Publication Type

Journal Article

Version

acceptedVersion

Publication Date

8-2007

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.

Keywords

Large deviations, Orthogonal polynomials, density estimator

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

Additional URL

https://doi.org/10.1017/s0266466607070260

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