Joint multifractal analysis based on wavelet leaders

Mutually interacting components form complex systems and these components usually have long- range cross-correlated outputs. Using wavelet leaders, we propose a method for characterizing the joint multifractal nature of these long-range cross correlations; we call this method joint multifractal analysis based on wavelet leaders （MF-X-WL）. We test the validity of tile MF-X-WL method by performing extensive numerical experiments on dual binomial measures with multifractal cross correlations and bivariate fractional Brownian motions （bFBMs） with monofractal cross correlations. Both experiments indicate that MF-X-WL is capable of detecting cross correlations in synthetic data with acceptable estimating errors. We also apply the MF-X-WL method to pairs of series from financial markets （returns and volatilities） and online worlds （online numbers of different genders and different societies） and determine intriguing joint multifractal behavior.