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 close 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 consider 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 sum of the autoregressive coefficients is highly dependent on "k" and adapts to the type of deterministic components present. We use a local asymptotic framework in which the moving-average root is local to - 1 to document how the "MIC" performs better in selecting appropriate values of "k". In Monte-Carlo experiments, the "MIC" is found to yield huge size improvements to the "DF-super-GLS" and the feasible point optimal "P-sub-T" test developed in Elliott, Rothenberg, and 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. Copyright The Econometric Society.