Determining number of factors under stability considerations

TL;DR

This paper introduces a new method for selecting the number of factors in linear models that emphasizes stability, using an instability measure based on principal angles and supported by random matrix theory.

Contribution

The paper presents a novel stability-based criterion for factor number determination that requires weaker assumptions and is validated through simulations and real data.

Findings

The proposed method is consistent under weaker asymptotic conditions.

Simulation studies show improved accuracy over existing methods.

Application to real data demonstrates practical effectiveness.

Abstract

This paper proposes a novel method for determining the number of factors in linear factor models under stability considerations. An instability measure is proposed based on the principal angle between the estimated loading spaces obtained by data splitting. Based on this measure, criteria for determining the number of factors are proposed and shown to be consistent. This consistency is obtained using results from random matrix theory, especially the complete delocalization of non-outlier eigenvectors. The advantage of the proposed methods over the existing ones is shown via weaker asymptotic requirements for consistency, simulation studies and a real data example.