Power Law in Price Falls larger than a Critical Level in Financial Time Series

Abstract

The study of financial time series was addressed looking for evidence of self- organization. A methodology was developed to identify as units of study each one of price declines from a recent maximum level and back to the original level. An interval in the space of states in which price falls could be explained as a process that follows a power law was seek. A critical level in the size of falls was identified separating the set of falls operating under a random regime (falls smaller than the critical level), from the set which follows a power law (falls larger than the critical level). This critical level is presumed to be a phase transition point towards a self-organized system. Both the methodology and the approach are original and add a new way to bring out that fluctuations in financial prices obey the power law, a relevant element to build a new systemic theory of price generation in financial markets, more proper to explain deep falls than the Efficient Market Hypothesis.