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

TL;DR

This paper combines Empirical Mode Decomposition with graph transformations of the MSCI World index to analyze multiscale topological structures, aiding the design of more effective graph neural network models for financial data.

Contribution

It introduces a multiscale topological analysis framework that transforms decomposed financial signals into graphs, revealing scale-dependent structures for improved GNN modeling.

Findings

High-frequency IMFs form dense small-world graphs

Low-frequency IMFs produce sparser networks with longer paths

Visibility methods are more amplitude-sensitive, recurrence better preserves temporal dependencies

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.