Regression with Slowly Varying Regressors and Nonlinear Trends

• Main Author: PHILLIPS, Peter C. B.
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2007
• Subjects: Large deviations; Orthogonal polynomials; density estimator; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/246; https://ink.library.smu.edu.sg/context/soe_research/article/1245/viewcontent/Regression_with_Slowly_Varying_Regressors_2007_ET.pdf
• Institution: Singapore Management University

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.