Testing Separability in Spatio-Temporal Functional Marked Point Processes

The paper addresses the issue of testing separability of spatio-temporal locations and functional marks in spatio-temporal functional marked point processes (STFMPPs), where spatio-temporal events are associated with marks evolving along a lifetime domain. Separability assumptions are generally adopted to simplify inference, while tools to assess their validity in the presence of functional marks are lacking. We propose a separability test based on a finite-dimensional score representation of functional marks. Simulation studies and an application to seismic data show that the test effectively detects departures from separability.