State-Varying Factor Models of Large Dimensions

TL;DR

This paper introduces a new inferential framework for large-dimensional state-varying factor models, combining nonparametric methods with PCA, and demonstrates its effectiveness on financial data.

Contribution

It develops an estimator for state-dependent loadings and factors, derives their asymptotic properties, and introduces a test for changes in factor structure across states.

Findings

State-varying factors improve modeling of treasury yields during different economic states.

The proposed estimator achieves consistent estimation with known convergence rates.

State-dependent factors based on VIX explain more stock return variation.

Abstract

This paper develops an inferential theory for state-varying factor models of large dimensions. Unlike constant factor models, loadings are general functions of some recurrent state process. We develop an estimator for the latent factors and state-varying loadings under a large cross-section and time dimension. Our estimator combines nonparametric methods with principal component analysis. We derive the rate of convergence and limiting normal distribution for the factors, loadings and common components. In addition, we develop a statistical test for a change in the factor structure in different states. We apply the estimator to U.S. Treasury yields and S&P500 stock returns. The systematic factor structure in treasury yields differs in times of booms and recessions as well as in periods of high market volatility. State-varying factors based on the VIX capture significantly more variation and pricing information in individual stocks than constant factor models.