基于改进希尔伯特-黄变换算法的碳市场价格多尺度分解

Carbon Price Multiscale Decomposition Using an Improved Hilbert-Huang Transform Algorithm

作为一种新型非线性、非稳态数据的自适应处理算法,希尔伯特-黄变换(Hilbert-Huang Transform,HHT),近年来开始应用到人文社会科学领域。HHT的核心是经验模态分解(Empirical Mode Decomposition,EMD)算法。EMD分解过程中常会产生模态混叠和端点效应现象,造成分解结果失真。针对碳市场价格多尺度特征,改进HHT算法以提高碳市场价格多尺度分解质量。引入高斯白噪声到EMD分解中,建立集成EMD(Ensemble EMD,EEMD)算法来抑制EMD分解中存在的模态混叠现象;针对EEMD分解过程中存在的端点效应问题,通过5种端点延拓方法的比较,改进EEMD算法,得出适合碳市场价格多尺度分解的延拓方法;将改进HHT算法应用于两个不同到期时间的欧盟碳期货价格(DEC12、DEC14)进行多尺度分解,结果表明:改进HHT算法能显著提高碳市场价格分解精度,扩大了HHT在碳市场价格多尺度分析中的应用范围。

As a novel adaptive multiscale processing algorithm for non-linear and non-stationary data, Hilbert-Huang Transform（HHT） has been widely used in the fields of natural sciences and engineering, and has been applied in the field of humanities and social sciences in recent years. Empirical mode decomposition（EMD）is the core of HHT algorithm. In the processing of EMD, there may exist the phenomena of mode-mixing and end effect, which can lead to the decomposition results distortion. Aiming at carbon price multiscale decomposition, the HHT algorithm was improved to enhance the quality of EMD decomposition. Firstly, the ensemble EMD（EEMD）algorithm was built by introducing the Gaussian white noises into the EMD decomposition, which was applied to solve the mode-mixing phenomenon during EMD. Next, aiming at the end effect phenomenon, the extension method which was appropriate for dealing with carbon price was obtained by comparing five different kinds of extension methods for EEMD.Finally, taking two carbon future prices with different maturities called DEC12 and DEC14 under the European Union Emissions Trading System（EU ETS）as samples, empirical results showed that the improved HHT algorithm could effectively improve decomposition accuracy, and the application of HHT was extended.