Several widely used tests for a changing mean exhibit nonmonotonic power in ¯nite samples due to \incorrect" estimation of nuisance parameters under the alternative. In this paper, we study the issue of nonmonotonic power in testing for changing mean. We investigate the asymptotic power properties of the tests using a new framework where alternatives are characterized as having \large" changes. The asymptotic analysis provides a theoretical explanation to the power problem. Modi¯ed tests that have monotonic power against a wide range of alternatives of structural change are proposed. Instead of estimat- ing the nuisance parameters based on ordinary least squares residuals, the proposed tests use modi¯ed estimators based on nonparametric regression residuals. It is shown that tests based on the modi¯ed long-run variance estimator provide an improved rate of divergence of the tests under the alternative of a change in mean. Tests for structural breaks based on such an estimator are able to remain consistent while still retaining the same asymptotic distribution under the null hypothesis of constant mean.
