Statistical properties of volatility return intervals of Chinese stocks

The statistical properties of the return intervals τq 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 τq 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 f(τ/τ̄)∼e−α(τ/τ̄)γ with γ≈0.31 under the significance level of 5%, where τ̄ is the mean return interval. The investigation of the conditional probability distribution Pq(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.