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Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos

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  • Oliver Linton
  • Mototsugu Shintani

Abstract

This paper derives the asymptotic distribution of the nonparametric neural network estimator of the Lyapunov exponent in a noisy system. Positivity of the Lyapunov exponent is an operational definition of chaos. We introduce a statistical framework for testing the chaotic hypothesis based on the estimated Lyapunov exponents and a consistent variance estimator. A simulation study to evaluate small sample performance is reported. We also apply our procedures to daily stock return data. In most cases, the hypothesis of chaos in the stock return series is rejected at the 1% level with an exception in some higher power transformed absolute returns.

Suggested Citation

  • Oliver Linton & Mototsugu Shintani, 2003. "Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos," STICERD - Econometrics Paper Series 455, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:455
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    References listed on IDEAS

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    More about this item

    Keywords

    Artificial neural networks; nonlinear dynamics; nonlinear time series; nonparametric regression; sieve estimation;
    All these keywords.

    JEL classification:

    • 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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