Title: A new shift invariant Hill-type estimator for heavy tailed models
Authors: Xia Cai; Xiumin Li
Addresses: College of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei, 050018, China. ' College of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei, 050018, China
Abstract: In this paper, we build a new Hill-type estimator of extreme value index, which is close to the true value for a class of heavy-tailed models. The new estimator, which is based on the original Hill's estimator and generalised Hill's estimator, depends on a positive parameter. It is invariant for changes in both scale and shift. The simulation studies are presented to show that the new estimator performs well compared to the known ones when γ is between 1/2 and 2/3. Finally, we apply this new method to the logarithmic rate of return in stock market.
Keywords: extreme value index; shift invariant; scale invariant; heavy tailed models; Hill estimator; simulation; rates of return; stock markets.
DOI: 10.1504/IJMIC.2012.047728
International Journal of Modelling, Identification and Control, 2012 Vol.16 No.3, pp.206 - 211
Published online: 17 Dec 2014 *
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