This paper probabilistically explores a class of stationary count time series models built by superpositioning (or otherwise combining) independent copies of a binary stationary sequence of zeroes and ones. Superpositioning methods have proven useful in devising stationary count time series having prespecified marginal distributions. Here, basic properties of this model class are established and the idea is further developed. Specifically, stationary series with binomial, Poisson, negative binomial, discrete uniform, and multinomial marginal distributions are constructed; other marginal distributions are possible. Our primary goal is to derive the autocovariance function of the resulting series.

中文翻译：

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叠加的静止计数时间序列

本文概率性地探索了一类通过叠加（或以其他方式组合）零和一的二进制平稳序列的独立副本构建的平稳计数时间序列模型。叠加方法已被证明可用于设计具有预先指定的边际分布的固定计数时间序列。在这里，建立了这个模型类的基本属性，并进一步发展了这个想法。具体来说，构造了具有二项式、泊松、负二项式、离散均匀和多项边际分布的平稳序列；其他边际分布是可能的。我们的主要目标是推导出结果序列的自协方差函数。