多重分形理论的大盘股和中小盘股差异性分析

发布时间：2018-09-06 17:11

【摘要】：采用2007年1月15日～2011年7月29日间的中证100指数和中证500指数分别代表我国大盘股和中小盘股的走势,采集2种指数1分钟的高频数据生成指数收益率序列,利用统计方法和多重分形-降趋脉动分析(MF-DFA)方法,比较研究2种指数整体的统计特性和多重分形特性;并基于每个交易日数据的多重分形分析,构造新的风险度量指标MFV,用以比较大盘股和中小盘股的风险。结果表明:①2种指数整体分布呈现尖峰胖尾分布,中间部分均服从双指数分布,尾部极端收益率服从幂率分布;②中证500指数整体的谱宽度较大;③中证500指数的日MFV有70%左右大于中证100。由这些不同均可得到大盘股的风险小于中小盘股这一结论,也弥补了传统风险测度指标在金融市场复杂系统中的不足。
[Abstract]:From January 15, 2007 to July 29, 2011, the CSI 100 index and the CSI 500 index represent the trend of Chinese large-cap stocks and small-and-medium-sized stocks, respectively. The high frequency data of the two indices are collected in one minute to generate the index yield series. The statistical and multifractal characteristics of the two indices are compared by using the statistical method and the multifractal de-pulsation analysis (MF-DFA) method, and based on the multifractal analysis of the data of each trading day, A new risk measurement index, MFV, is constructed to compare the risk of large and medium cap stocks. The results showed that the whole distribution of the 12 indices showed a sharp and fat tail distribution, the middle part of the distribution was distributed from the double exponent, and the tail extreme rate of return from the distribution of power ratio was larger than that of the whole spectrum of the 500 index. About 70% of the daily MFV of the CSI 500 index is larger than that of the CSI 500 index. From these differences, we can get the conclusion that the risk of large-cap stocks is smaller than that of small and medium-sized stocks, and it also makes up for the deficiency of traditional risk measurement index in the complex financial market system.
【作者单位】：华东理工大学商学院;上海财经大学统计与管理学院;
【基金】：国家自然科学基金资助项目(71171083) 教育部人文社会科学研究基金资助项目(09YJC630075)
【分类号】：F830.91

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