Effect of noise on fractal structure

In this paper, I investigate the effect of dynamical noise on the estimation of the Hurst exponent and the fractal dimension of time series. Recently, Serletis et al. [Serletis, Apostolos, Asghar Shahmoradi, Demitre Serletis. Effect of noise on estimation of Lyapunov exponents from a time series. Chaos, Solitons & Fractals, forthcoming] have shown that dynamical noise can make the detection of chaotic dynamics very difficult, and Serletis et al. [Serletis, Apostolos, Asghar Shahmoradi, Demitre Serletis. Effect of noise on the bifurcation behavior of dynamical systems. Chaos, Solitons & Fractals, forthcoming] have shown that dynamical noise can also shift bifurcation points and produce noise-induced transitions, making the determination of bifurcation boundaries difficult. Here I apply the detrending moving average (DMA) method, recently developed by Alessio et al. [Alessio E, Carbone A, Castelli G, Frappietro V. Second-order moving average and scaling of stochastic time series. The Eur Phys J B 2002;27:197–200] and Carbone et al. [Carbone A, Castelli G, Stanley HE. Time-dependent Hurst exponent in financial time series. Physica A 2004;344:267–71; Carbone A, Castelli G, Stanley HE. Analysis of clusters formed by the moving average of a long-range correlated time series. Phys Rev E 2004;69:026105], to estimate the Hurst exponent of a Brownian walk with a Hurst exponent of 0.5, coupled with low and high intensity noise, and show that dynamical noise has no effect on fractal structure.