On factor models with random missing: EM estimation, inference, and cross validation

We consider the estimation and inference in approximate factor models with random missing values. We show that with the low rank structure of the common component, we can estimate the factors and factor loadings consistently with the missing values replaced by zeros. We establish the asymptotic distributions of the resulting estimators and those based on the EM algorithm. We also propose a cross-validation-based method to determine the number of factors in factor models with or without missing values and justify its consistency. Simulations demonstrate that our cross validation method is robust to fat tails in the error distribution and significantly outperforms some existing popular methods in terms of correct percentage in determining the number of factors. An application to the factor-augmented regression models shows that a proper treatment of the missing values can improve the out-of-sample forecast of some macroeconomic variables. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This study focuses on estimation and inference in approximate factor models with random missing values, demonstrating consistent estimation of factors and factor loadings with a low rank structure of the common component. The asymptotic distributions of estimators and those based on the EM algorithm are established, with a proposed cross-validation method to determine the number of factors in factor models. Simulations show the robustness of the cross-validation method in the presence of fat tails in the error distribution and its superior performance in determining the number of factors compared to existing methods.