Abstract
In this paper we consider the modelling of multivariate marked ultra-high-frequency data. Such data consists, for example, of the trading times of several stocks together with the associated prices. We give an example how this kind of data may be modelled in the framework of marked point processes. The proposed model is a multivariate model for the trading times and the associated returns. We suggest a simple generalization of existing GARCH–type models for univariate ultra-high-frequency data to the multivariate setting. Preliminary remarks concerning the the stationarity of the proposed model are given, and maximum likelihood estimation is discussed.