Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos

@inproceedings{Shintani2000NonparametricNN,
  title={Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos},
  author={Mototsugu Shintani},
  year={2000}
}
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… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 41 references

Improved Rates and Asymptotic Normality for Nonparametric Neural Network Estimators

IEEE Trans. Information Theory • 1999
View 8 Excerpts
Highly Influenced

Sieve extremum estimates for weakly dependent data.

X. Chen, X. Shen
Econometrica • 1998
View 20 Excerpts
Highly Influenced

Finding Chaos in Noisy Systems

Douglas Nychkatl, S. P. Ellner, Daniel McCafTrey, A. R. Gallanl
1991
View 10 Excerpts
Highly Influenced

FUNFITS: data analysis and statistical tools for estimating functions

D. Nychka, B. Bailey, S. Ellner, P. Haaland, M. O’Connell
North Carolina Institute of Statistics Mimeoseries • 1996
View 4 Excerpts
Highly Influenced

Random approximants and neural networks.

Y. Makovoz
Journal of Approximation Theory • 1996
View 4 Excerpts
Highly Influenced

Robustness of nonlinearity and chaos tests to measurement error, inference method, and sample size.

W. A. Barnett, A. R. Gallant, +3 authors M. J. Jensen
Journal of Economic Behavior and Organization • 1995
View 6 Excerpts
Highly Influenced

Convergence rates and data requirements for Jacobian-based estimates of Lyapunov exponents from data.

S. Ellner, A. R. Gallant, D. McCa¤rey, D. Nychka
Physics Letter A • 1991
View 5 Excerpts
Highly Influenced

Heteroskedasticity and autocorrelation consistent covariance matrix estimation.

D.W.K. Andrews
Econometrica • 1991
View 8 Excerpts
Highly Influenced

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