它可以灵活地对整数值时间序列进行建模。推导出该过程的一些统计特性。通过两种估计方法来估计过程的参数，并通过一些模拟研究来评估估计器的性能。最后，我们通过建模和分析有关 COVID-19 每日死亡人数的一些实际计数时间序列数据和药物呼叫数据，证明了所提出模型的有用性。