Latent Gaussian Count Time Series

Authors

Yisu Jia, University of North FloridaFollow
Stefanos Kechagias, SAS Institute, Inc.
James Livsey, U.S. Census Bureau
Robert Lund, University of California, Santa Cruz
Vladas Pipiras, The University of North Carolina at Chapel Hill

Document Type

Article

Publication Date

1-1-2021

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.

Publication Title

Journal of the American Statistical Association

Digital Object Identifier (DOI)

10.1080/01621459.2021.1944874

ISSN

01621459

E-ISSN

1537274X

Citation Information

Yisu Jia, Stefanos Kechagias, James Livsey, Robert Lund & Vladas Pipiras (2021) Latent Gaussian Count Time Series, Journal of the American Statistical Association, DOI: 10.1080/01621459.2021.1944874