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 $~\tau _{t}~$ 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 $\operatorname {E} (z_{t})=1$ 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 $~\alpha _{0}>0~$ , $\alpha _{i}\geq 0$ , $\beta _{i}\geq 0$ , $~i>0$ .

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.

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