Exact Simulation of Max-Infinitely Divisible Processes

Peng Zhong, Raphaël Huser, Thomas Opitz

Research output: Contribution to journalArticlepeer-review


Max-infinitely divisible (max-id) processes play a central role in extreme-value theory and include the subclass of all max-stable processes. They allow for a constructive representation based on the pointwise maximum of random functions drawn from a Poisson point process defined on a suitable function space. Simulating from a max-id process is often difficult due to its complex stochastic structure, while calculating its joint density in high dimensions is often numerically infeasible. Therefore, exact and efficient simulation techniques for max-id processes are useful tools for studying the characteristics of the process and for drawing statistical inferences. Inspired by the simulation algorithms for max-stable processes, theory and algorithms to generalize simulation approaches tailored for certain flexible (existing or new) classes of max-id processes are presented. Efficient simulation for a large class of models can be achieved by implementing an adaptive rejection sampling scheme to sidestep a numerical integration step in the algorithm. The results of a simulation study highlight that our simulation algorithm works as expected and is highly accurate and efficient, such that it clearly outperforms customary approximate sampling schemes. As a by-product, new max-id models, which can be represented as pointwise maxima of general location-scale mixtures and possess flexible tail dependence structures capturing a wide range of asymptotic dependence scenarios, are also developed.
Original languageEnglish (US)
JournalEconometrics and Statistics
StatePublished - Mar 11 2022

Bibliographical note

KAUST Repository Item: Exported on 2022-04-26
Acknowledged KAUST grant number(s): OSR-CRG2017-3434, OSR-CRG2020-4394
Acknowledgements: We thank the Editor, Associate Editor, and two anonymous reviewers for constructive comments that helped improve the paper. This publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Awards No. OSR-CRG2017-3434 and No. OSR-CRG2020-4394.


Dive into the research topics of 'Exact Simulation of Max-Infinitely Divisible Processes'. Together they form a unique fingerprint.

Cite this