Regression with Slowly Varying Regressors

Peter Phillips

No 1310, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: 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 (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Pages: 45 pages
Date: 2001-07
New Economics Papers: this item is included in nep-ecm, nep-ent, nep-ets and nep-net
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Citations: View citations in EconPapers (2)

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