High-Dimensional Factor Models with An Incomplete Set of Covariates: An Improved Estimator for Factor Analysis

Description

Factor models are widely used in economics and finance to analyze large datasets and uncover the fundamental drivers behind complex data patterns. However, challenges arise when modeling time-varying factor loadings using an incomplete set of covariates. In this research project, we propose a novel framework that addresses these challenges by incorporating both time-invariant and time-varying components in the factor loading matrix, leading to improved estimation of underlying factors. Our model considers two components in the factor loadings: one that varies over time based on observed covariates and another that remains constant and unexplained by the observed covariates. This approach offers a robust method to capture the essential factors and effectively model the time variations of the factor loadings. We develop an algorithm to compute estimators for the underlying factors and the two components in the factor loading matrix, and establish the consistency of our proposed estimators. Simulation results demonstrate that our algorithm produces more efficient estimators compared to existing methods. Moving forward, our research will focus on exploring the asymptotic distributions of our estimators and addressing model specification issues. We will develop a specification test to evaluate the contribution of the time-invariant component to the factor loading matrix and design a reliable method to estimate the number of factors in our model. Furthermore, we aim to extend our framework to handle scenarios where the observed covariates fail to predict the loadings on certain factors, ensuring the robustness and consistency of our factor estimator. By analyzing the large sample properties of our estimator, we will confirm its ability to handle situations where existing methods that rely solely on incomplete covariates fail to fully restore the entire factor space. This further highlights the robustness and effectiveness of our proposed framework in capturing the underlying factors even in scenarios with limited covariate information.