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Nonparametric Neutral Network Estimation of Lyapunov Exponents and a Direct Test for Chaos Author info | Abstract | Publisher info | Download info | Related research | Statistics Oliver Linton
Mototsugu Shintani
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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.
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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number
/2002/434.
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Date of creation: Mar 2002Date of revision:
Handle: RePEc:cep:stiecm:/2002/434Contact details of provider: Web page: http://sticerd.lse.ac.uk/publications/
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Keywords: Artificial neural networks nonlinear dynamics nonlinear time series nonparametric regression Sieve estimation. Other versions of this item:
This paper has been announced in the following NEP Reports :
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