Testing Linearity Using Power Transforms of Regressors
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.
|Date of creation:||Sep 2013|
|Date of revision:|
|Publication status:||Published in Journal of Econometrics (July 2015), 187(1): 376-384|
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References listed on IDEAS
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- Xiaoxia Shi & Peter C. B. Phillips, 2010.
"Nonlinear Cointegrating Regression under Weak Identification,"
Cowles Foundation Discussion Papers
1768, Cowles Foundation for Research in Economics, Yale University.
- 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.
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"Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis,"
RCER Working Papers
296, University of Rochester - Center for Economic Research (RCER).
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- Cho, Jin Seo & White, Halbert, 2010.
"Testing for unobserved heterogeneity in exponential and Weibull duration models,"
Journal of Econometrics,
Elsevier, vol. 157(2), pages 458-480, August.
- 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.
- Peter C.B. Phillips & Joon Y. Park, 1998.
"Asymptotics for Nonlinear Transformations of Integrated Time Series,"
Cowles Foundation Discussion Papers
1182, Cowles Foundation for Research in Economics, Yale University.
- 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.
- 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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