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

Abstract: 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/τf(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 γ , 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.