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Effect of noise on fractal structure

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  • Serletis, Demitre

Abstract

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.

Suggested Citation

  • Serletis, Demitre, 2008. "Effect of noise on fractal structure," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 921-924.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:4:p:921-924
    DOI: 10.1016/j.chaos.2007.01.031
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    References listed on IDEAS

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    1. El Naschie, M.S., 2006. "Elementary prerequisites for E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 579-605.
    2. Serletis, Apostolos & Shahmoradi, Asghar & Serletis, Demitre, 2007. "Effect of noise on the bifurcation behavior of nonlinear dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 914-921.
    3. He, Ji-Huan & Xu, Lan & Zhang, Li-Na & Wu, Xu-Hong, 2007. "Twenty-six dimensional polytope and high energy spacetime physics," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 5-13.
    4. Carbone, A. & Castelli, G. & Stanley, H.E., 2004. "Time-dependent Hurst exponent in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 267-271.
    5. Arianos, Sergio & Carbone, Anna, 2007. "Detrending moving average algorithm: A closed-form approximation of the scaling law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 9-15.
    6. Serletis, Apostolos & Shahmoradi, Asghar & Serletis, Demitre, 2007. "Effect of noise on estimation of Lyapunov exponents from a time series," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 883-887.
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