Extreme value analysis for mixture models with heavy-tailed impurity

TL;DR

This paper explores the extreme value behavior of mixture models with heavy-tailed impurities, revealing diverse limit distributions and demonstrating their application to modeling maximum stock returns.

Contribution

It introduces a novel analysis of extreme values in mixture models with heavy-tailed impurities, expanding the classical limit distribution framework.

Findings

Diverse limit distributions identified for heavy-tailed mixture models

Numerical examples show effectiveness in modeling stock return maxima

Heavy-tailed impurities significantly influence extreme value behavior

Abstract

This paper deals with the extreme value analysis for the triangular arrays, which appear when some parameters of the mixture model vary as the number of observations grow. When the mixing parameter is small, it is natural to associate one of the components with "an impurity" (in case of regularly varying distribution, "heavy-tailed impurity"), which "pollutes" another component. We show that the set of possible limit distributions is much more diverse than in the classical Fisher-Tippett-Gnedenko theorem, and provide the numerical examples showing the efficiency of the proposed model for studying the maximal values of the stock returns.