New LM tests for unit roots in seasonal ar processes

On the basis of marginal likelihood of the residual vector which is free of nuisance mean parameters, we propose new Lagrange Multiplier seasonal unit root tests in seasonal autoregressive process. The limiting null distribution of the tests is the standardized X-2-distribution. A Monte-Carlo simulation shows the new tests are more powerful than the tests based on the ordinary least squares (OLS) estimator, especially for large number of seasons and short time spans.