Latent Gaussian Count Time Series

This paper develops the theory and methods for modeling a stationary count time series via Gaussian transformations. The techniques use latent process distributional transformation to construct with very flexible correlation features that can have any pre-specified marginal distribution, including classical Poisson, generalized negative binomial, binomial structures. pseudo-likelihood implied Yule-Walker estimation paradigms, based on autocovariance function of series, are developed new Hermite expansion. Particle filtering sequential Monte Carlo used conduct likelihood estimation. Connections state space models made. Our approaches evaluated in simulation study analyze weekly retail sales.