Scaling and Memory Effect in Volatility Return Interval of the Chinese Stock Market

Abstract

We investigate the probability distribution of the volatility return intervals $\ddot{I}„$ for the Chinese stock market. We rescale both the probability distribution $P_q(\ddot{I}„)$ and the volatility return intervals $\ddot{I}„$ as $P_q(\ddot{I}„)=1/\bar{\ddot{I}}„f(\ddot{I}„/\bar{\ddot{I}}„)$ to obtain a uniform scaling curve for different threshold value $q$. The scaling curve can be well fitted by the stretched exponential function $f(x)\sim e^{-\hat{I}\pm x^3}$, which suggests memory exists in $\ddot{I}„$. To demonstrate the memory effect, we investigate the conditional probability distribution $P_q(\ddot{I}„|\ddot{I}{„}_0)$, the mean conditional interval $<\ddot{I}„|\ddot{I}{„}_0>$ and the cumulative probability distribution of the cluster size of $\ddot{I}„$. The results show clear clustering effect. We further investigate the persistence probability distribution $P_{\pm }(t)$ and find that $P_{-}(t)$ decays by a power law with the exponent far different from the value 0.5 for the random walk, which further confirms long memory exists in $\ddot{I}„$. The scaling and long memory effect of $\ddot{I}„$ for the Chinese stock market are similar to those obtained from the United States and the Japanese financial markets.

10 elsart pages including 7 eps figures