Realized volatility has become a standard tool for measuring latent variation in financial assets, and its forecasting is crucial for a wide range of financial applications. We propose a network-based model for forecasting a vector of realized variance processes through the heterogeneous autoregressive (HAR) approach. The generalised network HAR (GNHAR) model incorporates cross-sectional spillovers through a directed graph inferred from Granger-causality tests or connectedness indices, yielding a parsimonious multivariate time series model specification. In an application to ten equities over tranquil and crisis regimes, the proposed GNHAR model improves upon common HAR model benchmarks under both short- and long-term forecasting. We also compare the network-based specification when the jump-continuous decomposition or node-specific option-implied variances are considered. Finally, unlike overparameterised models, our approach yields a concise set of parameters that track the strengthening or weakening of cross-market dependencies, providing a time-varying quantitative assessment of market stability.

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