Title

Regression with Slowly Varying Regressors and Nonlinear Trends

Publication Type

Journal Article

Publication Date

2007

Abstract

Slowly varying (SV) regressors arise commonly in empirical econometric work, particularly in the form of semilogarithmic regression and log periodogram regression. These regressors are asymptotically collinear. Usual regression formulas for asymptotic standard errors are shown to 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 SV functions and central limit theorems with SV weights are given that assist in the development of a regression theory. Multivariate regression and polynomial regression with SV 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 the asymptotic theory of nonlinear trend regression are explored.The author thanks two referees and Pentti Saikkonen for comments and suggestions, Sidney Resnick for references on second-order regular variation, and a Kelly Fellowship and the NSF for partial research support under grants SBR 97-30295 and SES 04-142254. An original draft of the paper was written in June 2000 and circulated under the title “Regression with Slowly Varying Regressors.”

Discipline

Econometrics

Research Areas

Econometrics

Publication

Econometric Theory

Volume

23

Issue

4

First Page

557

Last Page

614

ISSN

0266-4666

Identifier

10.1017/s0266466607070260

Publisher

Cambridge University Press

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Additional URL

http://dx.doi.org/10.1017/s0266466607070260

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