Exact Simulation of Max-Infinitely Divisible Processes

Peng Zhong, Raphaël Huser and Thomas Opitz

Econometrics and Statistics, 2024, vol. 30, issue C, 96-109

Abstract: 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.

Keywords: Adaptive rejection sampling; Exact simulation; Extremal function; Max-infinitely divisible process; Max-stable process (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecosta:v:30:y:2024:i:c:p:96-109

DOI: 10.1016/j.ecosta.2022.02.007

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