Covariance design vs. robust loss

Background: The robustness of the RoME procedure is demonstrated against increasing proportions of bad forecasts, where using the simple OLS covariance design with LAD loss provides the best performance improvement. This suggests that complex covariance structures might be unnecessary when a robust loss function is employed.

Question / Future Work: Further systematic investigation is warranted regarding the necessary complexity of the covariance matrix estimation for out-of-sample forecasting errors when using robust loss functions in reconciliation, particularly to determine when simple designs, like OLS, suffice compared to more intricate ones.