Hawkes Models And Their Applications

TL;DR

This paper reviews Hawkes process models, highlighting their core properties, various generalizations, and applications across domains like seismology and finance, including details on construction and simulation methods.

Contribution

It provides a comprehensive overview of traditional and modern Hawkes models, detailing their construction, simulation algorithms, and key references for further study.

Findings

Hawkes processes effectively model self-exciting phenomena.

Generalizations include multivariate, spatial, and renewal-based models.

The paper offers detailed construction and simulation techniques.

Abstract

The Hawkes process is a model for counting the number of arrivals to a system which exhibits the self-exciting property - that one arrival creates a heightened chance of further arrivals in the near future. The model, and its generalizations, have been applied in a plethora of disparate domains, though two particularly developed applications are in seismology and in finance. As the original model is elegantly simple, generalizations have been proposed which: track marks for each arrival, are multivariate, have a spatial component, are driven by renewal processes, treat time as discrete, and so on. This paper creates a cohesive review of the traditional Hawkes model and the modern generalizations, providing details on their construction, simulation algorithms, and giving key references to the appropriate literature for a detailed treatment.