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09.07.2025 um 17:15 Uhr in Raum 69/125

Prof. Dr. Mathias Vetter (Christian-Albrechts-Universität zu Kiel)

On Goodness-Of-Fit Testing for Point Processes

Ultimately, this talk is about why applied mathematics can be fun -- for the scientists outside of math, for mathematicians who like to prove things, and for everybody in between.
Years ago, I was asked by colleagues from the geosciences, how to analyze a specific data set coming from volcanic eruptions recorded over time. Their main object of interest was to check whether there exist certain unknown periodicities in the temporal distribution of the eruption record. As the title of my talk suggests, we ultimately decided to interpret the data as observations coming from self-exciting point processes. These processes can in principle be used to model the distribution of whatever type of events over time, and applications range from the natural science and neurology to finance and even the social sciences.
In applications, these processes are often of a parametric form where the intensity function or an additional self-exciting component is known up to an unspecified parameter. A lot of research since the seminal paper by Ogata (1978) has been devoted to the estimation of these unknown parameters, but what has been missing is a consistent goodness-of-fit test, i.e. a statistical procedure which decides whether such a model is reasonable for the data at hand or not.
In this talk, we will review the concept of self-exciting point processes and discuss their main properties. Then, a novel goodness-of-fit statistic will be established, and we will look at the application of this procedure to the volcanological data.