Latent Gaussian Count Time Series

This article develops the theory and methods for modeling a stationary count time series via Gaussian transformations. The techniques use a latent Gaussian process and a distributional transformation to construct stationary series with very flexible correlation features that can have any prespecified marginal distribution, including the classical Poisson, generalized Poisson, negative binomial, and binomial structures. Gaussian pseudo-likelihood and implied Yule–Walker estimation paradigms, based on the autocovariance function of the count series, are developed via a new Hermite expansion. Particle filtering and sequential Monte Carlo methods are used to conduct likelihood estimation. Connections to state space models are made. Our estimation approaches are evaluated in a simulation study and the methods are used to analyze a count series of weekly retail sales. Supplementary materials for this article are available online.本文提出了基于高斯变换的平稳计数时间序列建模理论与方法。该方法借助隐高斯过程（latent Gaussian process）与分布变换，构建具备极强灵活相关特性的平稳序列，其边缘分布可预设为任意形式，涵盖经典泊松、广义泊松、负二项与二项分布结构。本文基于计数序列的自协方差函数，通过全新的埃尔米特（Hermite）展开方法，提出了高斯伪似然与隐含尤尔-沃克（Yule–Walker）估计范式。本文采用粒子滤波与序贯蒙特卡洛（sequential Monte Carlo）方法完成似然估计，并建立了与状态空间模型的关联。本文通过仿真研究评估了所提出的估计方法的性能，并将其用于分析周零售销售额的计数序列。本文的补充材料可在线获取。