Latent Gaussian Count Time Series

• 成果类型: Article
• 署名作者: Jia, Yisu; Kechagias, Stefanos; Livsey, James; Lund, Robert; Pipiras, Vladas
• 署名单位: State University System of Florida; University of North Florida; SAS Institute Inc; University of California System; University of California Santa Cruz; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.1944874
• 发表日期: 2023
• 页码: 596-606
• 关键词: specified marginals; copula models; distributions; optimization; Poisson

摘要

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.