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Multivariate Tail Coefficients: Properties and Estimation.
Irène Gijbels1, Vojtěch Kika1,2, Marek Omelka2
1Department of Mathematics and Leuven Statistics Research Center (LStat), KU Leuven, 3001 Leuven, Belgium.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This study enhances understanding of multivariate tail coefficients for analyzing extreme event dependencies. New measurements and estimation methods are proposed, with practical applications in financial market analysis.
Area of Science:
- Statistics
- Extreme Value Theory
- Financial Mathematics
Background:
- Bivariate tail coefficients are well-studied for extreme event dependencies.
- Multivariate tail coefficients require further investigation for complex systems.
Purpose of the Study:
- To thoroughly study existing multivariate tail coefficients and their properties.
- To propose novel multivariate tail measurements and estimation techniques.
- To analyze the behavior of these measurements with increasing data dimensions.
Main Methods:
- Theoretical analysis of multivariate tail coefficient properties.
- Development and proposal of new tail measurement methodologies.
- Asymptotic consistency analysis for coefficient estimation.
- Empirical validation using financial market data (EURO STOXX 50).
Main Results:
- A comprehensive evaluation of existing multivariate tail coefficients against desirable properties.
- Introduction of new, effective multivariate tail dependence measures.
- Demonstration of asymptotic consistency for the proposed estimation methods.
- Insights into how tail behavior changes with higher dimensions.
Conclusions:
- The proposed methods offer advancements in quantifying multivariate extreme dependencies.
- The study provides practical tools for analyzing financial market risks.
- Findings contribute to the broader understanding of extreme event interactions in high-dimensional settings.
Keywords:
archimedean copulaconsistencyestimationextreme-value copulamultivariate analysistail dependencyMore Related Videos
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