  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.
