Convergence rates and data requirements for Jacobian-based estimates of Lyapunov exponents from data

Abstract

We present a method for estimating the dominant Lyapunov exponent from time-series data, based on nonparametric regression. For data from a finite-dimensional deterministic system with additive stochastic perturbations, we show that the estimate converges to the true values as the sample size increases, and give the asymptotic rate of convergence.