Covariance Prediction for Financial Factor Returns: A Comparative Analysis of CM-IEWMA and MGARCH

Precise estimation of covariance matrices is essential in finance, playing a key role in portfolio optimization and robust risk management. This paper systematically evaluates and compares several covariance prediction models, specifically Rolling Window (RW), Exponentially Weighted Moving Average (EWMA), Iterated EWMA (IEWMA), Dynamic Conditional Correlation Multivariate GARCH (MGARCH), and Combined Multiple IEWMA (CM-IEWMA), focusing exclusively on widely-used financial factor returns from 1990–2022. Using direct statistical metrics including Mean Squared Error (MSE), Log-Likelihood, and Log-Likelihood Regret, we demonstrate that dynamic methods (MGARCH and CM-IEWMA) substantially outperform traditional benchmarks. Although MGARCH shows marginally superior numerical accuracy, statistical tests reveal no significant predictive difference compared to the simpler CM-IEWMA. Importantly, CM-IEWMA offers comparable responsiveness and adaptability, combined with significantly lower computational complexity, making it particularly attractive for practical financial applications. The study highlights CM-IEWMA's potential as an effective alternative to MGARCH, balancing computational simplicity with predictive robustness.