Bimodal Birnbaum–Saunders generalized autoregressive score model

ABSTRACT

Time series models based on the Birnbaum–Saunders ($\mathcal{B}\mathcal{S}$) distribution have not received much attention in the literature, there being only a few articles that address such models. In the present paper, we propose a generalized autoregressive score (GAS) model based on a bimodal Birnbaum–Saunders law. The proposed model, denoted by GBS2-GAS, generalizes an existing time series $\mathcal{B}\mathcal{S}$ model. We discuss conditional maximum likelihood parameter estimation, hypothesis testing inference, residual analysis and develop prediction intervals for the GBS2-GAS model. Additionally, we provide analytical expressions for the score vector and for the Hessian matrix. Two empirical applications, involving financial and hydrological data, are presented and discussed.

KEYWORDS:

• Birnbaum–Saunders
• generalized autoregressive score
• streamflow data
• trade duration data

Acknowledgements

We thank Helton Saulo for providing the trade duration data analyzed in this work. We also thank two anonymous referees and an associate editor for comments, suggestions and constructive criticism.

Disclosure statement

The authors have declared no conflict of interest.

ORCID

Rodney V. Fonseca  http://orcid.org/0000-0003-3948-3145

Additional information

Funding

Finally, we gratefully acknowledge partial financial support from Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) [grant numbers 300845/2010-3 and 132540/2015-0].