A competing risks interpretation of Hawkes processes

TL;DR

This paper presents a new interpretation of Hawkes processes as competing risks models, linking their self-excitation kernel to hazard functions, and introduces efficient simulation algorithms based on this perspective.

Contribution

It introduces a competing risks framework for Hawkes processes, connecting the kernel to hazard functions and proposing new models and fast simulation methods.

Findings

Established a link between Hawkes kernels and hazard functions.

Proposed new cure rate models for self-excitation kernels.

Developed a fast, general simulation algorithm.

Abstract

We give a construction of the Hawkes process as a piecewise competing risks model. We argue that the most natural interpretation of the self-excitation kernel is the hazard function of a defective random variable. This establishes a link between desired qualitative features of the process and a parametric form for the kernel, which we illustrate using examples from the literature. Two families of cure rate models taken from the survival analysis literature are proposed as new models for the self-excitation kernel. Finally, we show that the competing risks viewpoint leads to a general simulation algorithm which avoids inverting the compensator of the point process or performing an accept-reject step, and is therefore fast and quite general.