Cross-correlation of long-range correlated series

Abstract

A method for estimating the cross-correlation $C_{xy}(\tau )$ 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 of $C_{xy}(\tau )$ depends only on the lag $\tau$ (wide-sense stationarity) and scales as a power of $n$ with exponent $H_1+H_2$ for $\tau \to 0$. 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.

14 pages, 8 figures

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