.Stat.M ech.(2009)P03037 ournal of Statistical Mechanics: An IOP and SISSA journalJ Theory and Experiment Cross-correlation of long-range

doi:10.1088/1742-5468/2009/03/P03037 Abstract. A method for estimating the cross-correlation Cxy(τ) of long-range correlated series x(t) and y(t), at varying lags τ and scales n, is proposed. For fractional Brownian motions with Hurst exponents H1 and H2, the asymptotic expression for Cxy(τ) depends only on the lag τ (wide-sense stationarity) and scales as a power of n with exponent H1 + H2 for τ → 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