A Gaussian Test for Unit Roots with an Application to Great Ratios

Non-standard distributions, size distortions and extremely low power are well-known problems of the unit root tests that are currently in use. In this paper we use a mixed-frequency regression technique to develop a test primarily for cointegration under the null of stationarity. What is noteworthy about this MA unit root test, based on a variance-difference, is that, instead of having to deal with non-standard distributions, it takes testing back to the normal distribution and offers a way to increase power without having to increase the sample size substantially. Monte Carlo simulations show that the test offers substantial gains in power against near-null alternatives in moderate size samples. Although the null of stationarity is the research line to be pursued, we also consider an extension of the procedure to cover the AR unit root case that provides a Gaussian test with more power. An empirical exercise illustrates the usefulness of the test.