Latent Gaussian Count Time Series Modeling

Abstract

This paper develops theory and methods for the copula modeling of stationary count time series. 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 count structures. A Gaussian pseudo-likelihood estimation paradigm, based only on the mean and autocovariance function of the count series, is developed via some new Hermite expansions. Particle filtering methods are studied to approximate the true likelihood of the count series. Here, connections to hidden Markov models and other copula likelihood approximations are made. The efficacy of the approach is demonstrated and the methods are used to analyze a count series containing the annual number of no-hitter baseball games pitched in major league baseball since 1893