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Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime

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  • Rafal Weron

Abstract

Power-law tail behavior and the summation scheme of Levy-stable distributions is the basis for their frequent use as models when fat tails above a Gaussian distribution are observed. However, recent studies suggest that financial asset returns exhibit tail exponents well above the Levy-stable regime (0

Suggested Citation

  • Rafal Weron, 2001. "Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime," HSC Research Reports HSC/01/01, Hugo Steinhaus Center, Wroclaw University of Technology.
  • Handle: RePEc:wuu:wpaper:hsc0101
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    File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_01_01.pdf
    File Function: Final draft, 2001
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    References listed on IDEAS

    as
    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
    2. Weron, Rafal, 1996. "Correction to: "On the Chambers–Mallows–Stuck Method for Simulating Skewed Stable Random Variables"," MPRA Paper 20761, University Library of Munich, Germany, revised 2010.
    3. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Fernández-Martínez, M. & Sánchez-Granero, M.A. & Trinidad Segovia, J.E., 2013. "Measuring the self-similarity exponent in Lévy stable processes of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5330-5345.
    2. Barunik, Jozef & Vacha, Lukas, 2010. "Monte Carlo-based tail exponent estimator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4863-4874.
    3. Broda, Simon A. & Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Stable mixture GARCH models," Journal of Econometrics, Elsevier, vol. 172(2), pages 292-306.
    4. Scalas, Enrico & Kim, Kyungsik, 2006. "The art of fitting financial time series with Levy stable distributions," MPRA Paper 336, University Library of Munich, Germany.
    5. Nuyts, Jean & Platten, Isabelle, 2001. "Phenomenology of the term structure of interest rates with Padé Approximants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(3), pages 528-546.
    6. Giulio Bottazzi & Davide Pirino & Federico Tamagni, 2015. "Zipf law and the firm size distribution: a critical discussion of popular estimators," Journal of Evolutionary Economics, Springer, vol. 25(3), pages 585-610, July.
    7. Steinbacher, Matjaz, 2009. "Acceptable Risk in a Portfolio Analysis," MPRA Paper 13569, University Library of Munich, Germany.
    8. repec:gam:jecnmx:v:4:y:2016:i:2:p:25:d:69492 is not listed on IDEAS
    9. Thomas Alderweireld & Jean Nuyts, 2003. "Term Structure of Interest Rates. Emergence of Power Laws and Scaling Laws," EERI Research Paper Series EERI_RP_2003_05, Economics and Econometrics Research Institute (EERI), Brussels.
    10. Figueiredo, Annibal & Gleria, Iram & Matsushita, Raul & Da Silva, Sergio, 2005. "Financial volatility and independent and identically distributed variables," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(3), pages 484-498.
    11. Thomas Alderweireld & Jean Nuyts, 2003. "Term Structure of Interest Rates.Emergence of Power Laws and Scaling Laws," Econometrics 0306001, EconWPA.
    12. repec:gam:jjrfmx:v:11:y:2018:i:2:p:30-:d:151623 is not listed on IDEAS
    13. Adam Misiorek & Rafal Weron, 2010. "Heavy-tailed distributions in VaR calculations," HSC Research Reports HSC/10/05, Hugo Steinhaus Center, Wroclaw University of Technology.
    14. Marc S. Paolella, 2016. "Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability," Econometrics, MDPI, Open Access Journal, vol. 4(2), pages 1-28, May.
    15. Tabak, B.M. & Takami, M.Y. & Cajueiro, D.O. & Petitinga, A., 2009. "Quantifying price fluctuations in the Brazilian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(1), pages 59-62.
    16. Antypas, Antonios & Koundouri, Phoebe & Kourogenis, Nikolaos, 2013. "Aggregational Gaussianity and barely infinite variance in financial returns," Journal of Empirical Finance, Elsevier, vol. 20(C), pages 102-108.
    17. Raul Matsushita & Iram Gleria & Annibal Figueiredo & Sergio Da Silva, 2004. "The Econophysics of the Brazilian Real-US Dollar Rate," Finance 0407012, EconWPA.
    18. Figueiredo, Annibal & Gleria, Iram & Matsushita, Raul & Da Silva, Sergio, 2004. "Lévy flights, autocorrelation, and slow convergence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(3), pages 369-383.
    19. Szymon Borak & Adam Misiorek & Rafał Weron, 2010. "Models for Heavy-tailed Asset Returns," SFB 649 Discussion Papers SFB649DP2010-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    20. Kenneth Bruninx & Erik Delarue & William D'haeseleer, 2013. "Statistical description of the error on wind power forecasts via a Lévy α-stable distribution," RSCAS Working Papers 2013/50, European University Institute.
    21. Ko, Bonggyun & Kim, Kyungwon, 2017. "Simulation of sovereign CDS market based on interaction between market participant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 324-340.
    22. Gerardo-Giorda, Luca & Germano, Guido & Scalas, Enrico, 2015. "Large scale simulation of synthetic markets," LSE Research Online Documents on Economics 67563, London School of Economics and Political Science, LSE Library.
    23. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    24. Salhi, Khaled & Deaconu, Madalina & Lejay, Antoine & Champagnat, Nicolas & Navet, Nicolas, 2016. "Regime switching model for financial data: Empirical risk analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 148-157.
    25. repec:eee:phsmap:v:486:y:2017:i:c:p:628-637 is not listed on IDEAS

    More about this item

    Keywords

    Levy-stable distribution; Alpha-stable distribution; Tail exponent; Hill estimator;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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