Econometric theory paper: We provide theoretical grounds for the tests of equal forecasting accuracy and encompassing recently proposed in Pitarakis (2023a) and Pitarakis (2023b), when the competing forecasting model specification is that of a factor-augmented regression, whose loadings are allowed to be homogeneously/heterogeneously weak. This should be of interest for practitioners, as at the moment there is no theory available to justify the use of these simple and powerful tests in such context. References: Pitarakis, J.-Y. (2023a). Direct multi-step forecast based comparison of nested models via an encompassing test. arXiv preprint arXiv:2312.16099. Pitarakis, J.-Y. (2023b). A novel approach to predictive accuracy testing in nested envi- ronments. Econometric Theory, 1–44.