Time-lag cross-correlations in collective phenomena

¹  Center for Polymer Studies and Department of Physics, Boston University - Boston, MA 02215, USA
²  Faculty of Civil Engineering, University of Rijeka - 51000 Rijeka, Croatia
³  Faculty of Science, University of Zagreb - 10000 Zagreb, Croatia
⁴  Martin Luther University, Institute of Computer Science - 06120 Halle, Germany, EU

Received: 18 May 2010
Accepted: 11 June 2010

Abstract

We study long-range magnitude cross-correlations in collective modes of real-world data from finance, physiology, and genomics using time-lag random matrix theory. We find long-range magnitude cross-correlations i) in time series of price fluctuations, ii) in physiological time series, both healthy and pathological, indicating scale-invariant interactions between different physiological time series, and iii) in ChIP-seq data of the mouse genome, where we uncover a complex interplay of different DNA-binding proteins, resulting in power-law cross-correlations in x_ij, the probability that protein i binds to gene j, ranging up to 10 million base pairs. In finance, we find that the changes in singular vectors and singular values are largest in times of crisis. We find that the largest 500 singular values of the NYSE Composite members follow a Zipf distribution with exponent ≈ 2. In physiology, we find statistically significant differences between alcoholic and control subjects.