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

2022-09-01

Social Science Research Network

AI Summary

Existing conditional latent factor models lack a unified, robust estimation framework under high-dimensional settings. Method: This paper proposes a general estimation framework based on nuclear norm regularization, enabling joint convex optimization for multiple model classes—including conditional principal component analysis and factor-augmented regression. Theoretical analysis establishes statistical consistency and convergence rates under high-dimensional asymptotics. Contribution/Results: We introduce a novel homogeneity constraint that substantially improves out-of-sample prediction accuracy; develop a scalable algorithm integrated with a data-driven cross-validation procedure for hyperparameter selection. Empirically, the method is applied to predicting U.S. stock cross-sectional returns, achieving significantly higher forecasting precision than state-of-the-art alternatives. Additionally, we derive several new asymptotic inference results, including valid confidence intervals for estimated factors and loadings under high-dimensional dependence.

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.

Problem

• Estimates high-dimensional conditional latent factor models
• Unifies various conditional factor model estimations
• Improves out-of-sample predictability in stock returns

Innovation

• Constrained nuclear norm regularization for factor estimation
• Cross-validation for regularization parameter selection
• Unified framework enabling new asymptotic results