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Regression with Slowly Varying Regressors

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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.

Suggested Citation

  • Peter C.B. Phillips, 2001. "Regression with Slowly Varying Regressors," Cowles Foundation Discussion Papers 1310, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1310
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d13/d1310.pdf
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    Cited by:

    1. Patrick Marsh, "undated". "A Measure of Distance for the Unit Root Hypothesis," Discussion Papers 05/02, Department of Economics, University of York.
    2. Caner, Mehmet, 2008. "Nearly-singular design in GMM and generalized empirical likelihood estimators," Journal of Econometrics, Elsevier, vol. 144(2), pages 511-523, June.

    More about this item

    Keywords

    Asymptotic expansion; collinearity; Karamata representation; slow variation; smooth variation; trend regression;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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