Financial time series are approached from a systemic perspective, looking for evidence of URLanization. A methodology was developed to identify  as units of study, each fall from a given maximum price level. A range, within the space of states, in which price falls could be explained as a process that follows a power law was explored. A critical level in the depth of price falls was found to separate a segment operating under a random walk regime, from a segment operating under a power law. This level was interpreted as a point of phase transition in a URLanized system. Evidence of URLanization was found in all  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 suggests that price fluctuations adopt two different operating regimes. We propose to identify downward movements larger than the critical level , explainable as subject to the power law, as URLanized states, making allowance to explaining price descends smaller than the critical level, as a random walk with the Markov property.
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 URLanized system. Evidence of URLanization 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 URLanized states, and price decreases smaller than the critical level, as a random walk with the Markov property.
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