- 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 toGARCH . Indeed, in a continuous doubleauction (a common trading mechanism in manyfinancial 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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