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

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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.

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en

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application/pdf

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http://eprints.lse.ac.uk/2093/1/Nonparametric_Neutral_Network_Estimation_of_Lyapunov_Exponents_and_a_Direct_Test_for_Chaos_2002.pdf

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