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 → 0 as n → ∞. 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.
AIC, Consistency, Model selection, Nonparametric, Unit root