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

2024/05/30 by Gidaro, Rachel D., Harvill, Jane L.
#FOS: Computer and information sciences #Methodology (stat.ME)

paper · doi:10.48550/arxiv.2405.20342

Abstract

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.

Related

• Predictive Likelihood for Coherent Forecasting of Count Time Series
• Statistical Inference for Generalized Integer Autoregressive Processes
• Multivariate Count Autoregression
• A new integer-valued AR(1) process based on power series thinning operator
• Piecewise autoregression for general integer-valued time series