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Trivariate Windowed Cross-Correlation and the Association between Three Time Series

In time series analyses, it can be useful to understand patterns of similarity between several concurrent time series, especially when these patterns provide information about the underlying psychological dynamics. Previous approaches have focused on dyadic relationships between time series; the relationship between two signals represents both the simplest methodological and psychological case. These approaches have included cross-correlation and windowed cross-correlation (WCC; Boker, Rotondo, Xu, & King, 2002). WCC produces a matrix that concatenates correlation patterns representing the local dynamics of two time series. This matrix is a dense yet informative structure that can be aggregated into global synchrony metrics using a variety of methods, including Fisher’s z transformation, mean peak correlation, and the Pairwise Approximate Spatiotemporal Symmetry (PASS) algorithm (Sjobeck, Boker, Scheidt, & Tschacher, n.d.). The emphasis of previous approaches on bivariate relationships, however, precludes a full understanding