Bootstrap estimates of chaotic dynamics - art. no. 016213

Bootstrap sampling is a nonparametric method for estimating the standard er ror of a statistic. This paper describes the application of bootstrap sampl ing to estimate the error in local linear approximations of the dynamics on chaotic attractors reconstructed from time series measurements. We present an algorithm for identifying influential points, i.e., observations with a n especially large effect on a least-squares fit, and an algorithm to estim ate the standard error of regression coefficients obtained from total least squares. We also consider the application of bootstrap methods to assess t he uncertainty in Lyapunov exponent computations from chaotic time series.