【作者】 黄孟辉；

【导师】 陈振龙；

【作者基本信息】 浙江工商大学 ， 统计学， 2011， 硕士

【摘要】 本文通过对上海证券交易所的20支股票在2010年1月4日～2010年4月30日期间的共79个交易日的交易持续期数据,采取包括单分形和多分形等在内的多种分形分析方法进行了分析,描述了交易持续期在多个方面的特征。在对本文选取的数据的基本统计特征进行分析之后,我们发现：交易持续期表现出和其他金融高频数据同样的非正态性,“日内效应”以及非稳定性。这些基本的统计特征的描述提示我们,可以采用分形分析方法对交易持续期序列进行分析,可以更好更精确地描述该序列的长期记忆性以及某些局部特征。在使用单分形分析方法中的趋势消解分析法对交易持续期序列进行分析后,我们发现：交易持续期序列中确实存在着明显的长期记忆性,并且这种长期记忆性的存在是一种普遍现象,和股票所在行业、股票所属公司总流通市值以及总平均交易强度等指标没有直接的相关关系。另外,我们对交易持续期序列分别进行了三种不同的处理方式：去除“日内效应”、重排和傅立叶相位随机化,通过对处理后的数据的分析结果进行比较,可以看出,“日内效应”的存在对于交易持续期序列的长期记忆性并没有直接影响,长期记忆性的存在来自于序列的自身相关性,因为经过打乱重排后的序列并没有表现出明显的长期记忆性。同时我们发现,交易持续期的波动函数图像显示出斜率显著不同的两段,这表明在不同的时间尺度上,交易持续期序列的长期记忆特征也是有所不同的,也就是说,我们如果使用单一的时间尺度上的指标去量化整个序列的长期记忆特征是不甚科学和精确的。所以我们在下文中,选取了三种不同的多重分形分析方法,对交易持续期序列的多重分形特征进行了描述。多重分形分析方法的实证结果表明,交易持续期序列中确实存在着明显的多重分形特征,在不同时间尺度上,序列表现出显著不同的特征。为了对产生这种多重分形特征的原因进行分析,我们对原始数据采用了不同的处理方法,并对处理后的数据进行分析和比较,我们发现,交易持续期序列的多重分形特征主要来自于序列的内在相关性以及序列的非正态性,并且后者对多重分形特征的产生具有更大的影响。通过对交易持续期序列的单分形和多重分形分析后,我们更好地认识了中国股票市场中交易活动之间的一些内在关系,这对于我们理解和解释实际的股票交易活动具有很好的现实意义。更多还原

【Abstract】 In this thesis, we use kinds of fractal analysis methods, including monofractal and multi-fractal, to describe the intertrade durations’characteristics in many areas, based on the data of the 20 stocks in Shanghai Stock Exchange, in 79 trading days from January 4,2010 to April 30,2010. After analyzed the basic statistical characteristics of the intertrade durations, we found that, the intertrade durations performance long-range memory, intraday pattern and non-stability, as the other financial ultra-high frequency data. These basic descriptions of the statistical characteristics inform us that fractal analysis methods could be used to describe the long-range memory and some other local features of the intertrade duration much better and more accurately.In the using of the Detrended Fluctuation Analysis method, one of the monofractal analysis methods, to analysis of the data of intertrade duration we found that, there exists clear long-range memory in the series of intertrade duration, and the existence of such long-range memory is a common phenomenon, it dependent with these factors, such as the industry sector which the stocks in, total market capitalization and the total average trading intensity. In addition, the original data of the intertrade duration were carried out in three different approaches:removing the intraday pattern, shuffling and Fourier-phase randomization, the results of these different process upon the original data were compared, we can see that, the existence of the intraday pattern barely affects the long-range memory of intertrade duration, the long-range memory comes from the internal relevant of the series, because the series after shuffled doesn’t performances any significant long-rang memory. At the same times, we discover that, the curves of the fluctuation functions of the intertrade durations constitutes with two lines with different slopes, these suggest that in different time scales the long-range memory of the intertrade durations appear differently, so we conclude that it’s not reasonable and accuracy to quantify the long-range memory in different time scales of the whole series. Therefore, we use three different multi-fractal analyses method to describe the multi-fractal feathers of the intertrade durations.Multi-fractal analysis of the empirical results show that in the data of intertrade duration there exists clear multi-fractal feathers, in different time scales, the series show significantly different characteristics. In order to find the cause of the appearance of these multi-fractal feathers, we processed the original data using different approaches, and compare the analysis result, we found that the multi-fractal feathers of the intertrade durations mainly come from the inherent correlation within sequence and the non-normality of the sequence, and the latter has a greater impact on the existence of the multi-fractal characteristics.Through the monofractal and multi-fractal analysis of the intertrade duration, we have a better understanding of the intrinsic relationship between different trades in China’s stock market. It’s very useful for us to understand and explain the real activity of exchange in stock market.更多还原