Windowed detrended cross-correlation analysis of synchronization processes

The aim of this paper was to propose a formal approach of the Windowed Detrended Cross-Correlation (WDCC) analysis, a method designed for identifying the processes that underlie intra- and interpersonal synchronization. We present the three main theoretical frameworks that have been proposed for accounting for synchronization processes, (1) the information-processing approach, (2) the coupled oscillators model and (3) the complexity matching effect. We formally derive the WDCC results that could be expected from each model. We show by simulation that each model allows generating series that fit the expected results. We also analyze experimental data sets collected in situations that were supposed to selectively elicit the synchronization processes depicted in the three theoretical frameworks. Our results show that the information-processing and the complexity matching processes are both present in each situation, but with a clear dominance of one of these processes on the other. Finally our results lead us to cast some doubts about the relevance of the coupled oscillators model in interpersonal synchronization.