Local Structural Trend Break in Stationarity Testing

In a recently publicized study, Harvey et al. (2012) investigated procedures for unit root testing employing break detection methods under local break in trend. We apply this methodology to analyze asymptotic and unite sample behavior of procedures under local break to test the stationarity null hypothesis local to unit root, against alternative hypothesis about the pres- ence of a unit root. We extend the GLS-based stationarity test proposed by Harris et al. (2007) to the case of structural break and obtain asymptotic properties under local trend break. Two procedures are considered. The first procedure uses a with-break stationarity test, but with adaptive critical values. The second procedure utilizes the intersection of rejection testing strategy containing tests with and without a break. Application of these approaches help to prevent serious size distortions for small break magnitude that are otherwise undetectable. Additionally, in a similar approach as Harvey et al. (2013) and Busetti and Harvey (2001), we propose a test based on minimizing the sequence of GLS-based stationarity test statistics over all possible break dates. This infimum-test in contrast to Busetti and Harvey (2001) does not require an additional assumption about a faster rate of convergence of break magnitude. Asymptotic and unite sample simulations show that under local to zero behavior of the trend break the asymptotic analysis provides a good approximation of the unite sample behavior of the proposed procedures. Proposed procedures can be used for confirmatory analysis together with tests of Harvey et al. (2012) and Harvey et al. (2013).