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

Mototsugu Shintani () and Oliver Linton
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Mototsugu Shintani: Department of Economics, Vanderbilt University

No 309, Vanderbilt University Department of Economics Working Papers from Vanderbilt University Department of Economics

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)
JEL-codes: C14 C22 (search for similar items in EconPapers)
Date: 2003-05
New Economics Papers: this item is included in nep-cmp and nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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http://www.accessecon.com/pubs/VUECON/vu03-w09.pdf First version, 2003 (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 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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