A Robust Residual-Based Test for Structural Changes in Factor Models

TL;DR

This paper introduces a residual-based test for detecting structural changes in factor models that is robust, easy to implement, and effective against various change types and error dependencies, with proven theoretical properties and practical validation.

Contribution

It develops a new robust testing procedure for structural changes in factor models, including a novel CLT for panel data with dependence, and provides a simulation-based method for critical value selection.

Findings

Test performs well in simulations with high size and power.

Method is robust to over-specified factors and error correlations.

Real-world application confirms practical effectiveness.

Abstract

In this paper, we propose an easy-to-implement residual-based specification testing procedure for detecting structural changes in factor models, which is powerful against both smooth and abrupt structural changes with unknown break dates. The proposed test is robust against the over-specified number of factors, and serially and crosssectionally correlated error processes. A new central limit theorem is given for the quadratic forms of panel data with dependence over both dimensions, thereby filling a gap in the literature. We establish the asymptotic properties of the proposed test statistic, and accordingly develop a simulation-based scheme to select critical value in order to improve finite sample performance. Through extensive simulations and a real-world application, we confirm our theoretical results and demonstrate that the proposed test exhibits desirable size and power in practice.