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 $\operatorname(z_t) = 1$ and where the series $~\theta_t~$ is given by:

$\theta_t = \alpha_0 + \alpha_1 \tau_ + \cdots + \alpha_q \tau_ + \beta_1 \theta_ + \cdots + \beta_p\theta_ = \alpha_0 + \sum_^q \alpha_i \tau_ + \sum_^p \beta_i \theta_{t-i}$

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.

Time series
Mathematical finance