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

40 Pages Posted: 21 Jul 2008

See all articles by Oliver B. Linton

Oliver B. Linton

University of Cambridge

Mototsugu Shintani

Vanderbilt University - College of Arts and Science - Department of Economics

Date Written: March 2002

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.

JEL Classification: C13, C14

Suggested Citation

Linton, Oliver B. and Shintani, Mototsugu, Nonparametric Neutral Network Estimation of Lyapunov Exponents and a Direct Test for Chaos (March 2002). LSE STICERD Research Paper No. EM434, Available at SSRN: https://ssrn.com/abstract=1162609

Oliver B. Linton (Contact Author)

University of Cambridge ( email )

Faculty of Economics
Cambridge, CB3 9DD
United Kingdom

Mototsugu Shintani

Vanderbilt University - College of Arts and Science - Department of Economics ( email )

Box 1819 Station B
Nashville, TN 37235
United States

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