Count time series are widely encountered in practice. As with continuous valued data, many count series have seasonal properties. This paper uses a recent advance in stationary count time series to develop a general seasonal count time series modeling paradigm. The model permits any marginal distribution for the series and the most flexible autocorrelations possible, including those with negative dependence. Likelihood methods of inference can be conducted and covariates can be easily accommodated. The paper 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.
翻译:与连续估价数据一样,许多计数序列具有季节性特性。本文使用最新的固定计时时间序列先期来开发一个一般的季节计时时间序列模型模式。模型允许该序列的任何边际分布和可能最灵活的自动关系,包括负依赖关系。可以进行可能的推论方法,并很容易地采用共变法。本文首先开发了模型方法,这需要不同转换具有季节性动态的高斯进程。然后确定了这一模型类的属性,并开发了粒子过滤可能的参数估计方法。提供了模拟研究,展示了这些方法的功效,并应用了西雅图连续几周的降雨天数。