Before revision:  It turns out that the model can  reproduce several stylized facts of high-frequency financial time series  .
After revision:  It turns out that the model can reproduce several stylized facts of high-frequency financial time series . Moreover, using Monte Carlo simulations, we analyze order selection for this model class using three information criteria: Akaike's information criterion (AIC), the Bayesian information criterion (BIC) and the Hannan-Quinn information criterion (HQ). For comparison, we also perform a similar Monte Carlo experiment for the ACD (autoregressive conditional duration) model. Our results show that the information criteria work best for small parameter numbers for the compound Poisson type models, whereas for the ACD model the model selection procedure does not work well in certain cases .