Determining the number of factors in approximate factor models by twice K-fold cross validation

We propose a data driven determination method of the number of factors by cross validation (CV) in approximate factor models. A K-fold CV is applied along each of the two directions (individual and time) of a panel dataset. We prove the consistency of the proposed twice K-fold CV under mild conditions. Monte Carlo simulations demonstrate superior and robust performance of our selection method in comparison with existing approaches, especially at small panels with moderate units or time lengths. An empirical application to identify factor numbers in the UK is provided. (C) 2020 Elsevier B.V. All rights reserved.