Cross-correlation of long-range correlated series

A method for estimating the cross-correlation C-xy(t) of long-range correlated series x(t) and y(t), at varying lags tau and scales n, is proposed. For fractional Brownian motions with Hurst exponents H-1 and H-2, the asymptotic expression for C-xy(t) depends only on the lag tau (wide-sense stationarity) and scales as a power of n with exponent H-1 + H-2 for tau -> 0. The method is illustrated on: (i) financial series, to show the leverage effect; (ii) genomic sequences, to estimate the correlations between structural parameters along the chromosomes.