Abstract
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.
A first draft containing some of the results reported here was written in 1993. The present paper is an abridge version of Phillips and Lee (1996). Our thanks go to the NSF for research support under Grant Numbers SES 9122142 and SBR 94-22922.
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© 1996 Springer-Verlag New York, Inc.
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Phillips, P.C.B., Lee, C.C. (1996). Efficiency Gains from Quasi-Differencing under Nonstationarity. In: Robinson, P.M., Rosenblatt, M. (eds) Athens Conference on Applied Probability and Time Series Analysis. Lecture Notes in Statistics, vol 115. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2412-9_22
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DOI: https://doi.org/10.1007/978-1-4612-2412-9_22
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