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|
|Publication status:||Published in Journal of Econometrics (July 2015), 187(1): 376-384|
|Contact details of provider:|| Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA|
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.yale.edu/
More information through EDIRC
|Order Information:|| Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA|
References listed on IDEAS
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.:
- Shi, Xiaoxia & Phillips, Peter C.B., 2012.
"Nonlinear Cointegrating Regression Under Weak Identification,"
Cambridge University Press, vol. 28(03), pages 509-547, June.
- 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.
- 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.
- 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.
- Octavio A. Ramirez & Sukant Misra & James Field, 2003. "Crop-Yield Distributions Revisited," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 85(1), pages 108-120.
- Peter C.B. Phillips & Joon Y. Park, 1986.
"Statistical Inference in Regressions with Integrated Processes: Part 1,"
Cowles Foundation Discussion Papers
811R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1987.
- Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
- Bierens, H.J., 1989.
"A consistent conditional moment test of functional form,"
Serie Research Memoranda
0064, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
- Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-1458, November.
- Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
- Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
- Cho, Jin Seo & Ishida, Isao, 2012. "Testing for the effects of omitted power transformations," Economics Letters, Elsevier, vol. 117(1), pages 287-290.
- Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
- Richard E. Just & Quinn Weninger, 1999.
"Are Crop Yields Normally Distributed?,"
American Journal of Agricultural Economics,
Agricultural and Applied Economics Association, vol. 81(2), pages 287-304.
- Phillips, P.C.B., 1989.
"Partially Identified Econometric Models,"
Cambridge University Press, vol. 5(02), pages 181-240, August.
- Hansen, Bruce E, 1996.
"Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis,"
Econometric Society, vol. 64(2), pages 413-430, March.
- Tom Doan, "undated". "TAR: RATS procedure to estimate a threshold autoregression, tests for threshold effect," Statistical Software Components RTS00209, Boston College Department of Economics.
- 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, "undated". "RATS programs to replicate Hansen's threshold estimation and testing results," Statistical Software Components RTZ00091, Boston College Department of Economics.
- Jin Seo Cho & Isao Ishida & Halbert White, 2013. "Testing for Neglected Nonlinearity Using Twofold Unidentified Models under the Null and Hexic Expansions (published in: Essays in Nonlinear Time Series Econometrics, Festschrift in Honor of Timo Teras," Working papers 2013rwp-55, Yonsei University, Yonsei Economics Research Institute.
- 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.
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: (Matthew C. Regan)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.