Abstract

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.

摘要

本文开发了通过高斯变换对固定计数时间序列建模的理论和方法。这些技术使用潜在高斯过程和分布变换来构建具有非常灵活的相关特征的平稳序列，这些特征可以具有任何预先指定的边缘分布，包括经典泊松、广义泊松、负二项和二项结构。基于计数序列的自协方差函数的高斯伪似然和隐含的 Yule-Walker 估计范式是通过新的 Hermite 展开式开发的。粒子滤波和顺序蒙特卡洛方法用于进行似然估计。连接到状态空间模型。我们的估计方法在模拟研究中得到评估，这些方法用于分析每周零售额的一系列计数。本文的补充材料可在线获取。