Scaling and Memory Effect in Volatility Return Interval of the Chinese Stock Market
We investigate the probability distribution of the volatility return intervals $\tau$ for the Chinese stock market. We rescale both the probability distribution $P_{q}(\tau)$ and the volatility return intervals $\tau$ as $P_{q}(\tau)=1/\bar{\tau} f(\tau/\bar{\tau})$ to obtain a uniform scaling curve for different threshold value $q$. The scaling curve can be well fitted by the stretched exponential function $f(x) \sim e^{\alpha x^{\gamma}}$, which suggests memory exists in $\tau$. To demonstrate the memory effect, we investigate the conditional probability distribution $P_{q} (\tau\tau_{0})$, the mean conditional interval $<\tau\tau_{0}>$ and the cumulative probability distribution of the cluster size of $\tau$. The results show clear clustering effect. We further investigate the persistence probability distribution $P_{\pm}(t)$ 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 $\tau$. The scaling and long memory effect of $\tau$ for the Chinese stock market are similar to those obtained from the United States and the Japanese financial markets.
Year of publication: 
200805


Authors:  Qiu, Tian ; Guo, Liang ; Chen, Guang 
Institutions:  arXiv.org 
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