Monte Carlo-based tail exponent estimator

Arbeitspapier

In this paper we study the finite sample behavior of the Hill estimator under α-stable distributions. Using large Monte Carlo simulations we show that the Hill estimator overestimates the true tail exponent and can hardly be used on samples with small length. Utilizing our results, we introduce a Monte Carlo-based method of estimation for the tail exponent. Our method is not sensitive to the choice of k and works well also on small samples. The new estimator gives unbiased results with symmetrical confidence intervals. Finally, we demonstrate the power of our estimator on the main world stock market indices. On the two separate periods of 2002-2005 and 2006-2009 we estimate the tail exponent.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: IES Working Paper ; No. 6/2010

Classification and Topics

• Classification: Wirtschaft ; Estimation: General ; Statistical Simulation Methods: General
• Subject: Hill estimator ; α-stable distributions ; tail exponent estimation ; Statistische Verteilung ; Schätztheorie ; Monte-Carlo-Methode

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Baruník, Jozef ; Vácha, Lukáš
• Event: Veröffentlichung
• (who): Charles University in Prague, Institute of Economic Studies (IES)
• (where): Prague
• (when): 2010

Further information

• Handle: http://hdl.handle.net/10419/83431
• Last update: 10.03.2025, 11:41 AM CET