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Exact simulation of continuous max-id processes with applications to exchangeable max-id sequences

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  • Brück, Florian

Abstract

An algorithm for the unbiased simulation of continuous max-(resp. min-) infinitely divisible stochastic processes is developed. The algorithm only requires the simulation of finite Poisson random measures on the space of continuous functions and avoids the necessity of computing conditional distributions of infinite (exponent) measures. The complexity of the algorithm is characterized in terms of the expected number of simulated atoms of the Poisson random measures on the space of continuous functions. Special emphasis is put on the simulation of exchangeable max-(or min-) infinitely divisible sequences, in particular exchangeable Sato-frailty sequences. Additionally, exact simulation schemes of exchangeable exogenous shock models and exchangeable max-stable sequences are sketched.

Suggested Citation

  • Brück, Florian, 2023. "Exact simulation of continuous max-id processes with applications to exchangeable max-id sequences," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:jmvana:v:193:y:2023:i:c:s0047259x22001087
    DOI: 10.1016/j.jmva.2022.105117
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    References listed on IDEAS

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    1. Jan-Frederik Mai & Steffen Schenk & Matthias Scherer, 2017. "Two Novel Characterizations of Self-Decomposability on the Half-Line," Journal of Theoretical Probability, Springer, vol. 30(1), pages 365-383, March.
    2. Gregory P. Bopp & Benjamin A. Shaby & Raphaël Huser, 2021. "A Hierarchical Max-Infinitely Divisible Spatial Model for Extreme Precipitation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(533), pages 93-106, March.
    3. Clément Dombry & Sebastian Engelke & Marco Oesting, 2016. "Exact simulation of max-stable processes," Biometrika, Biometrika Trust, vol. 103(2), pages 303-317.
    4. Mai, Jan-Frederik, 2018. "Exact simulation of reciprocal Archimedean copulas," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 68-73.
    5. Matthias Scherer & Henrik Sloot, 2019. "Exogenous shock models: analytical characterization and probabilistic construction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(8), pages 931-959, November.
    6. Dombry, Clément & Eyi-Minko, Frédéric, 2012. "Strong mixing properties of max-infinitely divisible random fields," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3790-3811.
    7. Raphaël Huser & Thomas Opitz & Emeric Thibaud, 2021. "Max‐infinitely divisible models and inference for spatial extremes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 321-348, March.
    8. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    9. Padoan, Simone A., 2013. "Extreme dependence models based on event magnitude," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 1-19.
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