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Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos

Shintani, Mototsugu and Linton, Oliver (2002) Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos. Econometrics; EM/2002/434 (EM/02/434). 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 (Discussion Paper)
Official URL: http://sticerd.lse.ac.uk
Additional Information: © 2002 by the authors
Divisions: Financial Markets Group
Economics
STICERD
Subjects: H Social Sciences > HB Economic Theory
JEL classification: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C14 - Semiparametric and Nonparametric Methods
C - Mathematical and Quantitative Methods > C2 - Econometric Methods: Single Equation Models; Single Variables > C22 - Time-Series Models
Date Deposited: 27 Apr 2007
Last Modified: 13 Sep 2024 19:46
URI: http://eprints.lse.ac.uk/id/eprint/2093

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