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Multifractality and long memory of a financial index

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

Abstract

In this paper we will try to assess the multifractality displayed by the high-frequency returns of Madrid’s Stock Exchange Ibex35 index. A Multifractal Detrended Fluctuation Analysis shows that this index has a wide singularity spectrum which is most likely caused by its long-memory. Our findings also show that this long-memory can be considered as the superposition of a high-frequency component–related to the daily cycles of arrival of information to the market–over a slowly-varying component that reverberates for long periods of time and which shows no apparent relation with human/economic cycles. This latter component is therefore postulated to be endogenous to market’s dynamics and to be also the most probable source of some of the stylized facts commonly associated with financial time-series.

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  • 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.
  • Handle: RePEc:eee:phsmap:v:394:y:2014:i:c:p:226-234
    DOI: 10.1016/j.physa.2013.09.038
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    as
    1. Turiel, Antonio & Pérez-Vicente, Conrad J., 2003. "Multifractal geometry in stock market time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 629-649.
    2. Thomas Lux, 2003. "The Multi-Fractal Model of Asset Returns:Its Estimation via GMM and Its Use for Volatility Forecasting," Computing in Economics and Finance 2003 14, Society for Computational Economics.
    3. Laurent Calvet & Adlai Fisher, 2002. "Multifractality In Asset Returns: Theory And Evidence," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 381-406, August.
    4. Wei-Xing Zhou, 2009. "The components of empirical multifractality in financial returns," Papers 0908.1089, arXiv.org, revised Oct 2009.
    5. 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.
    6. Wang, Dong-Hua & Yu, Xiao-Wen & Suo, Yuan-Yuan, 2012. "Statistical properties of the yuan exchange rate index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3503-3512.
    7. Wang, Hui & Xiang, Luojie & Pandey, R.B., 2012. "A multifractal detrended fluctuation analysis (MDFA) of the Chinese growth enterprise market (GEM)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3496-3502.
    8. Norouzzadeh, P. & Dullaert, W. & Rahmani, B., 2007. "Anti-correlation and multifractal features of Spain electricity spot market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 333-342.
    9. Petre Caraiani, 2012. "Evidence of Multifractality from Emerging European Stock Markets," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-9, July.
    10. Ausloos, M., 2012. "Measuring complexity with multifractals in texts. Translation effects," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1349-1357.
    11. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-436, June.
    12. Stanley, H.E. & Amaral, L.A.N. & Goldberger, A.L. & Havlin, S. & Ivanov, P.Ch. & Peng, C.-K., 1999. "Statistical physics and physiology: Monofractal and multifractal approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(1), pages 309-324.
    13. Eisler, Z. & Kertész, J., 2004. "Multifractal model of asset returns with leverage effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 603-622.
    14. B. B. Mandelbrot, 2001. "Scaling in financial prices: III. Cartoon Brownian motions in multifractal time," Quantitative Finance, Taylor & Francis Journals, vol. 1(4), pages 427-440.
    15. 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.
    16. Xu, Zhaoxia & Gençay, Ramazan, 2003. "Scaling, self-similarity and multifractality in FX markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 578-590.
    17. McCulloch, J Huston, 1997. "Measuring Tail Thickness to Estimate the Stable Index Alpha: A Critique," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 74-81, January.
    18. Norouzzadeh, P. & Rahmani, B., 2006. "A multifractal detrended fluctuation description of Iranian rial–US dollar exchange rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 328-336.
    19. Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1997. "Large Deviations and the Distribution of Price Changes," Cowles Foundation Discussion Papers 1165, Cowles Foundation for Research in Economics, Yale University.
    20. Zoltan Eisler & Janos Kertesz, 2004. "Multifractal model of asset returns with leverage effect," Papers cond-mat/0403767, arXiv.org, revised May 2004.
    21. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    22. Ivanova, K. & Shirer, H.N. & Clothiaux, E.E. & Kitova, N. & Mikhalev, M.A. & Ackerman, T.P. & Ausloos, M., 2002. "A case study of stratus cloud base height multifractal fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 308(1), pages 518-532.
    23. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    24. Adlai Fisher & Laurent Calvet & Benoit Mandelbrot, 1997. "Multifractality of Deutschemark/US Dollar Exchange Rates," Cowles Foundation Discussion Papers 1166, Cowles Foundation for Research in Economics, Yale University.
    25. Kantelhardt, Jan W & Koscielny-Bunde, Eva & Rego, Henio H.A & Havlin, Shlomo & Bunde, Armin, 2001. "Detecting long-range correlations with detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 441-454.
    26. Arneodo, A. & Audit, B. & Bacry, E. & Manneville, S. & Muzy, J.F. & Roux, S.G., 1998. "Thermodynamics of fractal signals based on wavelet analysis: application to fully developed turbulence data and DNA sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 254(1), pages 24-45.
    27. Wei-Xing Zhou, 2008. "Multifractal detrended cross-correlation analysis for two nonstationary signals," Papers 0803.2773, arXiv.org.
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