Al-Osh and Alzaid (1988) consider a Poisson moving average (PMA) model to describe the relation among integer-valued time series data; this model, however, is constrained by the underlying equi-dispersion assumption for count data (i.e., that the variance and the mean equal). This work instead introduces a flexible integer-valued moving average model for count data that contain over- or under-dispersion via the Conway-Maxwell-Poisson (CMP) distribution and related distributions. This first-order sum-of-Conway-Maxwell-Poissons moving average (SCMPMA(1)) model offers a generalizable construct that includes the PMA (among others) as a special case. We highlight the SCMPMA model properties and illustrate its flexibility via simulated data examples.

中文翻译：

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灵活的单变量移动平均时间序列模型，用于分散计数数据

Al-Osh和Alzaid（1988）考虑了泊松移动平均（PMA）模型来描述整数时间序列数据之间的关系。但是，该模型受计数数据的基本等散假设（即方差和均值相等）的约束。相反，这项工作为通过Conway-Maxwell-Poisson（CMP）分布和相关分布包含过度分散或分散不足的计数数据引入了灵活的整数值移动平均模型。这种一阶的Conway-Maxwell-Poissons移动平均和（SCMPMA（1））模型提供了一种可推广的结构，其中包括PMA（以及其他）作为特例。我们重点介绍SCMPMA模型的属性，并通过模拟数据示例说明其灵活性。