Time-Varying Mixing Weights in Mixture Autoregressive Conditional Duration Models

Abstract

Financial market price formation and exchange activity can be investigated by means of ultra-high frequency data. In this article, we investigate an extension of the Autoregressive Conditional Duration (ACD) model of Engle and Russell (1998) by adopting a mixture of distribution approach with time-varying weights. Empirical estimation of the Mixture ACD model shows that the limitations of the standard base model and its inadequacy of modelling the behavior in the tail of the distribution are suitably solved by our model. When the weights are made dependent on some market activity data, the model lends itself to some structural interpretation related to price formation and information diffusion in the market.

Keywords:

• Autoregressive
• Conditional Durations
• Financial durations
• Mixture of distributions
• Time-varying weights

JEL Classification:

• C22
• C52
• C53

ACKNOWLEDGMENTS

Thanks are due to Estela Bee Dagum, Silvano Bordignon, and Tommaso Proietti for their support and encouragement throughout this research project. Various participants in the Conference Statistical Inference on Linear and Nonlinear Dynamics in Time Series in Bressanone, June 9–11, 2005, and in the International Conference on Finance in Copenhagen, September 2–4, 2005 provided useful comments. Without implicating, we mention in particular Luc Bauwens, Nikolaus Hautsch, Søren Johansen, and Timo Teräsvirta who helped us focus more on the statistical issues and economic interpretation of what is being presented here. We would also like to thank an anonymous referee who pointed out some important aspects to be clarified. Financial support from the Italian MIUR (under PRIN and FISR grants) is gratefully acknowledged.

Notes

LR test (Model 2 vs Model 1): 87.07.

¹We thank Timo Teräsvirta for pointing this out to us.

LR test, Model 4 vs. Model 3: 44.34.