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 School of Economics and Political Science, 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
Uncontrolled Keywords:	Artificial neural networks; nonlinear dynamics; nonlinear time series; nonparametric regression; Sieve estimation
Library of Congress subject classification:	H Social Sciences > HB Economic Theory
Journal of Economic Literature Classification System:	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
Sets:	Research centres and groups > Financial Markets Group (FMG) Collections > Economists Online Departments > Economics Research centres and groups > Suntory and Toyota International Centres for Economics and Related Disciplines (STICERD)
Rights:	http://www.lse.ac.uk/library/rights/LSERO.htm
Identification Number:	EM/02/434
URL:	http://eprints.lse.ac.uk/2093/

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