Multivariate modelling of time series count data: an autoregressive conditional Poisson model

This paper introduces a new multivariate model for time series count data. The Multivariate Autoregressive Conditional Poisson model (MACP) makes it possible to deal with issues of discreteness, overdispersion (variance greater than the mean) and both auto- and cross-correlation. 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 both positive 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.