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Abstract:

Econometrics Paper
Nonparametric Neutral Network Estimation of Lyapunov Exponents and a Direct Test for Chaos
Oliver Linton and Mototsugu Shintani March 2002
Paper No' EM/2002/434:
Full Paper (pdf)

Tags: artificial neural networks; nonlinear dynamics; nonlinear time series; nonparametric regression; sieve estimation.

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.