中国股市多标度的幂律分布与相关性关联研究

对上海证券交易所综合股价指数（SSECI）收益率多标度条件下幂律分布与相关性的关联研究发现,加速幂律衰减,对收益率的相关性没有显著影响;短程、非线性和非线性长程相关性不同程度地维持着幂律分布特征,消除某一特定类型的相关性均会弱化收益率的胖尾,同时加速幂律衰减和渐进收敛速度,其中非线性长程相关性的影响最为显著,但这一影响过程以一定的临界标度作为前提,大于临界标度,相关性的作用显著减弱,幂律分布表现出完全的标度依赖性.

Relation between Correlation and Power-law Distribution of Multiscale for Chinese Stock Market

The relation of returns between power-law distribution and correlation of multiscale for Chinese stock market is analyzed.The data include 5-min high-frequency records of the Shanghai Stock Exchange Compound Index(SSECI) from January 2,2003 to June 1,2006.The empirical results show that quickening decaying of power-law distribution doesn't significantly change the correlation properties of returns,but stabilizes one of absolute returns.Furthermore,we also argue that the special correlations underlying returns,by studying three different shuffling series,maintain the characteristics of power-law distribution of returns.Removing correlations thins the fat tails of returns distribution and accelerates the velocity of decay and convergence.The non-linear long range correlation plays the most important role compared to short-rang and non-linear correlations.However,the controlling process has a premise of time scale.When exceeding the criticality of the scale,the effect of correlations would evidently weaken or disappear.The power-law distribution exhibits the entire scale-dependency.