Latent Gaussian Count Time Series. Issue 541 (2nd January 2023)

• Record Type: Journal Article
• Authors: Jia, Yisu; Kechagias, Stefanos; Livsey, James; Lund, Robert; Pipiras, Vladas
• Is Part Of: Journal of the American Statistical Association. Volume 118:Issue 541(2023)
• Page Start: 596
• Page End: 606
• Publication Date: 2023-01-02
• Subjects: Count distributions -- Hermite expansions -- Likelihood estimation -- Particle filtering -- Sequential Monte Carlo -- State-space models; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2021.1944874
• Languages: English
• ISSNs: 0162-1459

Abstract

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.