Statistical properties of volatility return intervals of Chinese stocks

The statistical properties of the return intervals τ_q between successive 1-min volatilities of 30 liquid Chinese stocks exceeding a certain threshold q are carefully studied. The Kolmogorov-Smirnov (KS) test shows that 12 stocks exhibit scaling behaviors in the distributions of τ_q for different thresholds q. Furthermore, the KS test and weighted KS test show that the scaled return interval distributions of 6 stocks (out of the 12 stocks) can be nicely fitted by a stretched exponential function with γ≈0.31 under the significance level of 5%, where is the mean return interval. The investigation of the conditional probability distribution P_q(τ|τ₀) and the mean conditional return interval 〈τ|τ₀〉 demonstrates the existence of short-term correlation between successive return interval intervals. We further study the mean return interval 〈τ|τ₀〉 after a cluster of n intervals and the fluctuation F(l) using detrended fluctuation analysis, and find that long-term memory also exists in the volatility return intervals.