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

Shintani, Mototsugu and Linton, Oliver (2003) Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos. Econometrics; EM/2003/455, EM/03/455. 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 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.

Item Type:	Monograph (Discussion Paper)
Official URL:	http://sticerd.lse.ac.uk
Additional Information:	© 2003 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/03/455
URL:	http://eprints.lse.ac.uk/2097/

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