Forecasting trade durations via ACD models with mixture distributions

Abstract

Under Autoregressive Conditional Duration model framework, suitably modelling the positive valued innovations has been challenging. Most often, irregularly spaced trade duration data display a long right tail and a high density close to zero. Many subtle features and intricacies inherent in such time series demand flexible distributions to adequately capture these features. This paper introduces two mixture models by extending the mixture of exponential distributions of De Luca and Gallo [Mixture processes for financial intradaily durations. Stud. Nonlinear Dyn. Econ., 2004, 8(2), 1–20] to include more flexible and general distributions. In the initial extension, a Weibull distribution replaces one exponential component and, subsequently, a generalised beta of type 2 distribution is considered to further improve flexibility and extreme quantile estimation. Both these models are extended by incorporating dynamic mixture weights. Parameter estimation is done with a Bayesian methodology based on a Markov chain Monte Carlo sampling scheme. Simulation experiments are conducted to evaluate its performance and practical usefulness is assessed with empirical applications of trade durations from the Australian Securities Exchange. The performance of the proposed mixture models in comparison to several other competing distributions is evaluated in terms of model fit and forecast analysis via Time-at-Risk (TaR) quantiles and conditional expectation TaR (CTaR).