Autoregressive conditional duration explained

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} ~ , wherez _{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} + … + \alpha _{q} \tau _{t-q} + \beta _{1} \theta _{t-1} + … + \beta _{p\theta} _{t-p} = \alpha _{0} + \sum ^{q} _{i =1} \alpha _{i} \tau _{t-i} + \sum ^{p} _{i =1} \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.