Multifractal Dynamics of Stock Markets

• Authors: Ł. Czarnecki , D. Grech
• Languages of publication: EN

Abstracts

EN

We present a comparative analysis of multifractal properties of financial time series built on stock indices from developing (WIG) and developed (S&P500) financial markets. It is shown how the multifractal image of the market is altered with the change of the length of time series and with the economic situation on the market. We emphasize that the proper adjustment of scaling range for multiscaling power laws is essential to obtain the multifractal image of time series. We analyze in this paper multifractal properties of real financial time series using Hölder f(α) representation and multifractal-detrended fluctuation analysis method. It is also investigated how multifractal properties of stocks change with variety of "surgeries" done on the initial real financial time series. This way we reveal main phenomena on the market influencing its multifractal dynamics. In particular, we focus on examining how multifractal picture of real time series changes when one cuts off extreme events like crashes or rupture points, and how fluctuations around the main trend in time series influence the multifractal behavior of financial series in the long-time horizon for both developed and developing markets.

Keywords

EN

89.65.Gh; 89.75.Da; 89.20.-a

Discipline

• 89.20.-a: Interdisciplinary applications of physics
• 89.65.Gh: Economics; econophysics, financial markets, business and management(for economic issues regarding production and use of renewable energy, see 88.05.Lg)
• 89.75.Da: Systems obeying scaling laws

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2010
• Volume: 117
• Issue: 4
• Pages: 623-629

Dates

published

2010-04

Contributors

author

Ł. Czarnecki

• Institute of Theoretical Physics University of Wrocław, PL-50-204 Wrocław, Poland

author

D. Grech

• Institute of Theoretical Physics University of Wrocław, PL-50-204 Wrocław, Poland

References

• 1. J.W. Kantelhardt, arXiv: 0804.0747v1 [physics. data-an]
• 2. Z. Eisler, J. Kertész, Physica A 343, 603 (2004)
• 3. H.G.E. Hentschel, I. Procaccia, Physica D 8, 435 (1983)
• 4. T.C Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia, B.I. Shraiman, Phys. Rev. A 33, 1141 (1983)
• 5. P. Oświęcimka, J. Kwapień, S. Drożdż, A.Z. Górski, R. Rak, Acta Phys. Pol. A 114, 547 (2008)
• 6. J.W. Kantelhardt, E. Koscielny-Bunde, H.H.A. Rego, S. Havlin, A. Bunde, Physica A 295, 441 (2001)
• 7. C.-K. Peng, S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley, A.L. Golberger, Phys. Rev. E 49, 1685 (1994)
• 8. N. Vandewalle, M. Ausloos, Physica A 246, 454 (1997)
• 9. M. Ausloos, N. Vandewalle, Ph. Boveroux, A. Minguet, K. Ivanova, Physica A 274, 229 (1999)
• 10. G.M. Viswanathan, C.-K. Peng, H.E. Stanley, A.L. Goldberger, Phys. Rev. E 55, 845 (1997)
• 11. K. Hu, P. Ch. Ivanov, Z. Chen, P. Carpena, H.E. Stanley, Phys. Rev. E 64, 011114 (2001)
• 12. H.E. Hurst, Trans. Am. Soc. Civ. Eng. 116, 770 (1951)
• 13. B.B. Mandelbrot, J.R. Wallis, Water Resour. Res. 5, 321 (1969)
• 14. J.W. Kantelhardt, S.A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, H.E. Stanley, Physica A 316, 87 (2002)
• 15. P. Oświęcimka, J. Kwapień, S. Drożdż, A.Z. Górski, R. Rak, Acta Phys. Pol. B 36, 2447 (2005)
• 16. F. Feder, Fractals, Plenum Press, New York 1988
• 17. H.-O. Peitgen, H. Jürgens, D. Saupe, Chaos and Fractal, Springer, Berlin 2004
• 18. http://finance.yahoo.com/
• 19. http://gielda.wp.pl/
• 20. K. Ohashi, L.A.N Amaral, B.H. Natelson, Y. Yamamoto, Phys. Rev. E 68, 065204(R) (2003)
• 21. N.B. Ferreira, R. Menezes, D.A. Mendes, Physica A 382, 73 (2007)
• 22. R.H. Voss, Random fractal forgeries, in: Fundamental Algorithm for Computer Graphics, NATO ASI Series, Ed. R.A. Earnshaw, Vol. F17, Springer, Berlin 1985

Identifiers

DOI

10.12693/APhysPolA.117.623