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Statistical tests for Lyapunov exponents of deterministic systems

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  • Wolff, Rodney C.
  • Yao, Qiwei
  • Tong, Howell

Abstract

In order to develop statistical tests for the Lyapunov exponents of deterministic dynamical systems, we develop bootstrap tests based on empirical likelihood for percentiles and expectiles of strictly stationary processes. The percentiles and expectiles are estimated in terms of asymmetric least deviations and asymmetric least squares methods. Asymptotic distributional properties of the estimators are established.

Suggested Citation

  • Wolff, Rodney C. & Yao, Qiwei & Tong, Howell, 2004. "Statistical tests for Lyapunov exponents of deterministic systems," LSE Research Online Documents on Economics 154, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:154
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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. Yao, Qiwei & Tong, Howell, 1996. "Asymmetric least squares regression estimation: a nonparametric approach," LSE Research Online Documents on Economics 19423, London School of Economics and Political Science, LSE Library.
    3. Fan, Jianqing & Yao, Qiwei & Tong, Howell, 1996. "Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems," LSE Research Online Documents on Economics 6704, London School of Economics and Political Science, LSE Library.
    4. 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.
    5. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    6. Yao, Qiwei & Tong, Howell, 1998. "A bootstrap detection for operational determinism," LSE Research Online Documents on Economics 6697, London School of Economics and Political Science, LSE Library.
    7. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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    Cited by:

    1. Park, Joon Y. & Whang, Yoon-Jae, 2012. "Random walk or chaos: A formal test on the Lyapunov exponent," Journal of Econometrics, Elsevier, vol. 169(1), pages 61-74.
    2. BenSaïda, Ahmed & Litimi, Houda, 2013. "High level chaos in the exchange and index markets," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 90-95.
    3. Kugiumtzis Dimitris, 2008. "Evaluation of Surrogate and Bootstrap Tests for Nonlinearity in Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(1), pages 1-26, March.

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    More about this item

    Keywords

    bootstrap; chaos; empirical likelihood; expectile; percentile;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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