Jack Olinde
(Advisor: Dr. Martin Short)
will defend a doctoral thesis entitled,
A Self-limiting Hawkes Process: Interpretation, Estimation, and Use in Crime Modeling
On
Friday, April 1st at 1:00 p.m.
Skiles 268
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.
Committee
● Dr. Martin Short – School of Mathematics (advisor)
● Dr. Sung Ha Kang – School of Mathematics
● Dr. Haomin Zhou – School of Mathematics
● Dr. Wenjing Liao – School of Mathematics
● Dr. Karen Yan – School of Economics