Adaptive PORT–MVRB estimation: an empirical comparison of two heuristic algorithms

Abstract

In this article, we deal with an empirical comparison of two data-driven heuristic procedures of estimation of a positive extreme value index (EVI), working thus with heavy right tails. The semi-parametric EVI-estimators under consideration, the so-called peaks over random threshold (PORT)–minimum-variance reduced-bias (MVRB) EVI-estimators, are location and scale-invariant estimators, based on the PORT methodology applied to second-order MVRB EVI-estimators. Trivial adaptations of these algorithms make them work for a similar estimation of other parameters of extreme events, such as the Value-at-Risk at a level p, the expected shortfall and the probability of exceedance of a high level x, among others. Applications to simulated data sets and to real data sets in the field of finance are provided.

Keywords:

• statistics of extremes
• extreme value index
• semi-parametric estimation
• adaptive choices
• heuristic methods
• bias reduction
• location/scale invariant estimation
• GARCH processes

Acknowledgements

Research partially supported by National Funds through FCT — Fundação para a Ciência e a Tecnologia, project PEst-OE/MAT/UI0006/2011, PTDC/FEDER and grants SFRH/BPD/72184/2010, SFRH/BPD/77319/2011.