Bayesian estimation for novel geometric INGARCH model

TL;DR

This paper proposes a new geometric distribution-based INGARCH model, explores Bayesian and maximum likelihood estimation methods, and demonstrates its effectiveness through simulations and real data forecasting.

Contribution

Introduces a novel geometric distribution-based INGARCH model and applies Bayesian estimation with HMC, enhancing modeling of count time series.

Findings

Bayesian estimators perform well in simulations

Model accurately captures data dynamics

Forecasting with Bayesian predictive distribution is effective

Abstract

This paper introduces an integer-valued generalized autoregressive conditional heteroskedasticity (INGARCH) model based on the novel geometric distribution and discusses some of its properties. The parameter estimation problem of the models are studied by conditional maximum likelihood and Bayesian approach using Hamiltonian Monte Carlo (HMC) algorithm. The results of the simulation studies and real data analysis affirm the good performance of the estimators and the model. Forecasting using the Bayesian predictive distribution has also been studied and evaluated using real data analysis.