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Peaks Over Thresholds Modeling With Multivariate Generalized Pareto Distributions

Journal article
Authors A. Kiriliouk
Holger Rootzén
J. Segers
J. L. Wadsworth
Published in Technometrics
Volume 61
Issue 1
Pages 123-135
ISSN 0040-1706
Publication year 2019
Published at Department of Mathematical Sciences
Pages 123-135
Language en
Links dx.doi.org/10.1080/00401706.2018.14...
Keywords Financial risk, Landslides, Multivariate extremes, Tail dependence, likelihood estimators, extreme rainfall, dependence, erosion
Subject categories Probability Theory and Statistics

Abstract

When assessing the impact of extreme events, it is often not just a single component, but the combined behavior of several components which is important. Statistical modeling using multivariate generalized Pareto (GP) distributions constitutes the multivariate analogue of univariate peaks over thresholds modeling, which is widely used in finance and engineering. We develop general methods for construction of multivariate GP distributions and use them to create a variety of new statistical models. A censored likelihood procedure is proposed to make inference on these models, together with a threshold selection procedure, goodness-of-fit diagnostics, and a computationally tractable strategy for model selection. The models are fitted to returns of stock prices of four UK-based banks and to rainfall data in the context of landslide risk estimation. Supplementary materials and codes are available online.

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