Note on two phase phenomena in financial markets

TL;DR

This paper investigates the bifurcation phenomenon in financial markets, specifically in the Hang-Seng index, revealing that it occurs under specific statistical conditions and may reflect underlying market information rather than universal behavior.

Contribution

The study identifies conditions under which bifurcation occurs in financial indices and distinguishes real market phenomena from artificial data through simulation analysis.

Findings

Bifurcation occurs when the absolute increment distribution's power-law exponent is between 1 and 2.

The phenomenon is not universal and depends on specific conditions.

Artificial data simulations show bifurcation is influenced by increment statistics but may not reflect core market behaviors.

Abstract

The two phase behavior in financial markets actually means the bifurcation phenomenon, which represents the change of the conditional probability from an unimodal to a bimodal distribution. In this paper, the bifurcation phenomenon in Hang-Seng index is carefully investigated. It is observed that the bifurcation phenomenon in financial index is not universal, but specific under certain conditions. The phenomenon just emerges when the power-law exponent of absolute increment distribution is between 1 and 2 with appropriate period. Simulations on a randomly generated time series suggest the bifurcation phenomenon itself is subject to the statistics of absolute increment, thus it may not be able to reflect the essential financial behaviors. However, even under the same distribution of absolute increment, the range where bifurcation phenomenon occurs is far different from real market to artificial data, which may reflect certain market information.