# Parameter-free quantification of stochastic and chaotic signals

## TL;DR

This paper introduces a parameter-free entropy measure based on recurrence microstates that effectively characterizes the complexity and correlation properties of stochastic and chaotic signals without requiring parameter tuning.

## Contribution

It presents a novel, parameter-free quantifier of time series complexity that distinguishes different types of stochastic and chaotic signals and reveals attractor properties.

## Key findings

- Max(S) effectively quantifies time correlation in stochastic signals.
- Max(S) distinguishes signals with different power-law spectra.
- The method provides new insights into attractor properties and chaos degree.

## Abstract

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.