COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1134 Efficiency Gains from Quasi-Differencing Under Nonstationarity Peter C. B. Phillips and Chin Chin Lee September 1996 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. |
