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Point process simulation of generalised hyperbolic Lévy processes

Published version
Peer-reviewed

Repository DOI


Change log

Authors

Kındap, Yaman 
Godsill, Simon 

Abstract

jats:titleAbstract</jats:title>jats:pGeneralised hyperbolic (GH) processes are a class of stochastic processes that are used to model the dynamics of a wide range of complex systems that exhibit heavy-tailed behavior, including systems in finance, economics, biology, and physics. In this paper, we present novel simulation methods based on subordination with a generalised inverse Gaussian (GIG) process and using a generalised shot-noise representation that involves random thinning of infinite series of decreasing jump sizes. Compared with our previous work on GIG processes, we provide tighter bounds for the construction of rejection sampling ratios, leading to improved acceptance probabilities in simulation. Furthermore, we derive methods for the adaptive determination of the number of points required in the associated random series using concentration inequalities. Residual small jumps are then approximated using an appropriately scaled Brownian motion term with drift. Finally the rejection sampling steps are made significantly more computationally efficient through the use of squeezing functions based on lower and upper bounds on the Lévy density. Experimental results are presented illustrating the strong performance under various parameter settings and comparing the marginal distribution of the GH paths with exact simulations of GH random variates. The new simulation methodology is made available to researchers through the publication of a Python code repository.</jats:p>

Description

Keywords

Series representations, Lévy process, Stochastic differential equations, Monte Carlo methods, Generalised inverse Gaussian process

Journal Title

Statistics and Computing

Conference Name

Journal ISSN

0960-3174
1573-1375

Volume Title

34

Publisher

Springer Science and Business Media LLC