Tests of nonnested hypotheses in nonstationary regressions with an application to modeling industrial production

In the context of I (1) time series, we provide some asymptotic results for the Davidson-MacKinnon J-type test. We examine both the case where our reg ressor sets x(1t) and x(2t) are not cointegrated, and the case where they a re. In the former case, the OLS estimator of the weighting coefficient from the artificial compound model converges at rate T to a mixed normal distri bution, and the associated t-statistic has an asymptotic standard normal di stribution. In the latter case, we find that the J-test also has power agai nst violation of weak exogeneity (with respect to the short-run coefficient s of the null model), which is caused by correlation between the disturbanc e of the null model and that of the cointegrating equation linking x(1t) an d x(2t). Moreover, unlike the previous case, the OLS estimator of the weigh ting coefficient from the artificial compound model converges at root T to an asymptotic normal distribution when the null model is specified correctl y. In an empirical illustration, we use the tests to examine an industrial production data set for six countries.