In Econometrics, an autoregressive conditional duration (ACD, Engle and Russell (1998)) model considers irregularly spaced and autocorrelated intertrade durations. ACD is analogous to GARCH.
Definition
Specifically, let <math> ~\tau_t~ </math> denote the duration (the waiting time between consecutive trades) and assume that <math> ~\tau_t=\theta_t z_t ~</math>, where <math> z_t \sim iid~</math>, positive and with <math> \operatorname{E}(z_t) = 1</math> and where the series <math> ~\theta_t~ </math> is given by <math> \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> ~\alpha_0>0~ </math>, <math> \alpha_i\ge 0</math>, <math> \beta_i \ge 0 </math>, <math>~i>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.
