Testing for fourth-order autocorrelation in regression disturbances when first-order autocorrrelation is present

This paper considers the problem of testing the null hypothesis of first-order autoregressive disturbances in the linear regression model against the alternative that the disturbances follow a joint first-order, simple fourth-order autoregressive process. The class of approximate point-optimal invariant tests are discussed and rules are given for choosing an appropriate member from this class of tests. The beneficial nature of these rules is illustrated by a limited empirical power comparison which shows the recommended test has good small-sample power properties.