Georgia Institute of Technology College of Sciences

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 talk, 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.