Bayesian GARMA models for count data

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 a 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. In addition, three real data sets were analyzed using the Bayesian approach on GARMA models.

Keywords:

• Bayesian inference
• binomial distribution
• generalized ARMA model
• negative
• Poisson distribution

Acknowledgements

The authors gratefully acknowledge the comments and constructive suggestions by an anonymous referee.

Funding

Breno Andrade gratefully acknowledges the financial support from Brazilian research agency CAPES. Ricardo Ehlers received support from São Paulo Research Foundation (FAPESP) - Brazil, under grant number 2015/00627-9.