  A methodology is developed to identify, as units of study, each decrease in
the value of a stock from a given maximum price level. A critical level in the
amount of price declines is found to separate a segment operating under a
random walk from a segment operating under a power law. This level is
interpreted as a point of phase transition into a self-organized system.
Evidence of self-organization was found in all the stock market indices studied
but in none of the control synthetic random series. Findings partially explain
the fractal structure characteristic of financial time series and suggest that
price fluctuations adopt two different operating regimes. We propose to
identify downward movements larger than the critical level apparently subject
to the power law, as self-organized states, and price decreases smaller than
the critical level, as a random walk with the Markov property.
