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The method of surrogates is one of the key concepts of nonlinear data analysis. Here, we demonstrate that commonly used algorithms for generating surrogates often fail to generate truly linear time series. Rather, they create surrogate realizations with Fourier phase correlations leading to non-detections of nonlinearities. We argue that reliable surrogates can only be generated, if one tests separately for static and dynamic nonlinearities.
We introduce new quantities for exploratory causal inference between bivariate time series. The quantities, called penchants and leanings, are computationally straightforward to apply, follow directly from assumptions of probabilistic causality, do n
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling relation over
The process of collecting and organizing sets of observations represents a common theme throughout the history of science. However, despite the ubiquity of scientists measuring, recording, and analyzing the dynamics of different processes, an extensi
Analyzing data from paleoclimate archives such as tree rings or lake sediments offers the opportunity of inferring information on past climate variability. Often, such data sets are univariate and a proper reconstruction of the systems higher-dimensi
Approaches for mapping time series to networks have become essential tools for dealing with the increasing challenges of characterizing data from complex systems. Among the different algorithms, the recently proposed ordinal networks stand out due to