Minimum spanning tree filtering of correlations for varying time scales and size of fluctuations.

Based on a recently proposed q-dependent detrended cross-correlation coefficient, ρ_{q} [J. Kwapień, P. Oświęcimka, and S.

Detrended cross-correlation analysis consistently extended to multifractality.

We propose an algorithm, multifractal cross-correlation analysis (MFCCA), which constitutes a consistent extension of the detrended cross-correlation analysis and is able to properly identify and quantify subtle characteristics of multifractal cross-correlations between two time series. Our motivation for introducing this algorithm is that the already existing methods, like multifractal extension, have at best serious limitations for most of the signals describing complex natural processes and often indicate multifractal cross-correlations when there are none. The principal component of the present extension is proper incorporation of the sign of fluctuations to their generalized moments.