New resampling method to assess the accuracy of the maximal Lyapunov exponent estimation

In this paper, we propose a novel method to assess standard errors and confidence intervals for the maximal Lyapunov exponent estimated on time continuous chaotic systems. The method is based on resampling the original series by means of spline interpolation in the time domain. In such a way, new time series of increased size are obtained, and the sample distribution of the estimators is constructed. The method is explained and tested on the basis of computer simulations both for clean and noisy series. We give evidence that the distribution of the maximal Lyapunov exponent calculated by this method fairly agrees with the one obtained by true series with different initial conditions. An empirical criterion for the choice of the parameters of the resampling is also suggested. © 2001 Elsevier Science B.V.