Autoregressive conditional duration

In financial econometrics, an autoregressive conditional duration (ACD, Engle and Russell (1998)) model considers irregularly spaced and autocorrelated intertrade durations. ACD is analogous to GARCH. Indeed, in a continuous double auction (a common trading mechanism in many financial markets) waiting times between two consecutive trades vary at random.

Definition

Specifically, let $~\; au\_t~$ denote the duration (the waiting time between consecutive trades) andassume that $~\; au\_t=\; heta\_t\; z\_t\; ~$, where$z\_t\; sim\; iid~$, positive and with $operatorname\{E\}(z\_t)\; =\; 1$ and wherethe series $~\; heta\_t~$ is given by

and where $~alpha\_0>0~$, $alpha\_ige\; 0$,, $~i>0$.

References

* Robert F. Engle and J.R. Russell. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data", "Econometrica", 66:1127-1162, 1998.

* N. Hautsch. "Modelling Irregularly Spaced Financial Data", Springer, 2004.