Bayesian inference for the Birnbaum–Saunders autoregressive conditional duration model with application to high-frequency financial data

Abstract Autoregressive conditional duration (ACD) models have been preponderant when the subject is the modeling of high-frequency financial data. A prominent model that has demonstrated great adjustment capacity is the ACD model based on the Birnbaum–Saunders distribution (BS-ACD). Recent works have shown that this model outperforms the existing models in the literature. Nevertheless, these works explore only classical estimation approaches. In this article, we perform a Bayesian approach of the BS-ACD model. The scale parameter was modeled considering a dynamic linear model. Estimation of posterior distribution of parameters was approximated through Markov chain Monte Carlo methods. A simulation study is conducted to evaluate the performance of Bayesian estimators and two applications to real high frequency data illustrate the proposed methodology.