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

  title={Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos},
  author={Mototsugu Shintani},
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… CONTINUE READING
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