CFDP 1917

Testing Linearity Using Power Transforms of Regressors


Publication Date: September 2013

Pages: 53


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.


Box Cox transform; Gaussian stochastic process; Neglected nonlinearity; Power transformation; Quasi-likelihood ratio test; Trend exponent; Trifold identification problem

JEL Classification Codes:  C12, C18, C46, C52

See CFP: 1483