Inference in Sparsity-Induced Weak Factor Models

In this article, we consider statistical inference for high-dimensional approximate factor models. We posit a weak structure, in which the loading matrix can be sparse and signal eigenvalues may diverge more slowly than cross-sectional dimension, N. propose novel inferential procedure to decide whether each component of loadings is zero or not, prove that controls false discovery rate (FDR) below preassigned level, while power tends unity. This “factor selection” primarily based on debiased version orthogonal regression (SOFAR) estimator; but also applicable principal (PC) estimator. After selection, resparsified SOFAR sparsified PC estimators are proposed their consistency established. Finite sample evidence supports theoretical results. apply our method FRED-MD dataset macroeconomic variables monthly firm-level excess returns constitute S&P 500 index. The results give very strong under identification restrictions exhibit clear associations factors categories variables. Furthermore, uncovers statistically significant residuals Fama-French five regression.