More Powerful LM Unit Root Tests with Non-normal Errors

Abstract

This paper extends the Lagrange Multiplier (LM) unit toot tests of Schmidt and Phillips (Oxford Bull. Econ. Stat. 54:257–285, 1992) to utilize information contained in non-normal errors. The new tests adopt the Residual Augmented Least Squares (RALS) estimation procedure of Im and Schmidt (J. Econ. 144:219–233, 2008). This paper complements the work of Im et al. (More powerful unit root tests with nonnormal errors, manuscript, 2012) who adopt the RALS procedure for DF-based tests. We provide the relevant asymptotic distribution and the corresponding critical values of our new tests. The RALS-LM tests show improved power over the RALS-DF tests. The main advantage of the RALS-LM tests lies in the invariance feature that the distribution does not depend on the nuisance parameter in the presence of level-breaks.