Cross-correlation of long-range correlated series

Abstract

A method for estimating the cross-correlation C xy (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 H 1 and H 2 , the asymptotic expression for C xy (τ) depends only on the lag τ (wide-sense stationarity) and scales as a power of n with exponent H 1 + H 2 for . 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.

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