On a quantile autoregressive conditional duration model

Autoregressive conditional duration (ACD) models are primarily used to deal with data arising from times between two successive events. These models are usually specified in terms of a time-varying conditional mean or median duration. In this work, we relax this assumption and consider a conditional quantile approach to facilitate the modeling of different percentiles. The proposed ACD quantile model is based on a skewed version of Birnbaum–Saunders distribution, which yields better fit of the tails than the traditional Birnbaum–Saunders distribution, in addition to facilitating the implementation of an expectation conditional maximization (ECM) algorithm. A Monte Carlo simulation study is performed to assess the behavior of the model as well as the parameter estimation method and the evaluation of a form of residuals. Two real financial transaction data sets are finally analyzed to illustrate the proposed approach.