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 P q ( τ ) and the volatility return intervals τ as P q ( 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 − α x γ , which suggests memory exists in τ . To demonstrate the memory effect, we investigate the conditional probability distribution P q ( τ | τ 0 ) , the mean conditional interval 〈 τ | τ 0 〉 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.