  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.
