Evidence of Self-Organization in Time Series of Capital Markets

TL;DR

This paper introduces a methodology to detect self-organization in stock market time series by identifying a critical level of price decline that separates random walk behavior from power-law dynamics, indicating phase transitions.

Contribution

It presents a novel approach to distinguish between random and self-organized regimes in financial data using a critical decline level as a phase transition point.

Findings

Self-organization observed in all studied stock indices.

Critical level separates random walk from power-law behavior.

Price fluctuations exhibit two distinct regimes.

Abstract

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.