Statistical properties of volatility return intervals of Chinese stocks

The statistical properties of the return intervals ${\tau }_q$ 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 ${\tau }_q$ for different thresholds $q$. Furthermore, the KS test and weighted KS test shows that the scaled return interval distributions of 6 stocks (out of the 12 stocks) can be nicely fitted by a stretched exponential function $f(\tau \mathrm{/}\bar{\tau })\sim e^{-\alpha (\tau \mathrm{/}\bar{\tau }{)}^{\gamma }}$ with $\gamma \approx 0.31$ under the significance level of 5%, where $\bar{\tau }$ is the mean return interval. The investigation of the conditional probability distribution $P_q(\tau \mathrm{\mid }{\tau }_0)$ and the mean conditional return interval $<\tau \mathrm{\mid }{\tau }_0>$ demonstrates the existence of short-term correlation between successive return interval intervals. We further study the mean return interval $<\tau \mathrm{\mid }{\tau }_0>$ 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.