Strong Anticipation and Long-Range Cross-Correlation: Application of Detrended Cross-Correlation Analysis to Human Behavioral Data

In this paper, we analyze empirical data, accounting for coordination processes between complex systems (bimanual coordination, interpersonal coordination, and synchronization with a fractal metronome), by using a recently proposed method: detrended cross-correlation analysis (DCCA). This work is motivated by the strong anticipation hypothesis, which supposes that coordination between complex systems is not achieved on the basis of local adaptations (i.e. correction, predictions), but results from a more global matching of complexity properties. Indeed, recent experiments have evidenced a very close correlation between the scaling properties of the series produced by two coordinated systems, despite a quite weak local synchronization. We hypothesized that strong anticipation should result in the presence of long-range cross-correlations between the series produced by the two systems. Results allow a detailed analysis of the effects of coordination on the fluctuations of the series produced by the two systems. In the long term, series tend to present similar scaling properties, with clear evidence of long-range cross-correlation. Short-term results strongly depend on the nature of the task. Simulation studies allow disentangling the respective effects of noise and short-term coupling processes on DCCA results, and suggest that the matching of long-term fluctuations could be the result of short-term coupling processes.