  We test three common information criteria (IC) for selecting the order of a
Hawkes process with an intensity kernel that can be expressed as a mixture of
exponential terms. These processes find application in high-frequency financial
data modelling. The information criteria are Akaike's information criterion
(AIC), the Bayesian information criterion (BIC) and the Hannan-Quinn criterion
(HQ). Since we work with simulated data, we are able to measure the performance
of model selection by the success rate of the IC in selecting the model that
was used to generate the data. In particular, we are interested in the relation
between correct model selection and underlying sample size. The analysis
includes realistic sample sizes and parameter sets from recent literature where
parameters were estimated using empirical financial intra-day data. We compare
our results to theoretical predictions and similar empirical findings on the
asymptotic distribution of model selection for consistent and inconsistent IC.
