Abstract Inspired by the Edgeworth–Portnoy model for Gaussian time series, a family of randomized moving window (RMW) and randomized moving sum (RMS) models for stationary count time series is proposed. For the RMW process, we derive Markov properties which, in turn, allow to conclude on a connection of the RMS model to the Hidden-Markov model. This connection is used to develop an efficient scheme for maximum likelihood estimation. Then, we derive marginal and serial moment properties of the RMS process. It commonly exhibits an autoregressive autocorrelation structure, but also forms of a long memory are possible. The latter holds in particular for the proposed extended RMS model, which also satisfies certain Markov properties.

中文翻译：

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关于计数时间序列的 Edgeworth 模型

摘要 受高斯时间序列的 Edgeworth-Portnoy 模型的启发，提出了一系列用于平稳计数时间序列的随机移动窗口 (RMW) 和随机移动和 (RMS) 模型。对于 RMW 过程，我们推导了马尔可夫特性，进而可以得出 RMS 模型与隐马尔可夫模型之间的联系的结论。此连接用于开发最大似然估计的有效方案。然后，我们推导出 RMS 过程的边际和序列矩属性。它通常表现出自回归自相关结构，但长记忆的形式也是可能的。后者尤其适用于所提出的扩展 RMS 模型，该模型也满足某些马尔可夫特性。