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Multivariate Tail Coefficients: Properties and Estimation.

Irène Gijbels1, Vojtěch Kika1,2, Marek Omelka2

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Summary
This summary is machine-generated.

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.

Keywords:
archimedean copulaconsistencyestimationextreme-value copulamultivariate analysistail dependency

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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.