Lag length selection and the construction of unit root tests with good size and power

It is widely known that when there are errors with a moving-average root cl ose to -1, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the AIC and the BIC tend to select a truncation lag (k) that is very small. We conside r a class of Modified Information Criteria (MIC) with a penalty factor that is sample dependent. It takes into account the fact that the bias in the s um of the autoregressive coefficients is highly dependent on k and adapts t o the type of deterministic components present. We use a local asymptotic f ramework in which the moving-average root is local to -1 to document how th e MIC performs better in selecting appropriate values of k. In Monte-Carlo experiments, the MIC is found to yield huge size improvements to the DFGLS and the feasible point optimal PT test developed in Elliott, Rothenberg, an d Stock (1996). We also extend the M tests developed in Perron and Ng (1996 ) to allow for GLS detrending of the data. The MIC along with GLS detrended data yield a set of tests with desirable size and power properties.