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 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article