Graph Signal Processing for Global Stock Market Realized Volatility Forecasting

Paper: arXiv 2410.22706

Authors: Zhengyang Chi, Junbin Gao, Chao Wang

Abstract

This paper introduces an innovative realized volatility (RV) forecasting framework that extends the conventional Heterogeneous autoregressive (HAR) model via integrating Graph Signal Processing (GSP). The study first evaluates various constructions of volatility-interrelationship networks by analyzing how the associated graph signal energy tracks global financial market volatility. Volatility spillovers are subsequently embedded into the proposed framework, which employs the graph Fourier transform (GFT) and its inverse to effectively capture global stock market dynamics in both the spectral and spatial domains. The framework not only provides a global context for modeling the volatility interrelationships, but also captures the nonlinearity and directionality of the volatility spillover effect. The empirical study using RV data of $24$ global stock market indices compares short-, mid- and long-term RV forecasts with various HAR-type benchmarks and a graph neural network-based HAR model. The proposed model consistently outperforms all comparators, demonstrating the effectiveness of integrating GSP into the HAR model for RV forecasting.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a novel application of Graph Signal Processing (GSP) and Graph Signal Energy to evaluate volatility network constructions and enhance HAR model forecasts across 24 global indices. It balances solid mathematical foundations (magnetic Laplacians, graph Fourier transform) with rigorous empirical backtesting and open-source code availability.

Research Flowchart

  flowchart TD
    A[Research Goal: Improve Global Stock Market RV Forecasting via GSP] --> B[Data Inputs: 24 Global Stock Market Indices RV Data]
    B --> C[Construct Volatility Networks & Evaluate Signal Energy]
    C --> D[Embed Volatility Spillovers using Graph Fourier Transform]
    D --> E[Combine GSP Spatial/Spectral Dynamics with HAR Model]
    E --> F[Forecast Short-, Mid-, & Long-Term Volatility]
    F --> G[Outcome: Outperforms Standard HAR & GNN Benchmarks]