Comparison of Cross-Correlation and Joint-Recurrence Quantification Analysis Based Methods for Estimating Coupling Strength in Non-linear Systems

Abstract

Time-delay stability (TDS) analysis is a method for quantifying interactions in multivariate systems by identifying stable temporal relationships in time series data [1]. This method has been used to create network representations of complex systems. As originally presented, the TDS method relies on cross-correlation—a linear analysis that is restricted to estimating relationships between unidimensional time series, and which, by itself, often does not adequately characterize interactions between many non-linear complex systems of theoretical and practical interest. Thus, modifying TDS so that it relies on joint recurrence quantification analysis (JRQA), an intrinsically non-linear multidimensional framework, and then comparing the ability of the two approaches to detect interactions in non-linear systems is an important task. In the present work, we first show how TDS can be extended using JRQA, a method which is capable of multidimensional assessment of relationships in non-linear systems. In our application of JRQA, we introduce a modification in the form of a weighting factor that accounts for the truncation of time series that results from time-delayed JRQA. We also modify TDS by correcting for a bias in the method and show how analogs of recurrence-based metrics can also be obtained for TDS. We evaluate how TDS results obtained with JRQA compare to those obtained with cross-correlation for known dynamics of coupled non-linear oscillators and from unknown dynamics of multivariate behavioral signals measured from dyads performing a joint problem-solving task. We conclude that TDS using cross-correlation provides results that are comparable to those obtained with JRQA at a much-reduced computational cost.