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

Oliver Linton and Mototsugu Shintani

STICERD - Econometrics Paper Series from Suntory and Toyota International Centres for Economics and Related Disciplines, LSE

Abstract: This paper derives the asymptotic distribution of the nonparametric neural network estimator of the Lyapunov exponent in a noisy system. 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 data. In most cases, the hypothesis of chaos in the stock return series is rejected at the 1% level with an exception in some higher power transformed absolute returns.

Keywords: Artificial neural networks; nonlinear dynamics; nonlinear time series; nonparametric regression; sieve estimation (search for similar items in EconPapers)
Date: 2003-05
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Citations: View citations in EconPapers (2)

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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 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)
Working Paper: Nonparametric neutral network estimation of lyapunov exponents and a direct test for chaos (2002)
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Persistent link: https://EconPapers.repec.org/RePEc:cep:stiecm:455

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