Autoregressive conditional duration


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 ~ au_t~ denote the duration (the waiting time between consecutive trades) andassume that ~ au_t= heta_t z_t ~, where z_t sim iid~, positive and with operatorname{E}(z_t) = 1 and wherethe series ~ heta_t~ is given by

heta_t = alpha_0 + alpha_1 au_{t-1} + cdots + alpha_q au_{t-q} + eta_1 heta_{t-1} + cdots + eta_p heta_{t-p} = alpha_0 + sum_{i=1}^q alpha_i au_{t-i} + sum_{i=1}^p eta_i heta_{t-i}

and where ~alpha_0>0~ , alpha_ige 0, eta_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.


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