2013/11/13 by Axel Bücher, Johan Segers, Bücher, Axel +1
Economics, Econometrics and Finance · Social Sciences · #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Market Dynamics and Volatility #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1311.3060
openalex publication_date 2013/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The core of the classical block maxima method consists of fitting an extreme\nvalue distribution to a sample of maxima over blocks extracted from an\nunderlying series. In asymptotic theory, it is usually postulated that the\nblock maxima are an independent random sample of an extreme value distribution.\nIn practice however, block sizes are finite, so that the extreme value\npostulate will only hold approximately. A more accurate asymptotic framework is\nthat of a triangular array of block maxima, the block size depending on the\nsize of the underlying sample in such a way that both the block size and the\nnumber of blocks within that sample tend to infinity. The copula of the vector\nof componentwise maxima in a block is assumed to converge to a limit, which,\nunder mild conditions, is then necessarily an extreme value copula. Under this\nsetting and for absolutely regular stationary sequences, the empirical copula\nof the sample of vectors of block maxima is shown to be a consistent and\nasymptotically normal estimator for the limiting extreme value copula.\nMoreover, the empirical copula serves as a basis for rank-based, nonparametric\nestimation of the Pickands dependence function of the extreme value copula. The\nresults are illustrated by theoretical examples and a Monte Carlo simulation\nstudy.\n