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We provide the theoretical foundation for the recently proposed tests of equal forecast accuracy and encompassing by Pitarakis (2023a,b), when the competing forecast specification is that of a factor-augmented regression model. This should be of interest for practitioners, as there is no theory justifying the use of these simple and powerful tests in such context. In pursuit of this, we employ a novel theory that allows factor loadings to be homogeneously/heterogeneously weak (empirically well-documented), and track their effect on the forecast comparison problem.
