Extremal correlation coefficient for functional data

TL;DR

This paper introduces a new extremal correlation coefficient for functional data that measures dependence between curves, especially focusing on extreme cases, with applications demonstrated in finance and climate data.

Contribution

It proposes a novel dependence measure for functional data based on regular variation, along with a consistent estimator and an empirical validation.

Findings

The coefficient effectively captures dependence in extreme functional data.

The estimator is consistent and supported by asymptotic analysis.

Applications show usefulness in financial and climate datasets.

Abstract

We propose a coefficient that measures dependence in paired samples of functions. It has properties similar to the Pearson correlation, but differs in significant ways: (i) it is designed to measure dependence between curves, (ii) it focuses only on extreme curves. The new coefficient is derived within the framework of regular variation in Banach spaces. A consistent estimator is proposed and justified by an asymptotic analysis and a simulation study. The usefulness of the new coefficient is illustrated on financial and and climate functional data.