Parameter-free quantification of stochastic and chaotic signals

Recurrence entropy \((\cal S)\) is a novel time series complexity quantifier based on recurrence microstates. Here we show that \(\mathsf{max}(\cal S)\) is a \textit{parameter-free} quantifier of time correlation of stochastic and chaotic signals, at the same time that it evaluates property changes of the probability distribution function (PDF) of the entire data set. \(\mathsf{max}(\cal S)\) can distinguish distinct temporal correlations of stochastic signals following a power-law spectrum, \(\displaystyle P(f) \propto 1/f^\alpha\) even when shuffled versions of the signals are used. Such behavior is related to its ability to quantify distinct subsets embedded in a time series. Applied to a deterministic system, the method brings new evidence about attractor properties and the degree of chaoticity. The development of a new parameter-free quantifier of stochastic and chaotic time series opens new perspectives to stochastic data and deterministic time series analyses and may find applications in many areas of science.