Enhancing financial risk management: a novel multivariate neural network approach for realized covariance matrix prediction

Abstract Accurate forecasting of realized covariance matrices (RCMs) is essential for informed portfolio allocation, asset pricing, and risk management. While artificial neural networks have shown promise in predicting realized volatility for individual stocks, their application to forecasting full RCMs remains largely unexplored. This study introduces realized covariance matrix neural basis expansion analysis with exogenous variables (RCM-NBEATSx), a novel multivariate neural network model that combines the NBEATSx architecture with matrix exponential and logarithm transformations to ensure positive semidefiniteness. Through comprehensive testing on four diverse datasets—encompassing equities, exchange rates, commodities, and stock indexes—RCM-NBEATSx consistently outperforms established benchmark models. It achieves improvements of 12.25%, 22.58%, and 31.23% in terms of the RMSE, MAE, and QLIKE for realized volatility forecasts, respectively, and yields 13.38% and 16.43% enhancements in the RMSE and MAE for realized correlation forecasts, respectively. These statistically significant gains highlight the model’s superior predictive accuracy over current state-of-the-art approaches. In conclusion, RCM-NBEATSx stands as a robust and versatile forecasting tool that can meaningfully enhance decision-making in financial markets, offering more reliable covariance matrix predictions that directly support more effective risk management and portfolio optimization strategies.