Count time series are widely encountered in practice. As with continuous valued data, many count series have seasonal properties. This article uses a recent advance in stationary count time series to develop a general seasonal count time series modeling paradigm. The model constructed here permits any marginal distribution for the series and the most flexible autocorrelations possible, including those with negative dependence. Likelihood methods of inference are explored. The article first develops the modeling methods, which entail a discrete transformation of a Gaussian process having seasonal dynamics. Properties of this model class are then established and particle filtering likelihood methods of parameter estimation are developed. A simulation study demonstrating the efficacy of the methods is presented and an application to the number of rainy days in successive weeks in Seattle, Washington is given.

中文翻译：

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季节性计数时间序列

计数时间序列在实践中广泛遇到。与连续值数据一样，许多计数序列都具有季节性属性。本文使用固定计数时间序列的最新进展来开发通用的季节性计数时间序列建模范例。此处构建的模型允许序列的任何边际分布和可能的最灵活的自相关，包括那些具有负相关性的自相关。探索了似然推理方法。本文首先开发了建模方法，该方法需要对具有季节性动态的高斯过程进行离散变换。然后建立该模型类的属性，并开发参数估计的粒子滤波似然法。