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: | 15 Sep 2023 22:51 |
| URI: | http://eprints.lse.ac.uk/id/eprint/2093 |
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