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Journal of Financial Econometrics Advance Access originally published online on November 22, 2007
Journal of Financial Econometrics 2008 6(1):143-170; doi:10.1093/jjfinec/nbm020
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© The Author 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Modeling a Multivariate Transaction Process

Ingmar Nolte
     University of Konstanz, CoFE

Address for correspondence: Department of Economics, Box D124, University of Konstanz, 78457 Konstanz, Germany. Tel.: +49-7531-88-3753; Fax: +4450, email: Ingmar.Nolte{at}uni-konstanz.de.


  Abstract

In this paper the dynamics of a joint transaction process are investigated. The transaction process is characterized by four marks: price changes, transaction volumes, bid–ask spreads and intertrade durations. Based on a copula approach, a model for their joint density is proposed, which avoids forcing a priori assumptions on the instantaneous causality relationships between the four variables as necessary in decomposition models, where the joint density is decomposed into its conditional and unconditional densities. The price change process is treated as a discrete process and specified with an integer count hurdle model and the transaction volumes, bid–ask spreads, and trade durations processes are modeled along the lines of fractionally integrated autoregressive conditional models, which are suited very well to capture the high persistency, empirically observed in these processes. The model is applied to three stocks traded at the New York Stock Exchange (NYSE) in May, 2001 and we investigate several market microstructure hypotheses in the empirical part of this paper.

KEYWORDS: copula functions, discrete price changes, fractionally integrated autoregressive conditional duration models, integer count hurdle model, market microstructure, transaction data

I gratefully acknowledge the financial support by the Fritz Thyssen Stiftung through the project "Dealer-Behavior and Price-Dynamics on the Foreign Exchange Market". I would like to thank Eric Renault (editor), the co-editor and two anonymous referees for constructive suggestions on previous drafts of the paper. Special thanks go to Nikolaus Hautsch, Sandra Nolte, Winfried Pohlmeier, and Valeri Voev, the participants of the conference "The Econometrics of the Microstructure of Financial Markets," April 23–24, 2004, CentER, Tilburg University, and the participants of the "59th European Meeting of the Econometric Society" August 20–24, 2004, Madrid for helpful comments.


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