Unit Root Model Selection

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 C_n→∞ and C_n/n→0 as n→∞. Strong consistency holds when C_n/(log logn)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.