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Generalized entropy approach to stable Lèvy distributions with financial application

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  • Matsuba, Ikuo
  • Takahashi, Hiroshi

Abstract

Employing the generalized entropy introduced by Tsallis, we propose a new method to estimate the scaling index of the stable Lèvy distribution. We investigate the scaling behavior of the daily Nikkei average sampled from January 1991 to December 2000 for the time intervals up to 75 days from two aspects, self-similarity of the distribution and long-range dependence in the autocorrelation function. It is found that the theoretically estimated scaling index μ∗=1.59 and Hurst exponent H∗=0.629 agree well with μ=1.50 and H=0.617 obtained from the measured data, respectively, suggesting the usefulness and fitness of the present method.

Suggested Citation

  • Matsuba, Ikuo & Takahashi, Hiroshi, 2003. "Generalized entropy approach to stable Lèvy distributions with financial application," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 458-468.
    • Handle: RePEc:eee:phsmap:v:319:y:2003:i:c:p:458-468
    DOI: 10.1016/S0378-4371(02)01451-6
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    References listed on IDEAS

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    1. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
    2. Crato, Nuno & de Lima, Pedro J. F., 1994. "Long-range dependence in the conditional variance of stock returns," Economics Letters, Elsevier, vol. 45(3), pages 281-285.
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    Cited by:

    1. Annibal Figueiredo & Iram Gleria & Raul Matsushita & Sergio Da Silva, 2004. "On the origins of truncated Lévy flights," Finance 0404013, University Library of Munich, Germany.
    2. 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.

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