## 金融时间序列的Hilbert谱分析研究

本文采用HHT方法对深证指数以及万科指数进行了分析，得到的主要结果如下：

Analysis Financial Time Series by Hilbert Spectral
Abstract: The analysis of financial time series has become an essential part in the study of  financial market. As we know, the financial time series is a non-linear and non-stationary process. Hilbert-Huang Transform ( HHT ) is a new method to analyze non-linear and non-stationary problems. HHT consists of two parts: Empirical Mode Decomposition ( EMD ) and Hilbert spectral analysis. EMD is the basic part , and it is widely applied and efficient.
Shenzhen stock index and Vanke index are investigated in this paper using the HHT method, the main results obtained are as follows:
First of all, the Shen Zhen and Vanke stock price wave motions in different modes are obtained through the EMD, and the movements in the last ten years. Then the index of the center frequency and wave are got by Hilbert spectral analysis . The general trend on stock price is analyses.

Secondly, according to the stock price in the previous ten years, gray model was used to predict the Shen Zhen stock index and Vanke price index's general trend in 2011.  And  the real value and the predict value are compared and analysised about the different and similar points between them.
Keyword: Hilbert-Huang Transform;EMD;IMF

1.1研究背景和意义    1
1.2 研究现状    2
1.3 研究目的与思路    3

2.1 EMD分解方法    4
2.2 Hilbert谱分析    7
2.3 小结    7

3.1 时间–频率分析的深证指数价格数据    9
3.2 时间–频率分析的万科股份价格数据    12
3.3 数据分析    14
3.3.1深证成指与个股的关系    14
3.3.2 股票指数不同尺度模态相关性分析    16
3.4 运用灰度模型预测数据    18
3.4.1累加生成运算    18
3.4.2 灰色系统建模，用最小二乘法估计得到参数    18
3.4.3 解一阶线性微分方程，得到时间响应函数    19
3.4.4 数据预测值    19
3.5 小结    21

4.1结论    22
4.2 展望    22

1.1研究背景和意义

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