Regression-type analysis for block maxima on block maxima

TL;DR

This paper introduces a regression model for analyzing the relationship between block maxima of response and covariates, accounting for their joint extreme value distribution, with applications to financial market data.

Contribution

It develops a novel regression framework for block maxima that incorporates extreme value copulas and Bayesian priors on angular densities, advancing extreme value analysis methods.

Findings

Good performance in numerical simulations

Effective modeling of extreme co-movements in finance

Insights into stock market extreme loss dependencies

Abstract

This paper devises a regression-type model for the situation where both the response and covariates are extreme. The proposed approach is designed for the setting where both the response and covariates are themselves block maxima, and thus contrarily to standard regression methods it takes into account the key fact that the limiting distribution of suitably standardized componentwise maxima is an extreme value copula. An important target in the proposed framework is the regression manifold, which consists of a family of regression lines obeying the latter asymptotic result. To learn about the proposed model from data, we employ a Bernstein polynomial prior on the space of angular densities which leads to an induced prior on the space of regression manifolds. Numerical studies suggest a good performance of the proposed methods, and a finance real-data illustration reveals interesting aspects on the comovements of extreme losses between two leading stock markets.