Bimodal Birnbaum–Saunders generalized autoregressive score model

Time series models based on the Birnbaum–Saunders ( $ \mathcal{BS} $ BS) 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{BS} $ BS 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.