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The rank-based nonlinear predictability score was recently introduced as a test for determinism in point processes. We here adapt this measure to time series sampled from time-continuous flows. We use noisy Lorenz signals to compare this approach against a classical amplitude-based nonlinear prediction error. Both measures show an almost identical robustness against Gaussian white noise. In contrast, when the amplitude distribution of the noise has a narrower central peak and heavier tails than the normal distribution, the rank-based nonlinear predictability score outperforms the amplitude-based nonlinear prediction error. For this type of noise, the nonlinear predictability score has a higher sensitivity for deterministic structure in noisy signals. It also yields a higher statistical power in a surrogate test of the null hypothesis of linear stochastic correlated signals. We show the high relevance of this improved performance in an application to electroencephalographic (EEG) recordings from epilepsy patients. Here the nonlinear predictability score again appears of higher sensitivity to nonrandomness. Importantly, it yields an improved contrast between signals recorded from brain areas where the first ictal EEG signal changes were detected (focal EEG signals) versus signals recorded from brain areas that were not involved at seizure onset (nonfocal EEG signals). R.G.A. acknowledges Grant No. FIS-2010-18204 of the Spanish Ministry of Education and Science and funding from the Volkswagen Foundation. K.S. and C.R. are grateful for support by the Swiss National Science Foundation (Projects No. SNF 320030-122010 and No. 33CM30-124089).

The detection of a nonrandom structure from experimental data can be crucial for the classification, understanding, and interpretation of the generating process. We here introduce a rank-based nonlinear predictability score to detect determinism from point process data. Thanks to its modular nature, this approach can be adapted to whatever signature in the data one considers indicative of deterministic structure. After validating our approach using point process signals from deterministic and stochastic model dynamics, we show an application to neuronal spike trains recorded in the brain of an epilepsy patient. While we illustrate our approach in the context of temporal point processes, it can be readily applied to spatial point processes as well. R.G.A. acknowledges Grant No. FIS-2010-18204 of the Spanish Ministry of Education and Science. R.G.A. and F.M. acknowledge funding from the Volkswagen Foundation. T.K. acknowledges funding from the European Commission through the Marie Curie Initial Training Network ‘Neural Engineering Transformative Technologies (NETT)’, Project No. 289146.

A rapidly growing number of studies deals with the prediction of epileptic seizures. For this purpose, various techniques derived from linear and nonlinear time series analysis have been applied to the electroencephalogram of epilepsy patients. In none of these works, however, the performance of the seizure prediction statistics is tested against a null hypothesis, an otherwise ubiquitous concept in science. In consequence, the evaluation of the reported performance values is problematic. Here, we propose the technique of seizure time surrogates based on a Monte Carlo simulation to remedy this deficit. C.E.E., T.K., K.L., F.M., and C.R. acknowledge support from the Deutsche Forschungsgemeinschaft.