On goodness‐of‐fit testing for self‐exciting point processes

Despite the wide usage of parametric point processes in theory and applications, a sound goodness‐of‐fit procedure to test whether a given parametric model is appropriate for data coming from a self‐exciting point process has been missing in the literature. In this work, we establish a bootstrap‐based goodness‐of‐fit test that empirically works for all kinds of self‐exciting point processes (and even beyond). In an infill‐asymptotic setting, we also prove its asymptotic consistency, albeit only in the particular case that the underlying point process is inhomogeneous Poisson.