On LM type tests for seasonal unit roots in quarterly data

In this paper the application of the score principle to test for unit roots in seasonal processes is analysed. In particular, tests based on the procedure proposed by Hylleberg et al.(1990, Journal of Econometrics, 44, 215–38) (HEGY) are introduced and the respective limit distributions derived in a local-to-unity context. It is shown that these statistics converge to distributions already tabulated in the literature. A Monte Carlo investigation contrasting the conventional HEGY procedure with the new Lagrange multiplier HEGY type tests reveals the latter to have a better performance. Furthermore, the limiting powers of the test statistic are also computed and compared.