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

TL;DR

This paper compares Poisson-Lindley integer autoregressive models with Gaussian forecasts for discrete time series, highlighting differences in modeling and forecasting accuracy through simulation and real data applications.

Contribution

It introduces a method to compare Poisson-Lindley AR models with Gaussian models by matching moments and evaluates their performance using various estimation techniques.

Findings

Poisson-Lindley models provide more coherent forecasts for discrete data.

Gaussian models may be inadequate for integer-valued time series.

Simulation results show differences in forecast accuracy between models.

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.