上证综指的概率密度分布和自相关特性的分析

Probability Distribution and Time-Correlation of Shanghai Stock Exchange Composite Index

分析了2000-2006年上海证券交易所综合股价指数（简称上证指数）的对数增量在不同时间间隔情况下的概率分布密度和自相关函数.发现上证指数的对数增量符合列维非高斯分布,高频指数的对数增量具有大约20 min的时间相关性且在5-15 min之间表现为负相关,对数增量绝对值的自相关函数按幂率分布缓慢衰减.上证指数的总体统计行为与国际成熟股市基本相同,但高频指数的负相关效应和一些定量的差异表明上海股市的投机性较强.

The probability distribution and correlation function for the changes of logarithmic of the Shanghai stock exchange composite index were analyzed at different time intervals over the seven year period, from January 2000 to December 2006. It is found that the logarithmic change of the index can be described by the non-Gaussian Levy distribution. The correlation time of the high frequency data is about 20 minutes, where negative correlation is found on intervals between 5 minutes to 15 minutes. The correlation of the absolute value of the logarithmic change of the index decays very slowly with a power law. The overall statistical characteristics of the index of Shanghai exchange is similar to the mature international markets, while the negative correlation and other quantitative difference with other markets indicate that Shanghai market has a higher level of speculation.