Interpretable Sparse Proximate Factors for Large Dimensions

This article proposes sparse and easy-to-interpret proximate factors to approximate statistical latent factors. Latent in a large-dimensional factor model can be estimated by principal component analysis (PCA), but are usually hard interpret. We obtain that easier interpret shrinking the PCA weights setting them zero except for largest absolute ones. show constructed with only 5%–10% of data sufficient almost perfectly replicate population without actually assuming structure or loadings. Using extreme value theory we explain why substitutes non-sparse derive analytical asymptotic bounds correlation appropriately rotated These provide guidance on how construct In simulations empirical analyses financial portfolio macroeconomic data, illustrate close average correlations around 97.5%, while being interpretable.