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Journal of Financial Econometrics Advance Access published online on November 4, 2009
Journal of Financial Econometrics, doi:10.1093/jjfinec/nbp023
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oupjournals.org

An ACD-ECOGARCH(1,1) Model

Claudia Czado
     Technische Universität München

Stephan Haug
     Technische Universität München

Address correspondence to Stephan Haug, Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, D-85748 Garching, Germany, or e-mail: haug{at}ma.tum.de.

JEL Classification: C32, C57


  Abstract

In this paper we introduce an ACD-ECOGARCH(1,1) model. An exponential autoregressive conditional duration model is used to describe the dependence structure in durations of ultra-high-frequency financial data. The innovation process of the ACD model then defines the interarrival times of a compound Poisson process. We use this compound Poisson process as the background driving Lévy process of an exponential continuous time GARCH(1,1) process. The dynamics of the random time transformed log-price process are then described by the latter process. To estimate its parameters we construct a quasi maximum likelihood estimator under the assumption that all jumps of the log-price process are observable. Finally, the model is fitted for illustrative purpose to General Motors tick-by-tick data of the New York Stock Exchange.

KEYWORDS: ACD, ECOGARCH, leverage effect, QMLE, ultra-high-frequency data

We are indebted to two anonymous referees for a number of very helpful comments. Furthermore, we would like to thank George Tauchen and an associate editor for further helpful suggestions. All of them helped to improve the paper considerably. C. Czado acknowledges the support by the DFG through grant CZ 86/1-3.

Received April 18, 2008; revised September 16, 2009; accepted September 22, 2009


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