CFDP 1130R

The Limiting Behavior of Kernel Estimates of the Lyapunov Exponent for Stochastic Time Series


Publication Date: August 1996

Revision Date: October 1997

Pages: 47


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.


Chaos, kernel, nonlinear dynamics, nonparametric regression, semiparametric

JEL Classification Codes:  C13, C14, C22


Published in Journal of Econometrics (July 1999), 91(1): 1-42 [DOI]