A Multivariate Method for Dynamic System Analysis: Multivariate Detrended Fluctuation Analysis Using Generalized Variance

Research output: Journal contributionsJournal articlesResearchpeer-review


Fractal fluctuations are a core concept for inquiries into human behavior and cognition from a dynamic systems perspective. Here, we present a generalized variance method for multivariate detrended fluctuation analysis (mvDFA). The advantage of this extension is that it can be applied to multivariate time series and considers intercorrelation between these time series when estimating fractal properties. First, we briefly describe how fractal fluctuations have advanced a dynamic system understanding of cognition. Then, we describe mvDFA in detail and highlight some of the advantages of the approach for simulated data. Furthermore, we show how mvDFA can be used to investigate empirical multivariate data using electroencephalographic recordings during a time-estimation task. We discuss this methodological development within the framework of interaction-dominant dynamics. Moreover, we outline how the availability of multivariate analyses can inform theoretical developments in the area of dynamic systems in human behavior.

Original languageEnglish
JournalTopics in Cognitive Science
Number of pages18
Publication statusE-pub ahead of print - 14.09.2023

Bibliographical note

Funding Information:
SW acknowledges funding from the German Science Foundation (DFG; Heisenberg programme, funding ID: 442405852). The project acknowledges funding from the Danish National Research Foundation's grant to CFIN and the MINDLab grant from the Danish Ministry of Science, Technology and Innovation.

Publisher Copyright:
© 2023 The Authors. Topics in Cognitive Science published by Wiley Periodicals LLC on behalf of Cognitive Science Society.

    Research areas

  • Detrended fluctuation analysis, Dynamic systems, Interaction-dominant dynamics, Multivariate analysis, R package, Time estimation
  • Psychology