COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1310 Regression with Slowly Varying Regressors Peter C. B. Phillips 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. JEL Classification: C22 Keywords: Asymptotic expansion, collinearity, Karamata representation, slow variation, smooth variation, trend regression |
