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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.
Whang, Yoon-Jae and Linton, Oliver B., "The Limiting Behavior of Kernel Estimates of the Lyapunov Exponent for Stochastic Time Series" (1996). Cowles Foundation Discussion Papers. 1376.