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Effect of noise on estimation of Lyapunov exponents from a time series

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  • Serletis, Apostolos
  • Shahmoradi, Asghar
  • Serletis, Demitre

Abstract

We argue that dynamical noise can dramatically change the dynamics of low-dimensional chaotic systems. Moreover, we show that chaos tests are highly sensitive to dynamical noise and this becomes worse when the intensity of the noise increases.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:2:p:883-887
    DOI: 10.1016/j.chaos.2005.11.048
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    References listed on IDEAS

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    1. Shintani, Mototsugu & Linton, Oliver, 2004. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," Journal of Econometrics, Elsevier, vol. 120(1), pages 1-33, May.
    2. Whang, Yoon-Jae & Linton, Oliver, 1999. "The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series," Journal of Econometrics, Elsevier, vol. 91(1), pages 1-42, July.
    3. Mototsugu Shintani & Oliver Linton, 2003. "Is There Chaos in the World Economy? A Nonparametric Test Using Consistent Standard Errors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(1), pages 331-357, February.
    4. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
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    Cited by:

    1. Serletis, Demitre, 2008. "Effect of noise on fractal structure," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 921-924.
    2. repec:mse:cesdoc:15045 is not listed on IDEAS
    3. Mihailović, Dragutin T. & Budinčević, Mirko & Perišić, Dušanka & Balaž, Igor, 2012. "Maps serving the combined coupling for use in environmental models and their behaviour in the presence of dynamical noise," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 156-165.
    4. Clément Goulet & Dominique Guegan & Philippe De Peretti, 2015. "Empirical probability density function of Lyapunov exponents," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01167097, HAL.
    5. Rehman, S. & Siddiqi, A.H., 2009. "Wavelet based hurst exponent and fractal dimensional analysis of Saudi climatic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1081-1090.

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