Before revision:  We analyse both the in-sample characteristics and the forecasting efficiency. In the forecasting part, artificial trajectories are simulated and then evaluated by calculating the \mathcal{L .
After revision:  We analyse both the in-sample characteristics and the probabilistic forecasting performance. In a rolling window forecasting study, we simulate many trajectories to evaluate the forecasts and gain significant insights into the model fit. The prediction accuracy is evaluated by a functional version of the MAE (mean absolute error), RMSE (root mean squared error) and CRPS (continuous ranked probability score) for the simulated count processes. This paper fills the gap in the literature regarding the intensity estimation of transaction arrivals and is a major contribution to the topic, yet leaves much of the field for further development .