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.
Phillips, Peter C.B., "Regression with Slowly Varying Regressors" (2001). Cowles Foundation Discussion Papers. 1569.