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Modelling a Multivariate Transaction Process

In this paper the dynamics of a joint transaction process is 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 the 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 modelled along the lines of fractionally integrated autoregressive conditional models, which are very well suited to capture the high persistency empirically observed in these processes. The model is applied to three stocks traded at the New York Stock Exchange (NSYE) in May, 2001 and we investigate several market microstructure hypothesis in the empirical part of this paper.