Detection of Functional Form Misspecification in Cointegrating Relations

A simple specification test based on fully modified residuals and the CUSUM test for cointegration of Xiao and Phillips (Journal of Econometrics, 2002) 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 infinite samples. The Dickey-Fuller test is also considered. The simulation results reveal that the first two tests per- form reasonably well. However, the Dickey-Fuller test performs poorly under functional form misspecification.