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.
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