Regression with Slowly Varying Regressors

46 Pages Posted: 25 Aug 2001

See all articles by Peter C. B. Phillips

Peter C. B. Phillips

Yale University - Cowles Foundation; University of Auckland; University of Southampton; Singapore Management University - School of Economics

Date Written: July 2001


Slowly varying regressors are asymptotically collinear in linear regression. Usual regression formulae for asymptotic standard errors remain valid but rates of convergence are affected and the limit distribution of the regression coefficients is shown to be one dimensional. Some asymptotic representations of partial sums of slowly varying functions and central limit theorems with slowly varying weights are given that assist in the development of a regression theory. Multivariate regression and polynomial regression with slowly varying functions are considered and shown to be equivalent, up to standardization, to regression on a polynomial in a logarithmic trend. The theory involves second, third and higher order forms of slow variation. Some applications to trend regression are discussed.

Keywords: Asymptotic Expansion, Collinearity, Karamata Representation, Slow Variation, Smooth Variation, Trend Regression

JEL Classification: C22

Suggested Citation

Phillips, Peter C. B., Regression with Slowly Varying Regressors (July 2001). Yale Cowles Foundation Discussion Paper No. 1310. Available at SSRN:

Peter C. B. Phillips (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3695 (Phone)
203-432-5429 (Fax)

University of Auckland ( email )

Private Bag 92019
Com. A room: 102
New Zealand
+64 9 373 7599 x7596 (Phone)

University of Southampton

Southampton, SO17 1BJ
United Kingdom

Singapore Management University - School of Economics

90 Stamford Road

Register to save articles to
your library


Paper statistics

Abstract Views
PlumX Metrics