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

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. Human behavior exhibits complex dynamics and is multidimensional. To investigate human behavior from a dynamic systems perspective, multivariate methods are needed that extract relevant parameters that can be used to link such human data to properties of dynamic systems. Here, we present an extension of multivariate fractal analysis to further such research.