LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power
Econometrica · 2001 · Volume 69 · Issue 6
Abstract
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 theAICand theBICtend 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 onkand 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 theMICperforms better in selecting appropriate values ofk. In Monte-Carlo experiments, theMICis found to yield huge size improvements to theDFGLSand the feasible point optimalPTtest developed in Elliott, Rothenberg, and Stock (1996). We also extend theMtests developed in Perron and Ng (1996) to allow forGLSdetrending of the data. TheMICalong withGLSdetrended data yield a set of tests with desirable size and power properties.
Keywords
Integrated processes, truncation lag, GLSdetrending, information criteria
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