Graph Signal Processing for Global Stock Market Realized Volatility Forecasting

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.