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Nonparametric neutral network estimation of lyapunov exponents and a direct test for chaos

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  • Linton, Oliver
  • Shintani, Mototsugu

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

  • Linton, Oliver & Shintani, Mototsugu, 2002. "Nonparametric neutral network estimation of lyapunov exponents and a direct test for chaos," LSE Research Online Documents on Economics 58170, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:58170
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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:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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