Testing for stationarity in series with a shift in the mean. A fredholm approach

Abstract

This paper analyses the normalised Locally Best Invariant statistic for testing the null hypothesis of stationarity around a level, showing its divergence when applied to series with a shift in its mean. This fact suggests an extension of the test allowing the study of stationarity around a level with an exogenous change. The characteristic function of the statistic is obtained through the Fredholm approach. The asymptotic behaviour of the proposed test is also examined by computing the limiting power under a sequence of local alternatives.