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Published on February 12th, 2014 | by Emily Corbett

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Estimation for ACD and log-ACD models

By Rebecca Barter, University of Sydney

This student took part in the 2012/13 AMSI Vacation Research Scholarship program. For more information on this years program please click here

The Autoregressive Conditional Duration (ACD) model is a time series model developed by Engle and Russel (1998). The ACD model is heavily used in finance to analyse data which arrives at irregular time intervals, such as irregular durations between trades or price changes of stocks. The model can be based on a large number of different statistical distributions (this project focused on four such distributions, namely the exponential, Weibull, generalised gamma and truncated skewed student-t distributions), and thus can be appropriately fitted to a huge variety of time series datasets involving irregular time intervals.

A variation on the ACD model is the logarithmic ACD (log-ACD) model, which although very similar to the ACD model, is often preferred to the ACD model due to the log-ACD being a more flexible model with fewer constraints. Each model (using each of the four distributions mentioned above) were used to do extensive simulations, and the datasets thus generated were used to study the maximum likelihood estimators (MLEs) for the parameters, each of which, as expected, were found to have a roughly Gaussian distribution.

A particular dataset containing transaction durations of IBM stocks on five consecutive trading days in 1990 was analysed using each of the ACD and log-ACD models, and by comparing forecasted (predicted) values generated from each model to the true IBM dataset observations, it was found that the log-ACD model which used a Weibull distribution was the best fit for the model. This model could then be used to predict future transaction durations for the IBM stocks.

I very much enjoyed my experience as an AMSI vacation scholar, and am grateful for the opportunity to present my work at the CSIRO Big Day In, which was altogether a thoroughly enjoyable experience. I would like to thank the support of AMSI, CSIRO and my supervisor, Associate Professor Shelton Peiris.

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