Multivariate maxima of moving multivariate maxima

TL;DR

This paper introduces a new class of multivariate maxima processes that generalize M4 processes, providing a detailed characterization of their extremal dependence and distributional properties for stationary multivariate time series.

Contribution

It defines a novel class of multivariate maxima processes, extending existing models, and derives their extremal dependence measures and joint distribution properties.

Findings

Characterization of joint distribution of extremes

Calculation of multivariate extremal index

Derivation of tail dependence coefficients

Abstract

We define a class of multivariate maxima of moving multivariate maxima, generalising the M4 processes. For these stationary multivariate time series we characterise the joint distribution of extremes and compute the multivariate extremal index. We derive the bivariate upper tail dependence coefficients and the extremal coefficient of the new limiting multivariate extreme value distributions.