Approximate simulation of Hawkes processes

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21 Citations (Scopus)

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.
Original languageEnglish
JournalMethodology and Computing in Applied Probability
Volume8
Issue number1
Pages (from-to)53-64
Number of pages12
ISSN1387-5841
Publication statusPublished - 2006

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Perfect Simulation
Simulation
Marked Point Process
Edge Effects
Point Process
Siméon Denis Poisson

Cite this

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title = "Approximate simulation of Hawkes processes",
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 M{\o}ller 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.",
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Approximate simulation of Hawkes processes. / Møller, Jesper; Rasmussen, Jakob Gulddahl.

In: Methodology and Computing in Applied Probability, Vol. 8, No. 1, 2006, p. 53-64.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Approximate simulation of Hawkes processes

AU - Møller, Jesper

AU - Rasmussen, Jakob Gulddahl

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

M3 - Journal article

VL - 8

SP - 53

EP - 64

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

SN - 1387-5841

IS - 1

ER -