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We present four novel tests of equal predictive accuracy and encompassing à la Pitarakis (2023, 2025) for factor-augmented regressions, where factors are estimated using cross-section averages (CAs) of grouped series. Our inferential theory is asymptotically normal and robust to an overspecification of the number of factors. Our tests are empirically relevant as they accommodate for different degrees of predictor persistence and remain invariant to the location of structural breaks in the loadings. Monte Carlo simulations indicate that our tests exhibit excellent local power properties. Finally, we apply our tests to the novel EA-MD-QD dataset by Barigozzi et. al. (2024) – which covers the Euro Area as a whole and its primary member countries – and show that factors estimated by CAs offer substantial predictive power.
