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 \sim iid~, positive and with  \operatorname{E}(z_t) = 1 and where the series  ~\theta_t~ is given by

 \theta_t = \alpha_0 %2B \alpha_1 \tau_{t-1} %2B \cdots %2B \alpha_q \tau_{t-q} %2B \beta_1 \theta_{t-1} %2B \cdots %2B \beta_p\theta_{t-p} = \alpha_0 %2B \sum_{i=1}^q \alpha_i \tau_{t-i} %2B \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