COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1130R

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

Yoon-Jae Whang and Oliver Linton

Revised October 1997

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.

Keywords: Chaos, kernel, nonlinear dynamics, nonparametric regression, semiparametric

JEL Classification: C13, C14, C22