Latent Gaussian Count Time Series
Abstract
This paper 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 pre-specified 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.
Cite
@article{arxiv.1811.00203,
title = {Latent Gaussian Count Time Series},
author = {Yisu Jia and Stefanos Kechagias and James Livsey and Robert Lund and Vladas Pipiras},
journal= {arXiv preprint arXiv:1811.00203},
year = {2021}
}
Comments
Two previous versions of this paper appeared on arxiv under the title, the first under the title "Latent Gaussian Count Time Series Modeling" and the second under the title "Count Time Series Modeling with Gaussian Copulas"