Lagrange multiplier unit root test in the presence of a break in the innovation variance

We show that the Lagrange multiplier (LM) unit root test exhibits size distortions when a break in the innovation variance exists but is ignored. We develop a modified LM unit root test that is based on a generalized least-squares transformation of the original series. The asymptotic null distribution of the new modified LM unit root test is derived. Finite-sample simulation evidence shows that the modified LM unit root test maintains its size and has reasonable power against the trend stationary alternative.