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 ρ_DCCA 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 ρ_q to be more discriminative in respect to the fluctuation amplitudes. We present application of ρ_q 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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