Probabilistic Quantile Factor Analysis

Abstract

This paper extends quantile factor analysis to a probabilistic variant that incorporates regularization and computationally efficient variational approximations. We establish through synthetic and real data experiments that the proposed estimator can, in many cases, achieve better accuracy than a recently proposed loss-based estimator. We contribute to the factor analysis literature by extracting new indexes of low, medium, and high economic policy uncertainty, as well as loose, median, and tight financial conditions. We show that the high uncertainty and tight financial conditions indexes have superior predictive ability for various measures of economic activity. In a high-dimensional exercise involving about 1000 daily financial series, we find that quantile factors also provide superior out-of-sample information compared to mean or median factors.

Keywords: variational Bayes, penalized factors, quantile regression JEL Classification: C11, C31, C32, C52, C53

JEL Classification: C11, C31, C32, C52, C53