Estimating a Large Covariance Matrix in Time-varying Factor Models

TL;DR

This paper introduces two new estimators for high-dimensional, time-varying covariance matrices based on factor models, demonstrating improved performance over traditional methods through simulations and empirical analysis.

Contribution

The paper develops and analyzes two novel estimators for time-varying covariance matrices in high dimensions, incorporating smoothly changing factor loadings and characteristics.

Findings

Time-varying estimators outperform time-invariant ones.

Characteristics improve loading estimation when they explain true loadings.

Estimators have favorable convergence rates.

Abstract

This paper deals with the time-varying high dimensional covariance matrix estimation. We propose two covariance matrix estimators corresponding with a time-varying approximate factor model and a time-varying approximate characteristic-based factor model, respectively. The models allow the factor loadings, factor covariance matrix, and error covariance matrix to change smoothly over time. We study the rate of convergence of each estimator. Our simulation and empirical study indicate that time-varying covariance matrix estimators generally perform better than time-invariant covariance matrix estimators. Also, if characteristics are available that genuinely explain true loadings, the characteristics can be used to estimate loadings more precisely in finite samples; their helpfulness increases when loadings rapidly change.