FLP estimation of semi-parametric models for space-time point processes and diagnostic tools

The conditional intensity function of a space-time branching model is defined by the sum of two main components: the long-run term intensity and short-run term one. Their simultaneous estimation is a complex issue that usually requires the use of hard computational techniques. This paper deals with a new mixed estimation approach for a particular space-time branching model, the Epidemic Type Aftershock Sequence model. This approach uses a simultaneous estimation of the different model components, alternating a parametric step for estimating the induced component by Maximum Likelihood and a non-parametric estimation step, for the background intensity, by FLP (Forward Predictive Likelihood).Moreover, proper graphical tools for diagnostics have been developed and collected, together with the used implemented code in a R package here introduced, named etasFLP.