Extreme Value Analysis for Mixture Models with Heavy-Tailed Impurity

Ekaterina Morozova and Vladimir Panov
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Ekaterina Morozova: Laboratory of Stochastic Analysis and Its Applications, HSE University, Pokrovsky Boulevard 11, 109028 Moscow, Russia

Mathematics, 2021, vol. 9, issue 18, 1-24

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 grows. When the mixing parameter is small, it is natural to associate one of the components with “an impurity” (in the 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.

Keywords: heavy-tailed distributions; extreme values; mixture model; triangular arrays (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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