Abnormal statistical properties of stock indexes during a financial crash

We investigate minute indexes of stock markets in 10 countries during financial crashes by dividing them into several stages according to their stock price tendencies: plunging stage (stage 1), fluctuating or rebounding stage (stage 2), and soaring stage (stage 3). The tail distributions of the returns satisfy a power law for developed markets but show a dual power-law structure for emerging markets. Prominent dual fractal structures are found during the plunging stage in developed markets, and after the plunging stage in emerging markets. The fractal analysis on the sign series of the returns yields similar dual fractal properties.