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Published online by Cambridge University Press: 01 March 2000
In the context of I(1) time series, we provide some asymptoticresults for the Davidson-MacKinnon J-type test. We examine both the case where our regressor sets x1t and x2t are notcointegrated, and the case where they are.In the former case, the OLS estimatorof the weighting coefficient from the artificial compound model converges at rate T to a mixed normal distribution, and the associated t-statistic has an asymptotic standard normal distribution.In the latter case, we find that the J-test also has power against violation ofweak exogeneity (with respect to the short-run coefficients of the null model),which is caused by correlation between the disturbance of the null model andthat of the cointegrating equation linking x1t and x2t.Moreover, unlike the previous case, theOLS estimator of the weighting coefficient from the artificial compound modelconverges at \sqrt{T} to an asymptotic normaldistribution when the null model is specified correctly.In an empirical illustration, we use the tests to examinean industrial production data set for sixcountries.