Chaos theory offers to the statistician new perspectives for time series analysis as well as concepts and ideas that have a through contribution to statistics. On the other hand, statistical methodology has shown to play a crucial role for the comprehension of nonlinear and chaotic phenomena. From this standpoint we present some essential notions for the analysis of chaotic time series. Particular attention is given to the problem of estimating Lyapunov exponents, together with the derivation of confidence intervals for estimates. For this latter problem we propose a solution based on resampling by means of spline interpolation. We show from simulations that the distribution of the maximal Lyapunov exponent obtained by way of resampling a single series with our method, agrees with the true distribution obtained from series with different initial conditions.
22 Oct 2007
Volume: 62 Issue: 3 Pages: 359-378