A Structural Autoregressive Conditional Duration Model
We propose a structural model for durations between events and associated marks. Our model is structural in the sense that both durations and marks are generated by an underlying Brownian motion. In particular, we model the durations as the successive passage times of this Brownian motion relative to in itself random boundaries. Additional Brownian motions serve as processes generating the marks, whose conditional distribution is a mixture of normals. Multivariate Brownian motions allow us to incorporate a vector of marks combined with a single duration generating process. Our model embeds in particular the standard autoregressive conditional duration model. Applied to high-frequency financial data, we derive the conditional distributions of the durations and the vector of price changes. A first empirical illustration, using transaction level data on a NYSE.