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Testing Linearity Using Power Transforms of Regressors

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Abstract

We develop a method of testing linearity using power transforms of regressors, allowing for stationary processes and time trends. The linear model is a simplifying hypothesis that derives from the power transform model in three different ways, each producing its own identification problem. We call this modeling difficulty the trifold identification problem and show that it may be overcome using a test based on the quasi-likelihood ratio (QLR) statistic. More specifically, the QLR statistic may be approximated under each identification problem and the separate null approximations may be combined to produce a composite approximation that embodies the linear model hypothesis. The limit theory for the QLR test statistic depends on a Gaussian stochastic process. In the important special case of a linear time trend regressor and martingale difference errors asymptotic critical values of the test are provided. The paper also considers generalizations of the Box-Cox transformation, which are associated with the QLR test statistic.

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File URL: http://cowles.econ.yale.edu/P/cd/d19a/d1917.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1917.

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Length: 53 pages
Date of creation: Sep 2013
Date of revision:
Handle: RePEc:cwl:cwldpp:1917

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Box Cox transform; Gaussian stochastic process; Neglected nonlinearity; Power transformation; Quasi-likelihood ratio test; Trend exponent; Trifold identification problem;

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  1. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
  2. Jin Seo Cho & Halbert White, 2009. "Testing for Unobserved Heterogeneity in Exponential and Weibull Duration Models," Discussion Paper Series 0912, Institute of Economic Research, Korea University.
  3. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March.
  4. Shi, Xiaoxia & Phillips, Peter C.B., 2012. "Nonlinear Cointegrating Regression Under Weak Identification," Econometric Theory, Cambridge University Press, vol. 28(03), pages 509-547, June.
  5. Phillips, Peter C.B., 2007. "Regression With Slowly Varying Regressors And Nonlinear Trends," Econometric Theory, Cambridge University Press, vol. 23(04), pages 557-614, August.
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