Scale-free avalanches in the multifractal random walk
Special Research Centre for the Subatomic Structure of Matter (CSSM), University of Adelaide, Adelaide, SA, 5005, Australia
Corresponding author: a email@example.com
Revised: 28 February 2007
Published online: 22 June 2007
Avalanches, or Avalanche-like, events are often observed in the dynamical behaviour of many complex systems which span from solar flaring to the Earth's crust dynamics and from traffic flows to financial markets. Self-organized criticality (SOC) is one of the most popular theories able to explain this intermittent charge/discharge behaviour. Despite a large amount of theoretical work, empirical tests for SOC are still in their infancy. In the present paper we address the common problem of revealing SOC from a simple time series without having much information about the underlying system. As a working example we use a modified version of the multifractal random walk originally proposed as a model for the stock market dynamics. The study reveals, despite the lack of the typical ingredients of SOC, an avalanche-like dynamics similar to that of many physical systems. While, on one hand, the results confirm the relevance of cascade models in representing turbulent-like phenomena, on the other, they also raise the question about the current state of reliability of SOC inference from time series analysis.
PACS: 89.65.Gh – Economics; econophysics, financial markets, business and management
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007