Four Methods to Distinguish between Fractal Dimensions in Time Series through Recurrence Quantification Analysis

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Fractal properties in time series of human behavior and physiology are quite ubiquitous, and several methods to capture such properties have been proposed in the past decades. Fractal properties are marked by similarities in statistical characteristics over time and space, and it has been suggested that such properties can be well-captured through recurrence quantification analysis. However, no methods to capture fractal fluctuations by means of recurrence-based methods have been developed yet. The present paper takes this suggestion as a point of departure to propose and test several approaches to quantifying fractal fluctuations in synthetic and empirical time-series data using recurrence-based analysis. We show that such measures can be extracted based on recurrence plots, and contrast the different approaches in terms of their accuracy and range of applicability.
Original languageEnglish
Article number1314
Issue number9
Number of pages14
Publication statusPublished - 19.09.2022

Bibliographical note

Funding Information:
We thank Stine Hollah and Gerke Feindt for collecting the timing data presented in this manuscript. S.W. acknowledges funding by the German Research Foundation (DFG; grant numbers 442405852 and 442405919).

Publisher Copyright:
© 2022 by the authors.

    Research areas

  • recurrence quantification analysis, fractals, monofractals, fractal time series
  • Engineering