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A comparative study of the applicability of the MF-DFA and the wavelet methods in the context of financial data

Paweł Oświęcimka 1Jarosław Kwapień 1Stanisław Drożdż 1,2

1. Polish Academy of Sciences, Institute of Nuclear Physics (IFJ PAN), Radzikowskiego 152, Kraków 31-342, Poland
2. University of Rzeszow, Institute of Physics, Rejtana 16, Rzeszów 35-310, Poland

Abstract

In recent years new tools have been developed in order to investigate multifractal properties of experimental and simulated data. One of them is based on the scaling behaviour of partition function calculated from the maxima of the wavelet transform coefficients. This method seems to be very useful for unfolding in the space-scale halfplane the hierarchical structure of fractal data. Another method proposed in this context is a multifractal generalization of the detrended fluctuation analysis (MF-DFA). Both methods are widely spread and commonly used for estimating the multifractal spectra of signals. We critically examine validity of each method if it is applied to high-frequency financial data and also compare the results obtained for some well-known mathematical multifractals.

 

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Presentation: oral at Symposium on Econo- and Sociophysics 2004, by Paweł Oświęcimka
See On-line Journal of Symposium on Econo- and Sociophysics 2004

Submitted: 2004-10-12 16:14
Revised:   2009-06-08 12:55