Essays on large-dimensional factor models

This dissertation advances the estimation and inferential theory of approximate factor models. Chapter 1 proposes a cross-section subsampling scheme that consistently reproduces the distribution of Principal Component (PC) factors even in the presence of general cross-sectional dependence amongst idiosyncratic errors. Further, it introduces a novel bias-corrected split-panel estimator for the estimation of the covariance matrix of the PC factors. Chapter 2 develops tests of equal forecast accuracy and encompassing that evaluate the predictive power of latent factors - which are estimated using cross-section averages of grouped variables - in factor-augmented regressions. It demonstrates theoretically that these tests are robust to an overspecification in the number of factors, are invariant to structural breaks in the factor loadings and accommodate persistent regressors. Chapter 3 proposes a novel methodology - which is inspired by the technique of binary segmentation - for estimating the threshold in sparse large-dimensional covariance matrices, which are fundamental to uncovering the residual dependence among the idiosyncratic terms of an approximate factor model.