Crossing of two mobile averages: A method for measuring the roughness exponent

Abstract

Self-affine signals characterized by a defined Hurst (roughness) exponent H can be investigated through mobile averages. The density \ensuremath{\rho} of crossing points between any two moving averages is a measure of long-range power-law correlations in the signal. The method is compared to the detrended fluctuation analysis. We take advantage of our findings in order to propose a practically powerful and accurate technique for determining H and apply it right away to cases with persistent or antipersistent correlations.