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

Oliver Linton and Mototsugu Shintani

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: artificial neural networks; nonlinear dynamics; nonlinear time series; nonparametric regression; sieve estimation (search for similar items in EconPapers)
JEL-codes: J1 (search for similar items in EconPapers)
Pages: 36 pages
Date: 2002-03
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http://eprints.lse.ac.uk/58170/ Open access version. (application/pdf)

Related works:
Journal Article: Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos (2004)
Working Paper: Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos (2003)
Working Paper: Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos (2003)
Working Paper: Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos (2003)
Working Paper: Nonparametric Neutral Network Estimation of Lyapunov Exponents and a Direct Test for Chaos (2002)
Working Paper: Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos (2002)
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