Evaluating Approximations of Count Distributions and Forecasts for Poisson-Lindley Integer Autoregressive Processes

Although many time series are realizations from discrete processes, it is often that a continuous Gaussian model is implemented for modeling and forecasting the data, resulting in incoherent forecasts. Forecasts using a Poisson-Lindley integer autoregressive (PLINAR) model are compared to variations of Gaussian forecasts via simulation by equating relevant moments of the marginals of the PLINAR to the Gaussian AR. To illustrate utility, the methods discussed are applied and compared using a discrete series with model parameters being estimated using each of conditional least squares, Yule-Walker, and maximum likelihood.