A Family of Autoregressive Conditional Duration Model under Random Environment

This article contains two novelties. First, we propose a new type of augmented ACD model under random environment. It turns out that flexible disturbance of the news impact function are necessary to appropriately model financial durations. The ACD model under random environment proposed in this paper seem to be a valuable alternative to existing approaches and have the best overall performance. Second, we give the transition probability of the process. Moreover by employing the transition probability, we give the probability properties of the ACD model under random environment, and give rigorous proofs of the probability properties.