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

Tian Qiu; Liang Guo; Guang Chen

doi:10.1016/j.physa.2008.09.002

paper

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

arXiv:0805.2194 · doi:10.1016/j.physa.2008.09.002

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 $P_{q} (τ) = 1/ τ ˉ f (τ / τ ˉ)$ to obtain a uniform scaling curve for different threshold value $q$ . The scaling curve can be well fitted by the stretched exponential function $f (x) \sim e^{- α x^{γ}}$ , 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 $P_{\pm} (t)$ 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 $τ$ . 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.

arXiv comment10 elsart pages including 7 eps figures

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

Abstract

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