A Unified Framework for Estimation of High-dimensional Conditional Factor Models

Abstract: This paper develops a general framework for estimation of high-dimensional conditional factor models via nuclear norm regularization. We establish large sample properties of the estimators, and provide an efficient computing algorithm for finding the estimators as well as a cross validation procedure for choosing the regularization parameter. The general framework allows us to estimate a variety of conditional factor models in a unified way and quickly deliver new asymptotic results. We apply the method to analyze the cross section of individual US stock returns, and find that imposing homogeneity may improve the model's out-of-sample predictability.