Extreme value analysis for mixture models with heavy-tailed impurity

2021/03/13 by Vladimir Panov, Ekaterina Morozova, Panov, Vladimir +1
Economics, Econometrics and Finance · #60F99 #60G70 #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2103.07689

openalex publication_date 2021/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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