A famous theorem on trend removal by OLS regression (usually attributed to Grenander and Rosenblatt, 1957) gave conditions for the asymptotic equivalence of GLS and OLS in deterministic trend extraction. When a time series has trend components that are stochastically nonstationary, this asymptotic equivalence no longer holds. We consider models with integrated and near-integrated error processes where this asymptotic equivalence breaks down. In such models, the advantages of GLS can be achieved through quasi-diﬀerencing and we give an asymptotic theory of the relative gains that occur in deterministic trend extraction in such cases. Some diﬀerences between models with and without intercepts are explored
Phillips, Peter C.B. and Lee, Chin Chin, "Efficiency Gains from Quasi-Differencing under Nonstationarity" (1996). Cowles Foundation Discussion Papers. 1382.