Estimating the Lyapunov Exponent of a Chaotic System with Nonparametric Regression
用非参数回归估计混沌系统的李雅普诺夫指数
We discuss procedures based on nonparametric regression for estimating the dominant Lyapunov Exponent λ1 from time series data generated by a nonlinear autoregressive system with additive noise. For systems with bounded fluctuations, λ1 > 0 is the defining feature of chaos. Thus our procedures can be used to examine time series data for evidence of chaotic dynamics. We show that a consistent estimator of the partial derivatives of the autoregression function can be used to…