Order selection in GARMA models for count time series: a Bayesian perspective

Area of Science:

• Statistics
• Time Series Analysis
• Econometrics

Background:

• Traditional estimation of Generalized Autoregressive Moving Average (GARMA) models relies on frequentist methods.
• Bayesian approaches for GARMA model estimation are less explored, though they show promise for point estimation.
• Information criteria, commonly used for model selection in count time series GARMA models, exhibit poor performance in simulations.

Purpose of the Study:

• To investigate Bayesian estimation for order selection in GARMA models for count time series.
• To address the limitations of information criteria in accurately identifying GARMA models.
• To propose and evaluate a novel Bayesian approach using Reversible Jump Markov Chain Monte Carlo (RJMCMC).

Main Methods:

• The study adopts a Bayesian perspective for order selection in GARMA models.
• Reversible Jump Markov Chain Monte Carlo (RJMCMC) is employed for Bayesian estimation.
• Monte Carlo simulation studies are conducted to assess finite sample performance, including point and interval inference.

Main Results:

• The proposed Bayesian RJMCMC approach demonstrates satisfactory point estimation for GARMA models.
• Simulation studies evaluate inference, sensitivity, burn-in, thinning, and prior choices.
• The method's effectiveness is showcased through real-world applications in Brazil's automobile production and bus exports.

Conclusions:

• The Bayesian RJMCMC approach offers a viable alternative for order selection in GARMA models for count time series.
• This method provides improved model identification compared to traditional information criteria.
• The flexibility and capability of the Bayesian approach are highlighted through practical data applications.