Robust Factor Number Specification for Large-dimensional Elliptical Factor Model

TL;DR

This paper introduces robust, efficient estimators for determining the number of factors in large-dimensional elliptical factor models, especially effective with heavy-tailed data, without requiring moment conditions.

Contribution

It proposes a novel estimator based on the multivariate Kendall's tau matrix that is consistent without moment restrictions in large N and T settings.

Findings

Performs well with heavy-tailed data

Comparable to existing methods in Gaussian cases

Demonstrated on macroeconomic data

Abstract

The accurate specification of the number of factors is critical to the validity of factor models and the topic almost occupies the central position in factor analysis. Plenty of estimators are available under the restrictive condition that the fourth moments of the factors and idiosyncratic errors are bounded. In this paper we propose efficient and robust estimators for the factor number via considering a more general static Elliptical Factor Model (EFM) framework. We innovatively propose to exploit the multivariate Kendall's tau matrix, which captures the correlation structure of elliptical random vectors. Theoretically we show that the proposed estimators are consistent without exerting any moment condition when both cross-sections N and time dimensions T go to infinity. Simulation study shows that the new estimators perform much better in heavy-tailed data setting while performing comparably with the state-of-the-art methods in the light-tailed Gaussian setting. At last, a real macroeconomic data example is given to illustrate its empirical advantages and usefulness.