Multivariate Modelling of Time Series Count Data: An Autoregressive Conditional Poisson Model

CORE Discussion Paper No. 2003/25

Posted: 3 Jan 2005

See all articles by Andréas Heinen

Andréas Heinen

University of Cergy-Pontoise - THEMA

Erick W. Rengifo

Fordham University - Department of Economics - Center for International Policy Studies (CIPS)

Date Written: March 2003

Abstract

This paper introduces a new multivariate model for time series count data. The Multivariate Autoregressive Conditional Poisson model (MACP) makes it possible to deal withissues of discreteness, overdispersion (variance greater thant then mean) and both auto- and crosscorrelation. We model counts as Poisson or double Poisson and assume that conditionally on past observations the means follow a Vector Autoregression. We use a copula to introduce contemporaneous correlation between the series. An important advantage of this model is that it can accommodate bothp ositive and negative correlation among variables. As a feasible alternative to multivariate duration models, the model is applied to the submission of market orders and quote revisions on IBM on the New York Stock Exchange. We show that a single factor cannot explain the dynamics of the market process, which confirms that time deformation, taken as meaning that all market events should accelerate or slow down proportionately, does not hold. We advocate the use of the Multivariate Autoregressive Conditional Poisson model for the study of multivariate point processes in finance, when the number of variables considered simultaneously exceeds two and looking at durations becomes too difficult.

Keywords: count data, time series, copula, market microstructure.

JEL Classification: C32, C35, G10

Suggested Citation

Heinen, Andréas and Rengifo, Erick W., Multivariate Modelling of Time Series Count Data: An Autoregressive Conditional Poisson Model (March 2003). CORE Discussion Paper No. 2003/25. Available at SSRN: https://ssrn.com/abstract=640321

Andréas Heinen

University of Cergy-Pontoise - THEMA ( email )

33 boulevard du port
F-95011 Cergy-Pontoise Cedex, 95011
France

Erick W. Rengifo (Contact Author)

Fordham University - Department of Economics - Center for International Policy Studies (CIPS) ( email )

United States
0017188174061 (Phone)
0017188173518 (Fax)

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