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On non-Gaussianity and dependence in financial time series: a nonextensive approach

  • S. M. Duarte Queiros
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    In this article a probability density function and dependence degree analysis of financial time series, namely the Dow Jones and NYSE, is presented. The present study, which aims to give theoretical support to some stylized empirical evidence, is performed under the present non-extensive framework for which the probability distributions that optimize its fundamental information measure form,  [image omitted], are also the (stationary) solutions of a nonlinear Fokker-Plank equation. One determines the rescaled coefficient of the drift force and diffusion coefficient for both market indices and various aggregated times. Using a generalized form of Kullback-Leibler mutual information, Iq, one analyses the non-Gaussianity of returns using the dependence between stock market index values. The same mutual information form is used to determine the degree of dependence between returns. The analysis shows that this dependence can be considered independent from the time distance τ result that is connected with the long-range correlation in volatility.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697680500244403
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    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 5 (2005)
    Issue (Month): 5 ()
    Pages: 475-487

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    Handle: RePEc:taf:quantf:v:5:y:2005:i:5:p:475-487
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    1. Lisa Borland, 2002. "A theory of non-Gaussian option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 415-431.
    2. Duarte Queirós, Sı́lvio M., 2004. "On the connection between ARCH time series and non-extensive statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(3), pages 619-625.
    3. Kaushik Matia & Yosef Ashkenazy & H. Eugene Stanley, 2003. "Multifractal Properties of Price Fluctuations of Stocks and Commodities," Papers cond-mat/0308012, arXiv.org.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    5. Yanhui Liu & Pierre Cizeau & Martin Meyer & Chung-Kang Peng & H. Eugene Stanley, 1997. "Correlations in Economic Time Series," Papers cond-mat/9706021, arXiv.org.
    6. Pierre Cizeau & Yanhui Liu & Martin Meyer & C. -K. Peng & H. Eugene Stanley, 1997. "Volatility distribution in the S&P500 Stock Index," Papers cond-mat/9708143, arXiv.org.
    7. Lisa Borland, 2002. "Option Pricing Formulas based on a non-Gaussian Stock Price Model," Papers cond-mat/0204331, arXiv.org, revised Sep 2002.
    8. Silvio M. Duarte Queiros, 2004. "On anomalous distributions in intra-day financial time series and Non-extensive Statistical Mechanics," Papers cond-mat/0403624, arXiv.org.
    9. Tsallis, Constantino & Anteneodo, Celia & Borland, Lisa & Osorio, Roberto, 2003. "Nonextensive statistical mechanics and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 89-100.
    10. Marc Potters & Rama Cont & Jean-Philippe Bouchaud, 1996. "Financial markets as adaptative systems," Science & Finance (CFM) working paper archive 500037, Science & Finance, Capital Fund Management.
    11. 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.
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    13. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    14. Liu, Yanhui & Cizeau, Pierre & Meyer, Martin & Peng, C.-K. & Eugene Stanley, H., 1997. "Correlations in economic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 437-440.
    15. J. Doyne Farmer, 1999. "Physicists Attempt to Scale the Ivory Towers of Finance," Working Papers 99-10-073, Santa Fe Institute.
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