Unit Root Model Selection

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 C_n -gt; infinite and C_n/n -gt; 0 as n -gt; infinite. Strong consistency holds when C_n/(log log n)^3 -gt; infinite 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