论文标题
中国股票市场指数的回报分配属性的精确度量
Precision measurement of the return distribution property of the Chinese stock market index
论文作者
论文摘要
本文系统地对上海和深圳证券交易所的17年期间（2005-2021）进行了对复合指数1分钟数据集的分析。为了揭示中国人和成熟股票市场之间的差异，在这里，我们精确地衡量了复合指数在时间尺度上的回报分布的财产，$ΔT$从1分钟到近4,000分钟不等。主要发现如下。 （1）返回分布提供了一种leptokurtic，胖尾和几乎对称的形状，与成熟市场相似。 （2）返回分配的中心部分由对称的lévy$α$稳定过程很好地描述，其稳定性参数可与美国股票市场提取的约1.4的稳定性参数相当。 （3）与Lévy$α$稳定分布更大的回报范围内，学生的T分布可以很好地描述回报分布。 （4）明显地，当$ΔT$增加时，稳定性参数显示出潜在的变化，因此观察到在15 $ <ΔT<$ 60分钟时的交叉区域。这与美国股票市场的发现不同，在美国股票市场的单一价值约为1 $ \leΔt\ le $ 1,000分钟。 （5）作为渐近幂律的小$ΔT$以大约3的指数，回报的尾巴分布衰减，这是成熟市场中广泛存在的价值。但是，当$ΔT\ ge $ 240分钟时，它呈指数衰减，这在成熟市场中未观察到。 （6）随着$ΔT$的增加，返回分布逐渐收敛到高斯。该观察结果与在美国股票市场的关键$ΔT= 4天的发现不同。
This paper systematically conducts an analysis of the composite index 1-min datasets over the 17-year period (2005-2021) for both the Shanghai and Shenzhen stock exchanges. To reveal the difference between the Chinese and the mature stock markets, here we precisely measure the property of return distribution of composite index over the time scale $Δt$ ranging from 1 min up to almost 4,000 min. The main findings are as follows. (1) Return distribution presents a leptokurtic, fat-tailed, and almost symmetrical shape, which is similar to that of mature markets. (2) The central part of return distribution is well described by the symmetrical Lévy $α$-stable process with a stability parameter comparable with the value of about 1.4 extracted in the U.S. stock market. (3) Return distribution can be well described by the student's t-distribution within a wider return range than the Lévy $α$-stable distribution. (4) Distinctively, the stability parameter shows a potential change when $Δt$ increases, and thus a crossover region at 15 $< Δt <$ 60 min is observed. This is different from the finding in the U.S. stock market where a single value of about 1.4 holds over 1 $\le Δt \le$ 1,000 min. (5) The tail distribution of returns at small $Δt$ decays as an asymptotic power-law with an exponent of about 3, which is a value widely existing in mature markets. However, it decays exponentially when $Δt \ge$ 240 min, which is not observed in mature markets. (6) Return distributions gradually converge to Gaussian as $Δt$ increases. This observation is different from the finding of a critical $Δt =$ 4 days in the U.S. stock market.
