Autoregressive conditional duration

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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.

[edit] 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 + \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\ge 0, \beta_i \ge 0 , ~i>0.

[edit] 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.