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Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos

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  • Shintani, Mototsugu
  • Linton, Oliver

Abstract

This paper derives the asymptotic distribution of nonparametric neural network estimator of the Lyapunov exponent in a noisy system proposed by Nychka et al (1992) and others. 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 datasets. In most cases we strongly reject the hypothesis of chaos; one mild exception is in some higher power transformed absolute returns, where we still find evidence against the hypothesis but it is somewhat weaker.

Suggested Citation

  • Shintani, Mototsugu & Linton, Oliver, 2002. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," LSE Research Online Documents on Economics 2093, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:2093
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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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