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Approximate Simulation of Hawkes Processes

  • Jesper MøllerEmail author
  • Jakob G. Rasmussen
Article

Abstract

Hawkes processes are important in point process theory and its applications, and simulation of such processes are often needed for various statistical purposes. This article concerns a simulation algorithm for unmarked and marked Hawkes processes, exploiting that the process can be constructed as a Poisson cluster process. The algorithm suffers from edge effects but is much faster than the perfect simulation algorithm introduced in our previous work Møller and Rasmussen (2004). We derive various useful measures for the error committed when using the algorithm, and we discuss various empirical results for the algorithm compared with perfect simulations. Extensions of the algorithm and the results to more general types of marked point processes are also discussed.

Keywords

Edge effects Hawkes process Marked point process Poisson cluster process Simulation 

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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Mathematical SciencesAalborg UniversityAalborgDenmark

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