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Monte Carlo-Based Tail Exponent Estimator
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SYSNO ASEP 0342493 Document Type J - Journal Article R&D Document Type The record was not marked in the RIV Subsidiary J Ostatní články Title Monte Carlo-Based Tail Exponent Estimator Author(s) Baruník, Jozef (UTIA-B) RID, ORCID
Vácha, Lukáš (UTIA-B) RIDSource Title IES Working Paper
Roč. 2010, č. 6 (2010), s. 1-26Number of pages 26 s. Language eng - English Country CZ - Czech Republic Keywords Hill estimator ; α-stable distributions ; tail exponent estimation Subject RIV AH - Economics R&D Projects GA402/09/0965 GA ČR - Czech Science Foundation (CSF) GD402/09/H045 GA ČR - Czech Science Foundation (CSF) GP402/08/P207 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10750506 - UTIA-B (2005-2011) Annotation 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 con_dence 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2011
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