Detection of functional form misspecification in cointegrating relations

Abstract

A simple specification test based on fully modified residuals and the cumulative sum (CUSUM) test for cointegration of Xiao and Phillips (2002, Journal of Econometrics, 108, 43-61) are considered as means of testing for functional form in long-run cointegrating relations. It is shown that both tests are consistent under functional form misspecification and lack of cointegration. A simulation experiment is carried out to assess the properties of the tests in finite samples. The Dickey-Fuller test is also considered. The simulation results reveal that the first two tests perform reasonably well. However, the Dickey-Fuller test performs poorly under functional form misspecification. © 2008 Cambridge University Press.