Abstract
The conventional method for estimating Lyapunov spectra can give spurious positive Lyapunov exponents when applied to random time series. We analyze this phenomenon by considering a situation in which the method is applied to completely random time series produced by a simple stochastic model. We show that the possible estimation of spurious positive Lyapunov exponents is due to the statistical nature and the finiteness of data. We also derive an upper bound of the largest Lyapunov exponent for the model, which is useful in testing positive Lyapunov exponents with random-shuffled surrogate data. The results suggest that the method should be applied very carefully to experimentally obtained chaotic time series with possible random contamination, so as to avoid spurious estimation of positive Lyapunov exponents as evidences of deterministic chaos.
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