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

Linton, Oliver and Shintani, Mototsugu (2002) Nonparametric neutral network estimation of lyapunov exponents and a direct test for chaos. Econometrics (EM/2002/434). The London School of Economics and Political Science, Suntory and Toyota International Centres for Economics and Related Disciplines, London, UK.

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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.

Item Type: Monograph (Report)
Official URL: http://sticerd.lse.ac.uk/
Additional Information: © 2002 The Authors
Divisions: STICERD
Subjects: H Social Sciences > HB Economic Theory
Sets: Research centres and groups > Suntory and Toyota International Centres for Economics and Related Disciplines (STICERD)
Date Deposited: 23 Jul 2014 11:39
Last Modified: 15 Jun 2019 23:10
Funders: National Science Foundation
URI: http://eprints.lse.ac.uk/id/eprint/58170

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