Testing for moving average regression disturbances

This paper considers a locally optimal procedure for testing for first order moving average disturbances in the linear regression model. For this hypothesis testing problem, the Durbin‐Watson test is shown to be approximately locally best invariant while the new test is most powerful invariant in a given neighbourhood of the alternative hypothesis. Two versions of the test procedure are recommended for general use; one for problems involving positively correlated disturbances and one for negatively correlated disturbances. An empirical comparison of powers shows the clear superiority of the recommended tests over the Durbin‐Watson test. Selected bounds for the tests' significance points are tabulated.