Double Unit Roots Testing, GLS-detrending and Uncertainty over the Initial Conditions

This paper proposes the extension of the Hasza and Fuller (1979) test for double unit roots based on GLS-detrending. The limiting distribution of this test is obtained under local to unity representation and coincides with the distribution of the conventional test in the absence of a deterministic component. The proposed test has both better asymptotic and _nite sample properties in comparison to tests based on OLS-detrending. This paper proposes modi_ed information criteria for the implementation of the proposed test for double unit roots in _nite samples in which an additional term is incorporated into the penalty function. This provides better size control under various data generating processes, especially for strongly negative moving average components. This paper also analyzes the power behavior of tests under non-negligible initial conditions and proposes union of rejection testing strategy of three tests following the Harvey et al. (2009) approach. This strategy is more robust across various magnitudes of the initial conditions and eliminates large power losses that occur due to the use of only one of the tests.