基于经验模态分解的上证综合指数时间序列分析

摘要

Shanghai composite index ( SCI) is decomposed into a series of intrinsic mode functions (IMFs) and a residual using the empirical mode decomposition (EMD) method. Fluctuation properties of each IMF are obtained. A basic statistic analysis and fitting on the distribution of the IMFs reveal that the "leptokurtosis, fat-tailed" characteristics of IMFs obey (-distribution with a degree of freedom 3. Fluctuation cycles and characteristics on widely concerned time scales, such as week, month, half year, etc., are obtained. Particularly, fluctuation properties of typical rising and dropping periods are analyzed.%采用经验模态分解(empirical mode decomposition,EMD)方法对上证综合指数(Shanghai composite index,SCI)进行研究,将其分解为多个内模函数(intrinsic mode functions,IMFs)和剩余项之和.通过对各阶内模函数进行基本统计分析和分布拟合,发现其“尖峰厚尾”的特点基本服从自由度为3的t分布.通过对各阶内模函数进行周期性分析,揭示各阶模态间不同的波动信息,并得到周、月、半年等时间尺度股指的波动特点,以及典型上涨和下跌时段的波动周期和波动特点.