Phase transition of dynamical herd behaviors for Yen–Dollar exchange rates

We study the herd behavior and the phase transition for the yen–dollar exchange rate in the Japanese financial market. It is obtained that the probability distribution of returns satisfies the power-law behavior P(R) R-β with scaling exponents β=3.11, 2.81, and 2.29 at time intervals τ=1min, 30min, and 1 h. The crash region in which the probability density increases with the increasing return appears, when the herding parameter h satisfies h 2.33 for the case of τ<30min. We especially obtain that no crash occurs τ>30min and that the probability distribution of price returns occurs in the phase transition at τ=30min