• Corpus ID: 220495915

Perfect Sampling of Multivariate Hawkes Process

@article{Chen2020PerfectSO,
  title={Perfect Sampling of Multivariate Hawkes Process},
  author={Xinyun Chen and Xiuwen Wang},
  journal={arXiv: Applications},
  year={2020}
}
As an extension of self-exciting Hawkes process, the multivariate Hawkes process models counting processes of different types of random events with mutual excitement. In this paper, we present a perfect sampling algorithm that can generate i.i.d. stationary sample paths of multivariate Hawkes process without any transient bias. In addition, we provide an explicit expression of algorithm complexity in model and algorithm parameters and provide numerical schemes to find the optimal parameter set… 

Figures and Tables from this paper

Conditional Uniformity and Hawkes Processes
Classic results show that the Hawkes self-exciting point process can be viewed as a collection of temporal clusters, where exogenously generated initial events give rise to endogenously driven

References

SHOWING 1-10 OF 16 REFERENCES
Perfect Sampling of Hawkes Processes and Queues with Hawkes Arrivals
  • Xinyun Chen
  • Computer Science, Mathematics
    Stochastic Systems
  • 2021
TLDR
This paper develops to the best knowledge the first perfect sampling algorithm for queues with Hawkes input and proposes a new perfect sampling algorithms for Hawkes processes with improved computational efficiency compared with the existing algorithm.
Exact Simulation of Hawkes Process with Exponentially Decaying Intensity
We introduce a numerically efficient simulation algorithm for Hawkes process with exponentially decaying intensity, a special case of general Hawkes process that is most widely implemented in
Perfect simulation of Hawkes processes
TLDR
By viewing Hawkes processes as Poisson cluster processes and using their branching and conditional independence structures, useful approximations of the distribution function for the length of a cluster are derived and used to construct upper and lower processes for the perfect simulation algorithm.
A cluster process representation of a self-exciting process
It is shown that all stationary self-exciting point processes with finite intensity may be represented as Poisson cluster processes which are age-dependent immigration-birth processes, and their
Multivariate Hawkes processes
TLDR
This thesis addresses theoretical and practical questions arising in connection with multivariate, marked, linear Hawkes processes, including the calculation of moment measures; and the existence and uniqueness of stationary solutions.
A Tutorial on Hawkes Processes for Events in Social Media
TLDR
This chapter provides an accessible introduction for point processes, and especially Hawkes processes, for modeling discrete, inter-dependent events over continuous time and describes a practical example drawn from social media data.
Point Spectra of Some Mutually Exciting Point Processes
IN contagious processes (e.g. measles, hijacking, etc.) the occurrence of events increases the probability of further events occurring in the near future. Also several series of events may interact
Estimating tranche spreads by loss process simulation
TLDR
This work considers two algorithms that exploit the direct specification of the loss process in terms of an intensity, based on the simulation of intensity paths, that facilitates exact simulation of default times and generates an unbiased estimator of the derivative price.
Applications of a multivariate Hawkes process to joint modeling of sentiment and market return events
To investigate the complex interactions between market events and investor sentiment, we employ a multivariate Hawkes process to evaluate dynamic effects among four types of distinct events: positive
...
...