Detecting and quantifying cross-correlations by analogous multifractal height cross-correlation analysis

A new algorithm, analogous multifractal height cross-correlation analysis (AMF-HXA), is proposed in this paper. Our novel method takes into consideration of both the fluctuation information and the sign information in the corresponding cross-covariance function. Numerical tests on artificially simulated series and real world series are performed to demonstrate that our method can accurately detect long-range cross-correlations for two simultaneously recorded series. A new cross-correlation coefficient is also defined to quantify the levels of cross-correlation between two series.