  Many complex systems generate multifractal time series which are long-range
cross-correlated. Numerous methods have been proposed to characterize the
multifractal nature of these long-range cross correlations. However, several
important issues about these methods are not well understood and most methods
consider only one moment order. We study the joint multifractal analysis based
on partition function with two moment orders, which was initially invented to
investigate fluid fields, and derive analytically several important properties.
We apply the method numerically to binomial measures with multifractal cross
correlations and bivariate fractional Brownian motions without multifractal
cross correlations. For binomial multifractal measures, the explicit
expressions of mass function, singularity strength and multifractal spectrum of
the cross correlations are derived, which agree excellently with the numerical
results. We also apply the method to stock market indexes and unveil intriguing
multifractality in the cross correlations of index volatilities.
