A Gaussian test for unit roots with an application to great ratios

Non-standard distributions are a common feature of many tests for unit-roots and cointegration that are currently available. The main problem with non-standard distributions is that when the true data generating process is unknown, which is the case in general, it is not easy to engage in a specification search because the distribution changes as the specification changes, especially with respect to deterministic components. We use a mixed-frequency regression technique to develop a test for cointegration under the null of stationarity of the deviations from a long-run relationship. 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 minimal size distortions even when the AR root is close to unity and 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 relative usefulness of the test further.