Different Fractal Properties of Positive and Negative Returns

P. Oświęcimka a, J. Kwapień a, A.Z. Górski a, S. Drożdż a, b and R. Rak b a Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, PL-31-342 Kraków, Poland b Institute of Physics, University of Rzeszów, PL-35-310 Rzeszów, Poland

Full Text PDF

Received: 22 11 2007;

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. By calculating the singularity spectra f(α) 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, which is manifested by larger values of the corresponding Hölder exponents. As regards the properties of dominant trends, a bear market is more persistent than the bull market irrespective of the sign of fluctuations.

DOI: 10.12693/APhysPolA.114.547 PACS numbers: 89.20.-a, 89.65.Gh