Monte Carlo-based tail exponent estimator
AbstractIn this paper we propose a new approach to estimation of the tail exponent in financial stock markets. We begin the study with 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 proposed method is not sensitive to the choice of tail size and works well also on small data samples. The new estimator also gives unbiased results with symmetrical confidence intervals. Finally, we demonstrate the power of our estimator on the international world stock market indices. On the two separate periods of 2002–2005 and 2006–2009, we estimate the tail exponent.
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Bibliographic InfoArticle provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.
Volume (Year): 389 (2010)
Issue (Month): 21 ()
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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/
Hill estimator; α-stable distributions; Tail exponent estimation;
Other versions of this item:
- Jozef Barunik & Lukas Vacha, 2012. "Monte Carlo-based tail exponent estimator," Papers 1201.4781, arXiv.org.
- Jozef Barunik & Lukas Vacha, 2010. "Monte Carlo-Based Tail Exponent Estimator," Working Papers IES 2010/06, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Apr 2010.
- C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- G0 - Financial Economics - - General
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