Statistical analysis of Lyapunov exponents from time series: A Jacobian approach

In this paper, we provide a statistical analysis for the Lyapunov exponents estimated from time series. Through the Jacobian estimation approach, the asymptotic distributions of the estimated Lyapunov exponents of discrete-time dynamical systems are studied and characterized based on the time series. Some new results under weak conditions are obtained. The theoretical results presented in the paper are illustrated by numerical simulations.