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 [math]\displaystyle{ ~\tau_t~ }[/math] denote the duration (the waiting time between consecutive trades) and assume that [math]\displaystyle{ ~\tau_t=\theta_t z_t ~ }[/math], where [math]\displaystyle{ z_t }[/math] are independent and identically distributed random variables, positive and with [math]\displaystyle{ \operatorname{E}(z_t) = 1 }[/math] and where the series [math]\displaystyle{ ~\theta_t~ }[/math] is given by:

[math]\displaystyle{ \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} }[/math]

and where [math]\displaystyle{ ~\alpha_0\gt 0~ }[/math], [math]\displaystyle{ \alpha_i\ge 0 }[/math], [math]\displaystyle{ \beta_i \ge 0 }[/math], [math]\displaystyle{ ~i\gt 0 }[/math].

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.