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. In a continuous double auction (a common trading mechanism in many financial markets) waiting times between two consecutive trades vary at random.

Definition

Let ${\tau }_t$ denote the duration (the waiting time between consecutive trades) and assume that ${\tau }_t={\theta }_t{z}_t$, where $z_t$ are independent and identically distributed random variables, positive and with $\mathrm{E}(z_t)=1$ and where the series ${\theta }_t$ is given by:

${\theta }_t={\alpha }_0+{\alpha }_1{\tau }_{t-1}+\cdots +{\alpha }_q{\tau }_{t-q}+{\beta }_1{\theta }_{t-1}+\cdots +{\beta }_p{\theta }_{t-p}={\alpha }_0+\sum _{i=1}^q{\alpha }_i{\tau }_{t-i}+\sum _{i=1}^p{\beta }_i{\theta }_{t-i}$

and where ${\alpha }_0>0$, ${\alpha }_i\ge 0$, ${\beta }_i\ge 0$, $i>0$.

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.