Scale-free avalanches in the multifractal random walk

TL;DR

This paper demonstrates that a modified multifractal random walk can exhibit avalanche-like dynamics similar to self-organized criticality, raising questions about the reliability of SOC detection in time series data.

Contribution

It shows that avalanche-like behavior can emerge in multifractal models without traditional SOC ingredients, challenging assumptions in SOC inference from time series.

Findings

Avalanche-like dynamics observed in a modified multifractal random walk.

Cascade models effectively represent turbulent-like phenomena.

Raises concerns about the reliability of SOC detection methods.

Abstract

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.