...variance.

In order to simplify the notation in mathematical derivations, we will assume throughout this paper that the mean of each time series has been subtracted and it has been rescaled to unit variance. Nevertheless, we will often transform back to the original experimental units when displaying results graphically.

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...quantity

We have omitted the commonly used normalisation to second moments since throughout this paper, time series and their surrogates will have the same second order properties and identical pre-factors do not enter the tests.

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...data,

Formally, digitisation is a non-invertible, nonlinear measurement and thus not included in the null hypothesis. Constraining the surrogates to take exactly the same (discrete) values as the data seems to be reasonably safe, though. Since for that case we haven't seen any dubious rejections due to discretisation, we didn't discuss this issue as a serious caveat. This decision may of course prove premature.

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...here.

Thanks to Bruce Gluckman for pointing this out to us.

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...chain.

Contrary to what is said in Ref. [24], binning a two dimensional distribution yields a first order (rather than a second order) Markov process, for which a three dimensional binning would be needed to include the image distribution as well.

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