The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series

This paper derives the asymptotic distribution of a smoothing-based estimator of the Lyapunov exponent for a stochastic time series under two general scenarios. In the first case, we are able to establish root- T consistency and asymptotic normality, while in the second case, which is more relevant...

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Bibliographic Details
Published in:Journal of econometrics 1999-07, Vol.91 (1), p.1-42
Main Authors: Whang, Yoon-Jae, Linton, Oliver
Format: Article
Language:English
Subjects:
Chaos
Convergence
Distribution theory
Exact sciences and technology
Inference from stochastic processes
time series analysis
Kernel
Mathematics
Nonlinear dynamics
Nonparametric inference
Nonparametric regression
Parametric inference
Probability and statistics
Sciences and techniques of general use
Semiparametric
Statistics
Stochastic processes
Time series
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Summary:This paper derives the asymptotic distribution of a smoothing-based estimator of the Lyapunov exponent for a stochastic time series under two general scenarios. In the first case, we are able to establish root- T consistency and asymptotic normality, while in the second case, which is more relevant for chaotic processes, we are only able to establish asymptotic normality at a slower rate of convergence. We provide consistent confidence intervals for both cases. We apply our procedures to simulated data.
ISSN:0304-4076
1872-6895
DOI:10.1016/S0304-4076(98)00047-5