Bayesian GARMA Models for Count Data

TL;DR

This paper introduces Bayesian methods for GARMA models tailored to count data, enhancing modeling flexibility for non-Gaussian time series with practical applications and simulation validation.

Contribution

It develops Bayesian estimation and model selection techniques for GARMA models with Poisson, binomial, and negative binomial distributions, extending their applicability.

Findings

Bayesian estimation performs well in simulations.

Model selection criteria effectively identify appropriate models.

Real data analyses demonstrate practical utility.

Abstract

Generalized autoregressive moving average (GARMA) models are a class of models that was developed for extending the univariate Gaussian ARMA time series model to a flexible observation-driven model for non-Gaussian time series data. This work presents Bayesian approach for GARMA models with Poisson, binomial and negative binomial distributions. A simulation study was carried out to investigate the performance of Bayesian estimation and Bayesian model selection criteria. Also three real datasets were analysed using the Bayesian approach on GARMA models.