Monotonic Power in Tests for Changing Mean

Abstract. Many tests for a changing mean in a time series require the estimation of a long run variance. Recent research of Crainiceanu and Vogelsang (2001) suggests that tests involving a long run variance estimate exhibit non-monotonic power. We propose an estimate of long run variances that allows for a time varying mean. In this way, we are able to avoid non-monotonic power while still retaining the same asymptotic distribution under the null hypothesis of constant parameters. A Monte Carlo experiment illustrates the increased power.