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.

翻译：本研究将经验模态分解应用于MSCI全球指数，并将得到的本征模态函数转化为图表示，以实现图神经网络的建模。通过使用CEEMDAN方法，我们提取了涵盖高频波动至长期趋势的九个本征模态函数。每个本征模态函数通过四种时间序列到图的转换方法转化为图结构：自然可见性图、水平可见性图、递归图与转移图。拓扑分析揭示了明显的尺度依赖结构：高频本征模态函数产生密集、高连接的小世界图，而低频本征模态函数则生成具有较长特征路径长度的稀疏网络。基于可见性的方法对振幅变化更为敏感，通常产生更高的聚类系数；递归图则能更好地保持时间依赖性。这些结果为针对分解成分的结构特性设计图神经网络架构提供了指导，有助于实现对金融时间序列更有效的预测建模。