Evaluating and comparing Gaussian forecasts for discrete process time series.

This dissertation is comprised of three research papers which focus on comparing a discrete time series processes to a discretized Gaussian autoregressive process and the traditional Gaussian autoregressive process. We first provide a brief introduction to relevant background information in chapter one. In the second chapter, we look specifically at the geometric integer autoregrssive process of order one. Forecasts using a geometric integer autoregressive (GINAR) model are compared to variations of Gaussian forecasts via simulation by equating relevant moments of the marginals of the GINAR to the Gaussian AR. To illustrate utility, the methods discussed are applied and compared using three discrete series with model parameters being estimated using each of conditional least squares, Yule-Walker, and maximum likelihood. We then perform similar methods and applications using the Poisson-Lindley integer autoregressive process. In chapter four we extend our work to the zero-inflated Poisson integer autoregressive process. We conclude with a brief summary and discussion in chapter five.