Tests for a Level Shift and the Non-Monotonic Power Problem

Abstract

This paper investigates tests for a shift in mean for serially correlated time series. It is known in the literature that LM-type tests suffer from the so-called non-monotonic power problem in the sense that the power decreases even if the magnitude of break gets larger. On the other hand, Wald-type tests do not have the non-monotonic power problem but they tend to suffer from over-size distortion. Several methods to overcome these problems have been developed in the literature and we propose a new test with a good finite sample property by modifying the existing test. We investigate the finite sample property of our new method and it turns out that our test performs better than the other tests in view of both size and power.