Multiscaling and non-universality in fluctuations of driven complex systems

¹ Department of Theoretical Physics, Budapest University of Technology and Economics Budapest, H-1111 Hungary
² Laboratory of Computational Engineering, Helsinki University of Technology Espoo, Finland
³ Center for Complex Network Research and Department of Physics University of Notre Dame - Notre Dame, IN 46556, USA

Corresponding author: eisler@maxwell.phy.bme.hu

Received: 8 November 2004
Accepted: 9 December 2004

Abstract

For many externally driven complex systems neither the noisy driving force, nor the internal dynamics are a priori known. Here we focus on systems for which the time-dependent activity of a large number of components can be monitored, allowing us to separate each signal into a component attributed to the external driving force and one to the internal dynamics. We propose a formalism to capture the potential multiscaling in the fluctuations and apply it to the high-frequency trading records of the New York Stock Exchange. We find that on the time scale of minutes the dynamics is governed by internal processes, while on a daily or longer scale the external factors dominate. This transition from internal to external dynamics induces systematic changes in the scaling exponents, offering direct evidence of non-universality in the system.