The generalized detrended cross-correlation coefficient ρq and its application to financial data.

Jarosław Kwapień 1Stanisław Drożdż 1,2Paweł Oświęcimka 1Rafał Rak 3

1. Polish Academy of Sciences, Institute of Nuclear Physics (IFJ PAN), Radzikowskiego 152, Kraków 31-342, Poland
2. Cracow University of Technology, Institute of Computing Science, Al. Jana Pawła II 37, Kraków 31-864, Poland
3. Faculty of Mathematics and Natural Sciences, University of Rzeszów, Rzeszów 35-959, Poland

Abstract

We propose a generalization of the detrended cross-correlation coefficient rho_DCCA introduced in ref. [1] that measures cross-correlations between the detrended fluctuations of two signals on different temporal scales by using the detrended cross-correlation and detrended fluctuation analyses (DCCA [2] and DFA [3], respectively). A rationale behind our work is that the ρDCCA coefficient performs well in many practical situations but its applicability is limited to detection of whether two signals are generally cross-correlated on different scales without possibility to obtain any information on the amplitude of the fluctuations involved in producing these cross-correlations. Our approach adds the related power to this measure by replacing the DCCA and DFA algorithms with their multifractal counterparts: MFCCA [4] and MFDFA [5], thus allowing the new, q-dependent coefficient ρq to be more discriminative in respect to the fluctuation amplitudes. We present application of ρq to time series produced by certain stochastic processes originated in financial market analysis and discuss its advantages over the standard rho_DCCA. Then we analyze selected empirical financial data and show the results. As a side-product of this analysis, we present arguments that oblige us to advocate the MFCCA algorithm as a superior one to the other variants of the multifractal extensions of DCCA known from literature.

[1] G.F. Zebende, Physica A 390, 614 (2011).
[2] B. Podobnik et al., Phys. Rev. Lett. 100, 084102 (2008).
[3] C.-K. Peng et al., Phys. Rev. E 49, 1685 (1994).
[4] P. Oświęcimka et al., Phys. Rev. E 89, 023305 (2014).
[5] J.W. Kantelhardt et al., Physica A 316, 87 (2002).

 

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Presentation: Invited oral at 8 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych", by Jarosław Kwapień
See On-line Journal of 8 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych"

Submitted: 2015-08-26 17:48
Revised:   2015-08-26 17:48