Bayesian Estimation for Negative Binomial INGARCH Models with Limited Prior Information

Music City Center 

This study introduces the NB-INGARCH model, tailored for over-dispersed count data, addressing limitations of traditional Poisson models. Estimating NB-INGARCH parameters poses challenges due to its complex likelihood function. We advocate Bayesian estimation using minimally informative and hierarchical priors, emphasizing data-driven inference. Markov Chain Monte Carlo methods yield numerical results, demonstrating the Bayesian approach's robustness and reliability over maximum likelihood estimation (MLE). Classical methods for estimating the dispersion parameter often rely on a two-step process-fixing the dispersion parameter while estimating others, followed by profile likelihood optimization. In contrast, Bayesian estimation jointly infers all parameters, simplifying the process, reducing uncertainty, and enhancing analysis coherence. Bayesian estimates exhibit smaller standard errors and more stable confidence intervals compared to the classical approach. Persistence parameters and long-term averages remain consistent across prior models, highlighting minimal prior influence. This work advances count time series analysis and provides practical tools for model.

NB-INGARCH

Bayesian Estimation

Minimally informative priors

Hierarchical priors

Markov Chain Monte Carlo

Over-dispersion 

Section on Bayesian Statistical Science