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 Pq(τ)=1/τ¯f(τ/τ¯) 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)∼e−αxγ, which suggests memory exists in τ. To demonstrate the memory effect, we investigate the conditional probability distribution Pq(τ|τ0), the mean conditional interval 〈τ|τ0〉 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.