High-Dimensional Granger Causality with GARCH-Filtered Returns: Risk Spillovers Modeling

Abstract

Stock markets are complex systems in which volatility and shocks can propagate rapidly across assets. Therefore, the perception of correlation between stocks is essential for identifying volatility transmission paths and systemic risks. However, the conventional Granger Causality Test is sensitive to the heteroskedastic and heavy-tailed nature of asset returns. This paper integrates the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model with the Post-Double-Selection (PDS) to study how shocks transmit across assets. Each return series is first fitted with the GARCH model, and the conditional variances are utilized to isolate Granger causalities across assets. The framework extends traditional causality analysis to actual financial systems, providing a new perspective on risk transmission and volatility spillovers. The empirical results show that the proposed GARCH-PDS Granger Causality approach substantially improves the detection of contagion pathways and enhances the interpretability of systemic interdependencies, with limited sensitivity to the dimensionality of data. These findings contribute to the econometric modeling of causal linkages across assets and provide practical implications for macroprudential risk monitoring.