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Order aggressiveness and order book dynamics 155<br />

5.1 Statistical results<br />

The ACI models were estimated by maximum likelihood us<strong>in</strong>g the MAXLIKprocedure<br />

<strong>of</strong> GAUSS. It should be stressed that despite <strong>of</strong> the <strong>high</strong>-dimensionality<br />

<strong>of</strong> the processes and the large number <strong>of</strong> parameters, the processes converged<br />

smoothly and without numerical difficulties. The follow<strong>in</strong>g statistical results can be<br />

summarized. First, for all processes, we f<strong>in</strong>d significantly decl<strong>in</strong><strong>in</strong>g backward<br />

recurrence functions as revealed by the estimated parameters p k

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