Combining Non-Cointegration Tests∗

The local asymptotic power of many popular non-cointegration tests has recently been shown to depend on a certain nuisance parameter. Depending on the value of that parameter, different tests perform best. This paper suggests combination procedures with the aim of providing meta tests that maintain high power across the range of the nuisance parameter. The local asymptotic power of the new meta tests is in general almost as high as that of the more powerful of the underlying tests. When the underlying tests have similar power, the meta tests are even more powerful than the best underlying test. At the same time, our new meta tests avoid the arbitrary decision which test to use if single test results conflict. Moreover it avoids the size distortion inherent in separately applying multiple tests for cointegration to the same data set. We apply our test to 161 data sets from published cointegration studies. There, in one third of all cases single tests give conflicting results whereas our meta tests provide an unambiguous test decision.