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Scaling, stability and distribution of the high-frequency returns of the Ibex35 index

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  • Suárez-García, Pablo
  • Gómez-Ullate, David

Abstract

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 Lévy-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 Generalized Hyperbolic distributions and certainly much better than the Lévy-stable laws. Furthermore, the right (resp. left) tail of the distribution seems to follow a power-law with exponent α≈4.60 (resp. α≈4.28). Finally, we present evidence that the observed stability is due to temporal correlations or non-stationarities of the data.

Suggested Citation

  • Suárez-García, Pablo & Gómez-Ullate, David, 2013. "Scaling, stability and distribution of the high-frequency returns of the Ibex35 index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1409-1417.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:6:p:1409-1417
    DOI: 10.1016/j.physa.2012.11.026
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    Cited by:

    1. Pablo Su'arez-Garc'ia & David G'omez-Ullate, 2013. "Multifractality and long memory of a financial index," Papers 1306.0490, arXiv.org.
    2. Shaw, Charles, 2018. "Regime-Switching And Levy Jump Dynamics In Option-Adjusted Spreads," MPRA Paper 94154, University Library of Munich, Germany, revised 27 May 2019.
    3. Suárez-García, Pablo & Gómez-Ullate, David, 2014. "Multifractality and long memory of a financial index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 226-234.
    4. Charles Shaw, 2022. "Portfolio Diversification Revisited," Papers 2204.13398, arXiv.org.

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