Discrimination between monotonic trends and long-range dependence

Abstract

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 -distribution with noncentrality parameter tending to 0 uniformly outside intervals . In the latter case it has λ α −1 times a central -distribution, 0 < α < 1.