文章基本信息

标题："Regression with Slowly Varying Regressors
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作者：Peter C. B. Phillips
期刊名称：COWLES Foundation Discussion Paper / Cowles Foundation for Research in Economics
出版年度：2001
卷号：2001
期号：1
出版社：Yale University
摘要：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.
关键词：Asymptotic expansion; collinearity; Karamata representation; slow variation; smooth variation; trend regression