Composite Quantile Factor Models

This paper introduces the method of composite quantile factor model for factor analysis in high-dimensional panel data. We propose to estimate the factors and factor loadings across different quantiles of the data, allowing the estimates to better adapt to features of the data at different quantiles while still modeling the mean of the data. We develop the limiting distribution of the estimated factors and factor loadings, and an information criterion for consistent factor number selection is also discussed. Simulations show that the proposed estimator and the information criterion have good finite sample properties for several non-normal distributions under consideration. We also consider an empirical study on the factor analysis for 246 quarterly macroeconomic variables. A companion R package cqrfactor is developed.