A test of the null hypothesis of cointegration
David Harris and Brett Inder
The cointegration tests of Engle and Granger ( 1987) test the null hypothesis of no cointegration. We extend the unit root testing framework of Kwiatkowskiet al. ( 1992) to testing the null hypothesis of cointegration. A test is developed which is asymptotically equivalent to the locally best invariant (LBI) test and is applicable to a wide range of nuisance parameters, and is dependent only on the number of regressors in the cointegrating regression. We tabulate asymptotic critical values for the test based on this distribution and report on a small power comparison with the Dickey-Fuller test.
In the literature on cointegrated time series, hypothesis tests developed for testing for cointegration have a null hypothesis of no cointegration. Such tests can be found in Engle and Granger ( 1987), Phillips and Ouliaris ( 1990) and Johansen ( 1988). However, there would seem to be some merit in constructing a test of the null hypothesis of cointegration. In fact, Engle is quoted in Phillips and Ouliaris ( 1990) as writing 'a null hypothesis of cointegration would be far more useful in empirical research than the natural null of non-cointegration'. Phillips and Ouliaris proceed to suggest two tests of this hypothesis, but then show that these tests are inconsistent. They leave the problem unsolved.
The merit in testing the null hypothesis of cointegration can be seen if we were building a model where the variables were believed, a priori, to be cointegrated. The classic example of aggregate consumption and income could be one such