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:|
|Contact details of provider:|| Postal: |
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC
|Order Information:|| Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Park, Joon Y. & Phillips, Peter C.B., 1999.
"Asymptotics For Nonlinear Transformations Of Integrated Time Series,"
Cambridge University Press, vol. 15(03), pages 269-298, June.
- 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.
- 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.
- 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.
- 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.
- Hansen, Bruce E, 1996.
"Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis,"
Econometric Society, vol. 64(2), pages 413-30, March.
- Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
- Tom Doan, . "TAR: RATS procedure to estimate a threshold autoregression, tests for threshold effect," Statistical Software Components RTS00209, Boston College Department of Economics.
- Tom Doan, . "RATS programs to replicate Hansen's threshold estimation and testing results," Statistical Software Components RTZ00091, Boston College Department of Economics.
- 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.
When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1917. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Glena Ames)
If references are entirely missing, you can add them using this form.