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

✍ Scribed by T. Qiu; L. Guo; G. Chen

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 919 KB
• Volume: 387
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2008.09.002

✦ Synopsis

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 -αx 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.