Suntory and Toyota International Centres for Economics and Related Disciplines (STICERD) LSE RSS Contact Us YouTube Twitter

Abstract:

Econometrics Paper
Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos
Oliver Linton and Mototsugu Shintani May 2003
Paper No' EM/2003/455:
Full Paper (pdf)

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

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.