Limit theorems for discrete Hawkes processes

Seol, Youngsoo

doi:10.1016/j.spl.2015.01.023

Cited by 20 publications

(7 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…every minute, every hour or every day. This motivates the study of Discrete-Time Hawkes Processes (DTHP) first introduced by Seol [10], where limit theorems have been established as time goes to infinity. In this paper we study the behaviour as the size of the time step goes to zero instead.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Convergence of the Discrete-Time Compound Hawkes Processwith Exponential or Erlang Kernel

Huang,

Khabou

2021

Preprint

View full text Add to dashboard Cite

Due to its clustering and self-exciting properties, the Hawkes process has been used extensively in numerous fields ranging from sismology to finance. Since data is often aquired on regular time intervals, we propose a piece-wise constant model based on a Discrete-Time Hawkes Process (DTHP). We prove that this discretetime model converges to the usual continuous-time Hawkes process as the time-step tends to zero. RésuméLes propriétés d'auto-excitation des processus de Hawkes permettent une alternative de modélisation efficace au processus de Poisson à intensité déterministe dans plusieurs domaines d'application comme la finance ou la sismologie. Dans certaines applications, l'accès aux données se fait à des dates déterministes et non de façon continue dans le temps. Ainsi, seulement une approximation à temps discret du processus de Hawkes sur une grille déterministe est observable. Dans cet article nous étudions la convergence de cette approximation à temps discret lorsque le pas de la subdivision tend vers zéro.

show abstract

Section: Introduction and Main Resultsmentioning

confidence: 99%

Convergence of the Discrete-Time Compound Hawkes Processwith Exponential or Erlang Kernel

Huang,

Khabou

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Seol [Seo15] proposed a 0-1 discrete Hawkes process as follows. Let (X n ) ∞ n=1 be a sequence taking values on {0, 1} defined as follows.…”

Section: Limit Theorems For Discrete Unmarked Hawkes Processesmentioning

confidence: 99%

“…Compared with continuous Hawkes processes, discrete-time Hawkes processes are not well studied yet. Seol [Seo15] proposed a 0-1 discrete-time Hawkes model and studied its limit theorems. In this paper, we propose a univariate marked discrete-time Hawkes process and derive the limit theorems for our model.…”

Section: Introductionmentioning

confidence: 99%

Limit theorems for a discrete-time Hawkes process

Wang

2020

Preprint

View full text Add to dashboard Cite

The Hawkes process is a self-exciting simple point process with wide applications in finance, social networks, criminology, seismology, and many other fields. The Hawkes process is defined for continuous time setting. However, in reality, data is often recorded in a discretetime scheme or the data only shows the aggregate results. In this paper, we propose a discrete-time marked Hawkes process and study the limit theorems for the model.

show abstract

“…Seol [Seo15] proposed a 0-1 discrete Hawkes model and studied its limit theorems. Let (X n ) ∞ n=1 be a sequence taking values on {0, 1} defined as follows.…”

Section: Introductionmentioning

confidence: 99%

Large and moderate deviations for a discrete-time marked Hawkes process

Wang¹

2020

Preprint

View full text Add to dashboard Cite

The Hawkes process is a simple point process with wide applications in finance, social networks, criminology, seismology, and many other fields. The Hawkes process is defined for continuous time setting. However, data is often recorded in a discrete-time scheme. In this paper, we study a discrete-time marked Hawkes process, which is appealing for applications. In particular, we study large deviations for the model.

show abstract

Limit theorems for discrete Hawkes processes

Cited by 20 publications

References 20 publications

Convergence of the Discrete-Time Compound Hawkes Processwith Exponential or Erlang Kernel

Convergence of the Discrete-Time Compound Hawkes Processwith Exponential or Erlang Kernel

Limit theorems for a discrete-time Hawkes process

Large and moderate deviations for a discrete-time marked Hawkes process

Contact Info

Product

Resources

About