Politická ekonomie 2012, 60(2):208-221 | DOI: 10.18267/j.polek.838

Efektivita kapitálových trhů: fraktální dimenze, Hurstův exponent a entropie

Ladislav Krištoufek, Miloslav Vošvrda
Ústav teorie informace a automatizace, AV ČR, v.v.i., Institut ekonomických studií FSV UK.

Capital Markets Efficiency: Fractal Dimension, Hurst Exponent and Entropy

In this paper, we introduce a new measure of capital market efficiency. For its construction, we use the approaches of fractal dimension, Hurst exponent and entropy. The method is applied on 41 stock indices from the beginning of 2000 till the end of August 2011 and interesting results are found ? the analyzed indices are not self-affine; for the majority of indices, the deviation from the efficient market is dominated by local inefficiencies; and the most efficient capital markets are the stock indices of the most developed countries (FTSE, SPX, NIKKEI and DAX).

Keywords: capital markets efficiency, fractal dimension, long-range, dependence, entropy
JEL classification: G14, G15

Published: April 1, 2012  Show citation

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Krištoufek, L., & Vošvrda, M. (2012). Capital Markets Efficiency: Fractal Dimension, Hurst Exponent and Entropy. Politická ekonomie60(2), 208-221. doi: 10.18267/j.polek.838
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References

  1. ALESSIO, E.; CARBONE, A.; CASTELLI, G.; FRAPPIETRO, V. 2002. Second-Order Moving Average and Scaling of Stochastic Time Series. European Physical Journal B. 2002, Vol. 27, No. 2, pp. 197-200 Go to original source...
  2. BARABASI, A.; SZEPFALUSY, P.; VICSEK, T. 1991. Multifractal Spectra of Multi-Affine Functions. Physica A. 1991, Vol. 178, pp. 17-28 Go to original source...
  3. BARUNÍK, J.; KRIŠTOUFEK, L. 2010. On Hurst Exponent Estimation under Heavy-Tailed Distributions. Physica A. 2010, Vol. 389, pp. 3844-3855 Go to original source...
  4. CAJUEIRO, D.; TABAK, B. 2007. Long-Range Dependence and Multifractality in the Term Structure of LIBOR Interest Rates. Physica A. 2007, Vol. 373, pp. 603-617 Go to original source...
  5. CARBONE, A.; CASTELLI, G.; STANLEY, H. E. 2004. Time-Dependent Hurst Exponent in Financial Time Series. Physica A. 2004, Vol. 344, pp. 267-271 Go to original source...
  6. COSTA, U.; LYRA, M.; PLASTINO, A.; TSALLIS, C. 1997. Power-Law Sensitivity to Initial Conditions within a Logisticlike Family of Maps: Fractality and Nonextensivity. Physical Review E. 1997, Vol. 56, pp. 245-250 Go to original source...
  7. DI MATTEO, T. 2007. Multi-Scaling in Finance. Quantitative Finance. 2007, Vol. 7, No. 1, pp. 21-36 Go to original source...
  8. FAMA, E. 1970. Efficient Capital Markets: A Review of Theory and Empirical Work. Journal of Finance. 1970, Vol. 25, No. 2, pp. 383-417 Go to original source...
  9. FAMA., E. 1991. Efficient Capital Markets: II. Journal of Finance. 1991, Vol. 46, No. 5, pp. 1575-1617. Go to original source...
  10. GNEITING, T.; SCHLATHER, M. 2004. Stochastic Models that Separate Fractal Dimension and the Hurst Effect. SIAM Review. 2004, Vol. 46, No. 2, pp. 269-282 Go to original source...
  11. HURST, E. 1951. Long-Term Storage Capacity of Reservoirs. Transactions of American Society of Civil Engineering. 1951, Vol. 116, pp. 770-808 Go to original source...
  12. KANTELHARDT, J.; ZSCHIEGNER, S.; KOSCIELNY-BUNDE, E.; HAVLIN, S. BUNDE, A.; STANLEY, H. E. 2002. Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series. Physica A. 2002, Vol. 316, pp. 87-114 Go to original source...
  13. KRIŠTOUFEK, L. 2010a. Dlouhá paměť a její vývoj ve výnosech burzovního indexu PX v letech 1997-2009. Politická ekonomie, 2010, Vol. 58, No. 4, pp. 471-487 Go to original source...
  14. KRIŠTOUFEK, L. 2010b. Rescaled Range Analysis and Detrended Fluctuation Analysis: Finite Sample Properties and Confidence Intervals. AUCO Czech Economic Review. 2010, Vol. 4, No. 3, pp. 315-330
  15. LYRA, M.; TSALLIS, C. 1998. Nonextensivity and Multifractality in Low-Dimensional Dissipative Systems. Physical Review Letters. 1998, Vol. 80, pp. 53-56 Go to original source...
  16. MALKIEL, B. 2003. The Efficient Market Hypothesis and Its Critics. Journal of Economic Perspectives. 2003, Vol. 17, No. 1, pp. 59-82 Go to original source...
  17. MANDELBROT, B.; van NESS, J. 1968. Fractional Brownian Motions, Fractional Noises and Applications. SIAM Review. 1968, Vol. 10, No. 4, pp. 422-437 Go to original source...
  18. PENG, C.; BULDYREV, S.; HAVLIN, S.; SIMONS, M.; STANLEY, H. E.; GOLDBERGER, A. 1994. Mosaic Organization of DNA Nucleotides. Physical Review E. 1994, Vol. 49, pp. 1685-1689 Go to original source...
  19. PETERS, E. 1994. Fractal Market Analysis: Applying Chaos Theory to Investment and Economics. John Wiley and Sons, New York, 1994, 315 p. ISBN 0-471-58524-6.
  20. TSALLIS, C.; PLASTINO, A.; ZHENG, W. 1997. Power-Law Sensitivity to Initial Conditions - New Entropic Representation. Chaos, Solitons & Fractals. 1997, Vol. 8, No. 6, pp. 885-891 Go to original source...
  21. VANDEWALLE, N.; AUSLOOS, M.; BOVEROUX, P. 1997. Detrended Fluctuation Analysis of the Foreign Exchange Market. Econophysics Workshop 1997. 1997, pp. 36-49
  22. WERON, R. 2002. Estimating Long-Range Dependence: Finite Sample Properties and Confidence Intervals. Physica A. 2002, Vol. 312, pp. 285-299. Go to original source...

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