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

José C. F. Kling; Mathias Vetter

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arXiv · 2407.09130

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

José C. F. Kling·Mathias Vetter

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Abstract

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 processes has been missing in the literature. In this work, we establish a bootstrap-based goodness-of-fit test which 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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José C. F. Kling, Mathias Vetter. 2024-07-12. On goodness-of-fit testing for self-exciting point processes. https://arxiv.org/abs/2407.09130

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