Power properties of the CUSUM and CUSUMSQ tests for parameter instability

Abstract

This article investigates the power of CUSUM and CUSUMSQ tests for parameter stability and demonstrates that this depends on the nature of the structural change taking place. If the break is in the intercept of the regression equation then the CUSUM test has higher power. However, if the structural change involves a slope coefficient or the variance of the error term, then the CUSUMSQ test has higher power. This may help to explain why the two tests often produce contradictory findings.