Outlier-robust methods for forecasting realized covariance matrices

This paper proposes two new approaches to improve the estimation of the coefficients of the multivariate HAR (MHAR) model with the primary purpose of improving forecast performance. A robust estimator of the covariance matrix is adopted to replace the realized covariance matrix while estimating the MHAR model. The robustness to outliers of the new estimator makes the OLS estimation scheme for the MHAR model more reliable. In addition, a robust estimation scheme is developed for the MHAR model, which is based on the multivariate least-trimmed squares method. Both approaches provide significant improvements in forecasting performance based on both statistical loss and portfolio outcomes. The forecast performance of the multivariate HARQ model can also be improved with the proposed approaches, as evidenced by robustness checks.