Large-dimensional Robust Factor Analysis with Group Structure

TL;DR

This paper develops a robust factor analysis method for large-dimensional data with group structures, leveraging hierarchical clustering and an information criterion to improve estimation accuracy in heavy-tailed datasets.

Contribution

It introduces a novel approach combining hierarchical clustering and robust estimation for identifying group structures in large factor models, with proven consistency and efficiency gains.

Findings

Consistent estimation of group membership and number of groups.

Achieves efficiency gains over traditional methods without group information.

Performs well in simulations and real data with heavy tails.

Abstract

In this paper, we focus on exploiting the group structure for large-dimensional factor models, which captures the homogeneous effects of common factors on individuals within the same group. In view of the fact that datasets in macroeconomics and finance are typically heavy-tailed, we propose to identify the unknown group structure using the agglomerative hierarchical clustering algorithm and an information criterion with the robust two-step (RTS) estimates as initial values. The loadings and factors are then re-estimated conditional on the identified groups. Theoretically, we demonstrate the consistency of the estimators for both group membership and the number of groups determined by the information criterion. Under finite second moment condition, we provide the convergence rate for the newly estimated factor loadings with group information, which are shown to achieve efficiency gains compared to those obtained without group structure information. Numerical simulations and real data analysis demonstrate the nice finite sample performance of our proposed approach in the presence of both group structure and heavy-tailedness.