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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Published in:
Scandinavian journal of statistics : SJS ; theory and applications / Danish Society for Theoretical Statistics ; Finnish Statistical Society ; Norwegian Statistical Society ; Swedish Statistical Society
Publisher:
Wiley
Almqvist & Wiksell
Publishing place:
Oxford
Stockholm
Vol.:
53
No.:
1
ISSN:
0303-6898
ISSN:
1467-9469
Pages:
102 - 139
Date Issued:
2025
URN:
urn:nbn:de:gbv:8:3-2026-00706-7
DOI:
10.1111/sjos.70029
Language:
English
Type of Resource:
Text
Publisher:
Wiley
Keywords:
goodness-of-fit test; Hawkes process; infill asymptotics; parametric bootstrap; Poisson process
Classification:
Published version
DDC subject of DNB:
310 Statistics
Hosting institution:
Faculties, Faculty of Mathematics and Natural Sciences
Hosting institution:
Affiliated Institutes, GEOMAR Helmholtz-Centre for Ocean Research Kiel

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