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Consistent Information Criteria for Selecting an Optimum Autoregressive Conditional Duration Model

G. Xie, P. Cowpertwait


The Akaike Information Criterion (AIC) and consistent AIC (Bozdogan, 1987) are applied to the problem of model selection when fitting a family of autoregressive conditional duration (ACD) models to high-frequency inter-trade time intervals. A range of ACD models are fitted to two data sets: the 1990 IBM New York stock exchange data and 2006 transaction
data for the company Darby BHD taken from the Kuala Lumpur stock exchange. Using the method of maximum likelihood, basic ACD models (Engle and Russell, 1998), threshold ACD models (Zhang, Russell and Tsay, 2001), and mixed distribution ACD model (Luca and Gallo, 2004) are fitted to each data set, and the consistent AIC calculated for each fitted model. A mixed distribution ACD model, obtained using lognormal and gamma distributions for the residuals, is found to provide the best fit to the IBM data, which is supported by a quantile plot of the residuals. Based on consistent AIC, the same model also provides the best overall fit to the Darby data, although in this case there is evidence of autocorrelation
in the residual series.


Akaike Information Criterion; high-frequency data; financial time series; transaction data.

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