Second-order moving average and scaling of stochastic time series

Long-range correlation properties of stochastic time series y(i) have been investigated by introducing the function sigma(MA)(2) = 1/N(max-n) Sigma(i=n)(Nmax) [y(i) - (y) over tilde (n)(i)](2), where (y) over tilde (i) is the moving average of y(i), defined as 1/n Sigma(k=0)(n-1) y(i - k), n the moving average window and N(max) is the dimension of the stochastic series. It is shown that, using an appropriate computational procedure, the function sigma(MA) varies as n(H) where H is the Hurst exponent of the series. A comparison of the power-law exponents obtained using respectively the function sigma(MA) and the Detrended Fluctuation Analysis has been also carried out. Interesting features denoting the existence of a relationship between the scaling properties of the noisy process and the moving average filtering technique have been evidenced.