Size performance of the Lagrange Multiplier (LM) unit root test in the presence of a neglected break under the null

Abstract

Via simulation, the size of the lagrange multiplier (LM) unit root test is examined, when there is a neglected level or trend break under the null hypothesis. It is found that unlike other more popular unit root tests in the literature, the size of the LM is not distorted/inflated. Thus, rejections of the LM tests must not be viewed as spurious with respect to this issue of neglected breaks.

Notes

¹ However, this modification imposes an unclear restriction and is not recommended in general.

² Note that A new levels estimator for ψ can be defined as . It is also inconsistent (as it is ); it can be proved that .