Abstract

Some limit properties for information based model selection criteria are given in the context of unit root evaluation and various assumptions about initial conditions. Allowing for a nonparametric short memory component, standard information criteria are shown to be weakly consistent for a unit root provided the penalty coefficient Cn →∞ and Cn/n → 0a sn →∞ . Strong consistency holds when Cn/(log log n) 3 → ∞ under conventional assumptions on initial conditions and under a slightly stronger condition when initial conditions are infinitely distant in the unit root model. The limit distribution of the AIC criterion is obtained.

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