Testing linear regression model with AR(1) errors against a first-order dynamic linear regression model with white noise errors: A point optimal testing approach

We know very little about the performance of point optimal (PO) and approximate point optimal (APO) tests in the presence of unavoidable nuisance parameters. Because marginal likelihood based tests are said to perform well in the presence of unavoidable nuisance parameters, this paper compares the performance of marginal likelihood based APO tests and classical tests using a testing problem which has been largely overlooked by econometric practitioners, namely testing for a static linear regression model with AR(1) errors against a dynamic linear regression model with white noise errors. It is well known that the classical tests are specifically designed for nested testing, they are applied to test for the significance of the dynamic coefficient of a dynamic linear regression model with AR(1) errors.