Discrimination between monotonic trends and long-range dependence

We show that the periodogram behaves differently for a weakly dependent process with a small monotonic trend and a stationary strongly dependent process. In the former case it has a non-central x2-distribution with noncentrality parameter tending to 0 uniformly outside intervals [0, eN- ], 8 < 2. In the latter case it has A ' times a central x2-distribution, 0 < a <1.