Testing Linearity Using Power Transforms of Regressors

54 Pages Posted: 18 Sep 2013

See all articles by Yaein Baek

Yaein Baek

Korea Institute for International Economic Policy

Jin Seo Cho

Yonsei University - Department of Economics

Peter C. B. Phillips

University of Auckland Business School; Yale University - Cowles Foundation; Singapore Management University - School of Economics

Date Written: September 18, 2013

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

JEL Classification: C12, C18, C46, C52

Suggested Citation

Baek, Yaein and Cho, Jin Seo and Phillips, Peter C. B., Testing Linearity Using Power Transforms of Regressors (September 18, 2013). Cowles Foundation Discussion Paper No. 1917, Available at SSRN: https://ssrn.com/abstract=2327635 or http://dx.doi.org/10.2139/ssrn.2327635

Yaein Baek

Korea Institute for International Economic Policy ( email )

[30147] Building C, Sejong National Research Compl
Seoul, 370
Korea, Republic of (South Korea)

Jin Seo Cho

Yonsei University - Department of Economics ( email )

50 Yonsei-Ro
Seoul, 120-749
Korea
+822-2123-5448 (Phone)
+822-2123-8638 (Fax)

Peter C. B. Phillips (Contact Author)

University of Auckland Business School ( email )

12 Grafton Rd
Private Bag 92019
Auckland, 1010
New Zealand
+64 9 373 7599 x7596 (Phone)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3695 (Phone)
203-432-5429 (Fax)

Singapore Management University - School of Economics

90 Stamford Road
178903
Singapore

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