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Scaling, stability and distribution of the high-frequency returns of the IBEX35 index

  • Pablo Su\'arez-Garc\'ia
  • David G\'omez-Ullate
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    In this paper we perform a statistical analysis of the high-frequency returns of the IBEX35 Madrid stock exchange index. We find that its probability distribution seems to be stable over different time scales, a stylized fact observed in many different financial time series. However, an in-depth analysis of the data using maximum likelihood estimation and different goodness-of-fit tests rejects the L\'evy-stable law as a plausible underlying probabilistic model. The analysis shows that the Normal Inverse Gaussian distribution provides an overall fit for the data better than any of the other subclasses of the family of the Generalized Hyperbolic distributions and certainly much better than the L\'evy-stable laws. Furthermore, the right (resp. left) tail of the distribution seems to follow a power-law with exponent \alpha=4.60 (resp. \alpha =4.28). Finally, we present evidence that the observed stability is due to temporal correlations or non-stationarities of the data.

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    File URL: http://arxiv.org/pdf/1208.0317
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    Paper provided by arXiv.org in its series Papers with number 1208.0317.

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    Date of creation: Aug 2012
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    Publication status: Published in Physica A, 392(6) 2013 1409 -1417
    Handle: RePEc:arx:papers:1208.0317
    Contact details of provider: Web page: http://arxiv.org/

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    1. Eckhard Platen & Renata Rendek, 2007. "Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices," Research Paper Series 194, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-24, October.
    3. Skjeltorp, Johannes A, 2000. "Scaling in the Norwegian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(3), pages 486-528.
    4. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    6. Weron, Rafa┼é, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt-Universit├Ąt Berlin, Center for Applied Statistics and Economics (CASE).
    7. Y. Malevergne & V. Pisarenko & D. Sornette, 2005. "Empirical distributions of stock returns: between the stretched exponential and the power law?," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 379-401.
    8. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-80, April.
    9. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    10. Burnecki, Krzysztof & Gajda, Janusz & Sikora, Grzegorz, 2011. "Stability and lack of memory of the returns of the Hang Seng index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(18), pages 3136-3146.
    11. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
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