The ACD model, proposed in Engle-Russell (1998), is aimed at analysing the transaction process: it is the first appropriate statistical tool available for testing the microstrauctural hypotheses. The ACD model addresses the problem of the irregular time spacing of transaction data. Notice that it would be inappropriate to aggregate over time in order to get equally spaced data, since the time spacing of transactions is one of the relevant issues in the market behaviour, and hence aggregating over time would lead to a loss of information. Often the information systems of the stock markets provide also information about the behaviour of the market maker, as the bid and ask prices, the corresponding depth, and the timing of change of the quota. In the recent literature some bivariate extensions of the ACD model have been proposed, in order to make a joint analysis of the transaction process and the activity of the market maker (Russell, 1998 and Engle-Lunde, 1999). However, these models are in a very early stage of development, and it is our opinion that they can be significantly improved on both theoretical and empirical ground.
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