Scaling and memory effect in volatility return interval of the Chinese stock market

We investigate the probability distribution of the volatility return intervals τ for the Chinese stock market. We rescale both the probability distribution Pq(τ) and the volatility return intervals τ as to obtain a uniform scaling curve for different threshold value q. The scaling curve can be well fitted by the stretched exponential function , which suggests memory exists in τ. To demonstrate the memory effect, we investigate the conditional probability distribution Pq(ττ0), the mean conditional interval ττ0 and the cumulative probability distribution of the cluster size of τ. The results show clear clustering effect. We further investigate the persistence probability distribution P±(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 τ. The scaling and long memory effect of τ for the Chinese stock market are similar to those obtained from the United States and the Japanese financial markets.