  Complex systems are composed of mutually interacting components and the
output values of these components are usually long-range cross-correlated. We
propose a method to characterize the joint multifractal nature of such
long-range cross correlations based on wavelet analysis, termed multifractal
cross wavelet analysis (MFXWT). We assess the performance of the MFXWT method
by performing extensive numerical experiments on the dual binomial measures
with multifractal cross correlations and the bivariate fractional Brownian
motions (bFBMs) with monofractal cross correlations. For binomial multifractal
measures, the empirical joint multifractality of MFXWT is found to be in
approximate agreement with the theoretical formula. For bFBMs, MFXWT may
provide spurious multifractality because of the wide spanning range of the
multifractal spectrum. We also apply the MFXWT method to stock market indexes
and uncover intriguing joint multifractal nature in pairs of index returns and
volatilities.
