用经验模态分解和图转换分析全球股市，为金融时序建模提供新思路。
Empirical Mode Decomposition and Graph Transformation of the MSCI World Index: A Multiscale Topological Analysis for Graph Neural Network Modeling
- 将指数分解为9个不同频率的内在模态函数，再转为图结构用于建模
- 高频分量生成密集小世界图，低频分量则形成稀疏长路径网络
- 可视图对波动敏感，递归图更保时间依赖性，适合不同场景建模
本研究采用改进的集合经验模态分解（CEEMDAN）对MSCI世界指数进行分解，提取出9个涵盖高频波动到长期趋势的内在模态函数（IMFs）。每个IMF通过四种时序转图方法——自然可视图、水平可视图、递归图和转移图——转化为图表示，用于图神经网络建模。拓扑分析显示，高频IMF生成密集、高度连通的小世界图，而低频IMF则形成稀疏网络且特征路径更长。可视图方法对振幅变化更敏感，通常产生更高聚类系数；递归图能更好保留时间依赖关系。这些发现为针对分解成分结构特性的图神经网络架构设计提供了依据，有助于提升金融时序预测建模效果。
原文摘要 · Abstract (English)
This study applies Empirical Mode Decomposition (EMD) to the MSCI World index and converts the resulting intrinsic mode functions (IMFs) into graph representations to enable modeling with graph neural networks (GNNs). Using CEEMDAN, we extract nine IMFs spanning high-frequency fluctuations to long-term trends. Each IMF is transformed into a graph using four time-series-to-graph methods: natural visibility, horizontal visibility, recurrence, and transition graphs. Topological analysis shows clear scale-dependent structure: high-frequency IMFs yield dense, highly connected small-world graphs, whereas low-frequency IMFs produce sparser networks with longer characteristic path lengths. Visibility-based methods are more sensitive to amplitude variability and typically generate higher clustering, while recurrence graphs better preserve temporal dependencies. These results provide guidance for designing GNN architectures tailored to the structural properties of decomposed components, supporting more effective predictive modeling of financial time series.
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