Scaling and memory effect in volatility return interval of the Chinese stock market |
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Authors: | T. Qiu L. Guo |
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Affiliation: | a School of Electronic and Information Engineering, NanChang Hangkong University, Nanchang, 330063, China b School of Business, East China University of Science and Technology, Shanghai, 200237, China |
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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 to obtain a uniform scaling curve for different threshold value q. The scaling curve can be well fitted by the stretched exponential function , 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. |
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Keywords: | 89.65.Gh -05.45.Tp 89.75.Da |
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