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Different fractal properties of positive and negative returns

Author

Listed:
  • P. Oswiecimka
  • J. Kwapien
  • S. Drozdz
  • A. Z. Gorski
  • R. Rak

Abstract

We perform an analysis of fractal properties of the positive and the negative changes of the German DAX30 index separately using Multifractal Detrended Fluctuation Analysis (MFDFA). By calculating the singularity spectra $f(\alpha)$ we show that returns of both signs reveal multiscaling. Curiously, these spectra display a significant difference in the scaling properties of returns with opposite sign. The negative price changes are ruled by stronger temporal correlations than the positive ones, what is manifested by larger values of the corresponding H\"{o}lder exponents. As regards the properties of dominant trends, a bear market is more persistent than the bull market irrespective of the sign of fluctuations.

Suggested Citation

  • P. Oswiecimka & J. Kwapien & S. Drozdz & A. Z. Gorski & R. Rak, 2008. "Different fractal properties of positive and negative returns," Papers 0803.1374, arXiv.org.
    • Handle: RePEc:arx:papers:0803.1374
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    Cited by:

    1. Argyroudis, G. & Siokis, F., 2018. "The complexity of the HANG SENG Index and its constituencies during the 2007–2008 Great Recession," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 463-474.
    2. El Alaoui, Marwane & Benbachir, Saâd, 2013. "Multifractal detrended cross-correlation analysis in the MENA area," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5985-5993.
    3. El Alaoui, Marwane, 2017. "Price–volume multifractal analysis of the Moroccan stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 473-485.
    4. Ghosh, Koushik & Basu, Tapasendra, 2015. "Search for the periodicity of the prime Indian and American stock exchange indices using date-compensated discrete Fourier transformAuthor-Name: Samadder, Swetadri," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 149-157.
    5. Wang, Yudong & Wei, Yu & Wu, Chongfeng, 2011. "Analysis of the efficiency and multifractality of gold markets based on multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 817-827.
    6. Benbachir, Saâd & El Alaoui, Marwane, 2011. "A Multifractal Detrended Fluctuation Analysis of the Moroccan Stock Exchange," MPRA Paper 49003, University Library of Munich, Germany.
    7. Siokis, Fotios M., 2014. "European economies in crisis: A multifractal analysis of disruptive economic events and the effects of financial assistance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 283-292.

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