In macroeconomic forecasting, principal component analysis (PCA) has been the most preva-lent approach to the recovery of factors, which summarize information in a large set of macro predictors. Nevertheless, the theoretical justification of this approach often relies on a con- venient and critical assumption that factors are pervasive. This thesis, however, delves into the terrain of ’weak factors’—elements that are not pervasively influential but nonetheless critical for precise predictions. To incorporate information from weaker factors, in Chapter 1, we propose a new predic- tion procedure based on supervised PCA, which iterates over selection, PCA, and projection. The selection step finds a subset of predictors most correlated with the prediction target, whereas the projection step permits multiple weak factors of distinct strength. Our ap- proach is theoretically supported within an asymptotic framework where sample size and cross-sectional dimension may increase at potentially different rates. In Chapter 2, we transition the discussion to empirical asset pricing, where weak factors and the selection of test assets are identified as interconnected challenges. Since weak fac- tors are those to which test assets have limited exposure, an appropriate selection of test assets can improve the strength of factors. Building on this insight, we design the SPCA methodology for risk premia estimation and factor model diagnosis. The theoretical efficacy of this approach is validated through its asymptotic properties. Chapter 3 showcases SPCA’s empirical applications. The first application highlights the role of weak factors in predicting inflation, industrial production growth, and changes in unemployment. The second application employs SPCA to estimate the risk premia of a variety of observable factors, and to diagnose observable factor models. All chapters are adopted from my joint research work with Stefano Giglio and Dacheng Xiu in Giglio et al. [2023] and Giglio et al. [2021].