Testing Linearity Using Power Transforms of Regressors

Yae In Baek, Jin Seo Cho (jinseocho@yonsei.ac.kr) and Peter Phillips
Additional contact information
Yae In Baek: Yonsei University

No 1917, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

Keywords: Box Cox transform; Gaussian stochastic process; Neglected nonlinearity; Power transformation; Quasi-likelihood ratio test; Trend exponent; Trifold identification problem (search for similar items in EconPapers)
JEL-codes: C12 C18 C46 C52 (search for similar items in EconPapers)
Pages: 53 pages
Date: 2013-09
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Journal of Econometrics (July 2015), 187(1): 376-384

Downloads: (external link)
https://cowles.yale.edu/sites/default/files/files/pub/d19/d1917.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found

Related works:
Journal Article: Testing linearity using power transforms of regressors (2015)
Working Paper: Testing Linearity Using Power Transforms of Regressors (2015)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cwl:cwldpp:1917

Ordering information: This working paper can be ordered from
Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
The price is None.

Access Statistics for this paper

More papers in Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University Yale University, Box 208281, New Haven, CT 06520-8281 USA. Contact information at EDIRC.
Bibliographic data for series maintained by Brittany Ladd (cowles@yale.edu).