A new test for fourth-order autoregressive disturbances

This paper proposes a new test for simple fourth-order autoregressive disturbances in the linear regression model. The test is shown to be most powerful invariant in a given neighourhood of the alternative hypothesis for all design matrices. An empirical power comparison suggests that the test is generally more powerful than the Wallis test, the difference in power probably being slight for most economic applications, although for certain design matrices, the power advantage of the new test is very real. Selected bounds for the test's significance points are tabulated.