基于EEMD的上证综合指数时间序列的多尺度分析

发布时间：2018-06-09 11:08

本文选题：上证综合指数 + 整体经验模态分解　；参考：《长春工业大学》2014年硕士论文

【摘要】：非线性、非平稳信号处理是近年来数据分析领域的热点问题和难点问题。本文系统总结希尔伯特-黄变换理论,阐述了经验模态分解(Empirical Mode Decomposition, EMD)流程,为了有效地解决数据模态混叠现象,构建整体经验模态分解(Ensemble Empirical Mode Decomposition, EEMD)算法。本文以我国上证综合指数为研究对象,利用EEMD方法对其进行波动性和周期性分析。首先,利用EEMD方法分析上证综合指数,将原始时间序列分解为多个固有模态函数和趋势项,对分解后的固有模态函数进行统计分析和分布拟合,得到其分布的特点。其次,针对上证综合指数序列中的两个典型阶段,即上涨阶段和下跌阶段,分别采用EEMD方法进行分析。最后,通过对各阶模态函数进行波动性和周期性分析,揭示上证综合指数在不同尺度上的波动特点,以及典型上涨和下跌时间段的波动周期和波动特点。引入EEMD算法实现上证综合指数序列的多尺度分析,将给股票数据处理提供一种新的、有效的分析方法,把握股价波动的规律,具有重要的理论意义和应用价值。
[Abstract]:Nonlinear and non-stationary signal processing is a hot and difficult problem in the field of data analysis in recent years. In this paper, the Hilbert-Huang transform theory is systematically summarized, and the empirical Mode decomposition (EMDM) process is expounded. In order to solve the data mode aliasing effectively, the whole empirical Mode decomposition (EEMDM) algorithm is constructed. In this paper, the volatility and periodicity of Shanghai Composite Index are analyzed by EEMD method. Firstly, the composite index of Shanghai Stock Exchange is analyzed by EEMD method, and the original time series is decomposed into several inherent modal functions and trend terms. The statistical analysis and distribution fitting of the decomposed intrinsic modal functions are carried out, and the distribution characteristics of the original time series are obtained. Secondly, the EEMD method is used to analyze the two typical stages of the Shanghai Composite Index sequence, namely, the rising stage and the falling stage. Finally, by analyzing the volatility and periodicity of various modal functions, the volatility characteristics of Shanghai Composite Index on different scales, as well as the fluctuation periods and volatility characteristics of typical rising and falling periods are revealed. The introduction of EEMD algorithm to the multi-scale analysis of Shanghai Composite Index sequence will provide a new and effective analysis method for stock data processing and grasp the law of stock price fluctuation, which has important theoretical significance and application value.
【学位授予单位】：长春工业大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F830.9

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