Title:
A Self-limiting Hawkes Process: Interpretation, Estimation, and Use in Modeling
A Self-limiting Hawkes Process: Interpretation, Estimation, and Use in Modeling
Author(s)
Olinde, John Garnier
Advisor(s)
Short, Martin B.
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Abstract
Many real life processes that we would like to model have a self-exciting property, i.e. the occurrence of one event causes a temporary spike in the probability of other events occurring nearby in space and time. Examples of processes that have this property are earthquakes, crime in a neighborhood, or emails within a company. In 1971, Alan Hawkes first used what is now known as the Hawkes process to model such processes. Since then much work has been done on estimating the parameters of a Hawkes process given a data set and creating variants of the process for different applications.
In this thesis, we propose a new variant of a Hawkes process, called a self-limiting Hawkes process, that takes into account the effect of police activity on the underlying crime rate and an algorithm for estimating its parameters given a crime data set. We show that the self-limiting Hawkes process fits real crime data just as well, if not better, than the standard Hawkes model.We also show that the self-limiting Hawkes process fits real financial data at least as well as the standard Hawkes model.
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Date Issued
2022-04-28
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Text
Resource Subtype
Dissertation