Multiscaling behavior in the volatility return intervals of Chinese indices

Abstract

We investigate the probability distribution of the return intervals $\tau$ between successive 1-min volatilities of two Chinese indices exceeding a certain threshold $q$. The Kolmogorov-Smirnov (KS) tests show that the two indices exhibit multiscaling behavior in the distribution of $\tau$, which follows a stretched exponential form $f_q(\tau/< \tau >)\sim e^{- a(\tau/ < \tau >)^{\gamma}}$ with different correlation exponent $\gamma$ for different threshold $q$, where $<\tau>$ is the mean return interval corresponding to a certain value of $q$. An extended self-similarity analysis of the moments provides further evidence of multiscaling in the return intervals.