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Market Efficiency, Roughness and Long Memory in the PSI20 Index Returns: Wavelet and Entropy Analysis

Listed author(s):
  • Rui Pascoal

    (Faculty of Economics, University of Coimbra, Portugal)

  • Ana Margarida Monteiro


    (GEMF/Faculty of Economics, University of Coimbra, Portugal)

In this study, features of financial returns of PSI20 index, related to market efficiency, are captured using wavelet and entropy based techniques. This characterization includes the following points. First, the detection of long memory, associated to low frequencies, and a global measure of the time series: the Hurst exponent estimated by several methods including wavelets. Second, the degree of roughness, or regularity variation, associated to the Hölder exponent, fractal dimension and estimation based on multifractal spectrum. Finally, the degree of the unpredictability of the series, estimated by approximate entropy. These aspects may also be studied through the concepts of non-extensive entropy and distribution using, for instance, the Tsallis q-triplet. They allow to study the existence of efficiency in the nancial market. On the other hand, the study of local roughness is performed by considering wavelet leaders based entropy. In fact, the wavelet coefficients are computed from a multiresolution analysis, and the wavelet leaders are defined by the local suprema of these coefficients, near the point we are considering. The resulting entropy is more accurate in that detection than the Hölder exponent. These procedures enhance the capacity to identify the occurrence of financial crashes.

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Paper provided by GEMF, Faculty of Economics, University of Coimbra in its series GEMF Working Papers with number 2013-27.

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Length: 32 pages
Date of creation: Dec 2013
Publication status: Published in Entropy 16: 2768-2788, 2014.
Handle: RePEc:gmf:wpaper:2013-27.
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  1. Tsallis, Constantino, 2004. "Dynamical scenario for nonextensive statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 1-10.
  2. Cortines, A.A.G. & Riera, R., 2007. "Non-extensive behavior of a stock market index at microscopic time scales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 181-192.
  3. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
  4. Ferri, G.L. & Reynoso Savio, M.F. & Plastino, A., 2010. "Tsallis’ q-triplet and the ozone layer," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1829-1833.
  5. Kristoufek, Ladislav & Vosvrda, Miloslav, 2013. "Measuring capital market efficiency: Global and local correlations structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 184-193.
  6. S. M.D. Queirós & L. G. Moyano & J. de Souza & C. Tsallis, 2007. "A nonextensive approach to the dynamics of financial observables," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(2), pages 161-167, 01.
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