The tests of Robinson (1994) for fractional integration. Time domain versus frequency domain

This article examines the finite sample behaviour of time and frequency domain versions of the tests of Robinson (1994) for testing roots in the unit circle, with integer or fractional orders of integration. In finite samples, the two versions differ, in some cases considerably. We show analytically that the difference between the two statistics is Op(T−1/2). Several Monte Carlo experiments are conducted, and a small empirical application, illustrating this problem, is also carried out at the end of the article.