Method to distinguish possible chaos from colored noise and to determine embedding parameters

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Abstract
We present a computational method to determine if an observed time series possesses structure statistically distinguishable from high-dimensional linearly correlated noise, possibly with a nonwhite spectrum. This method should be useful in identifying deterministic chaos in natural signals with broadband power spectra, and is capable of distinguishing between chaos and a random process that has the same power spectrum. The method compares nonlinear predictability of the given data to an ensemble of random control data sets. A nonparametric statistic is explored that permits a hypothesis testing approach. The algorithm can detect underlying deterministic chaos in a time series contaminated by additive random noise with identical power spectrum at signal to noise ratios as low as 3 dB. With less noise, this method can also be used to get good estimates of the parameters (the embedding dimension and the time delay) needed to perform the standard phase-space reconstruction of a chaotic time series.