Combining non‐cointegration tests

Abstract

The local 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.1 We demonstrate the local power of the new meta tests to be in general almost as high as that of the most powerful of the underlying tests. When the underlying tests have similar power, the meta tests even appear more powerful than the best underlying test. At the same time, our new meta tests avoid the arbitrary decision which test to use if individual test results conflict. Moreover it avoids the size distortion inherent in separately applying multiple tests for cointegration to the same dataset. We use the new tests to investigate 286 datasets from published cointegration studies. There, in one‐third of all cases individual tests give conflicting results whereas our meta tests provide an unambiguous test decision.