The Birnbaum–Saunders autoregressive conditional duration model

In this paper we introduce the Birnbaum–Saunders autoregressive conditional duration (BS-ACD) model as an alternative to the existing ACD models which allow a unimodal hazard function. The BS-ACD model is the first ACD model to integrate the concept of conditional quantile estimation into an ACD model by specifying the time-varying model dynamics in terms of the conditional median duration, instead of the conditional mean duration. In the first half of this paper we illustrate how the BS-ACD model relates to the traditional ACD model, and in the second half we discuss the assessment of goodness-of-fit for ACD models in general. In order to facilitate both of these points, we explicitly illustrate the similarities and differences between the BS-ACD model and the Generalized Gamma ACD (GG-ACD) model by comparing and contrasting their formulation, estimation, and results from fitting both models to samples for six NYSE securities.