Empirical Mode Decomposition and Graph Transformation of the MSCI World Index: A Multiscale Topological Analysis for Graph Neural Network Modeling

ArXiv ID: 2512.12526 “View on arXiv”

Authors: Agustín M. de los Riscos, Julio E. Sandubete, Diego Carmona-Fernández, León Beleña

Abstract

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.

Keywords: Empirical Mode Decomposition, Graph Neural Networks, Time Series Decomposition, MSCI World, Visibility Graphs

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail
  • Why: The paper involves advanced signal processing (CEEMDAN) and graph theory with mathematical formulations, while providing a detailed empirical methodology with specific dataset descriptions, statistical tests, and topological analysis, making it highly backtest-ready.
  flowchart TD
    A["Research Goal: Analyze MSCI World index<br>using EMD and GNNs"] --> B["Data Input: MSCI World<br>Index Time Series"]
    B --> C["Method: CEEMDAN Decomposition<br>into 9 IMFs"]
    C --> D["Graph Transformation:<br>4 Methods per IMF"]
    D --> E["Topological Analysis:<br>Scale-Dependent Structure"]
    E --> F["Key Outcome: High-Freq IMFs<br>Dense Small-World Graphs"]
    E --> G["Key Outcome: Low-Freq IMFs<br>Sparse Long-Path Graphs"]
    F --> H["Conclusion: Guidance for<br>GNN Architecture Design"]
    G --> H