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Regression-type analysis for multivariate extreme values
Miguel de Carvalho1, Alina Kumukova2, Gonçalo Dos Reis1,3
1School of Mathematics, University of Edinburgh, Edinburgh, UK.
Extremes
|October 31, 2022
Summary
This study introduces a new regression model for extreme values, accounting for multivariate extreme value distributions and extreme value copulas. The model offers insights into financial market risks, particularly extreme losses.
Area of Science:
- Statistics
- Extreme Value Theory
- Econometrics
Background:
- Standard regression models often fail with extreme data.
- Extreme value theory is crucial for understanding rare events.
- Multivariate extreme value distributions capture dependencies in extreme data.
Purpose of the Study:
- To develop a novel regression model for situations with extreme responses and covariates.
- To incorporate extreme value copulas into a regression framework.
- To analyze the conditional risk of extreme losses in financial markets.
Main Methods:
- A regression-type model is devised for multivariate extreme value data.
- The model leverages extreme value copulas, unlike standard methods.
- Bernstein polynomial priors are used on angular densities for model learning.
Main Results:
- Numerical studies indicate strong performance of the proposed methods.
- The framework identifies a regression manifold based on asymptotic results.
- Analysis of financial data reveals insights into extreme loss risks.
Conclusions:
- The proposed model effectively handles extreme response and covariate data.
- The approach provides a robust framework for analyzing extreme value dependencies.
- The findings have implications for understanding and managing financial risks.
Keywords:
Angular measureBernstein polynomialsExtreme value copulaJoint extremesMultivariate extreme value distributionQuantile regressionStatistics of extremesMore Related Videos
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