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The Asymptotic Distribution of Nonparametric Estimates of the Lyapunov Exponent for Stochastic Time Series

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Abstract

This paper derives the asymptotic distribution of a smoothing-based estimator of the Lyapunov exponent for a stochastic time series under two general scenarios. In the first case, we are able to establish root-T consistency and asymptotic normality, while in the second case, which is more relevant for chaotic processes, we are only able to establish asymptotic normality at a slower rate of convergence. We provide consistent confidence intervals for both cases. We apply our procedures to simulated data.

Suggested Citation

  • Yoon-Jae Whang & Oliver Linton, 1997. "The Asymptotic Distribution of Nonparametric Estimates of the Lyapunov Exponent for Stochastic Time Series," Cowles Foundation Discussion Papers 1130R, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1130r
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    References listed on IDEAS

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    1. Brock, W. A., 1986. "Distinguishing random and deterministic systems: Abridged version," Journal of Economic Theory, Elsevier, vol. 40(1), pages 168-195, October.
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    6. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-972, July.
    7. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
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    9. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    10. Dechert, W D & Gencay, R, 1992. "Lyapunov Exponents as a Nonparametric Diagnostic for Stability Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 41-60, Suppl. De.
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    More about this item

    Keywords

    Chaos; kernel; nonlinear dynamics; nonparametric regression; semiparametric;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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