COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1653

Unit Root Model Selection

Peter C. B. Phillips

May 2008

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 -> infinity and C_n/n -> 0 as n -> infinity. Strong consistency holds when C_{n}/(loglog n)^3 -> infinity 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.

Keywords: AIC, Consistency, Model selection, Nonparametric, Unit root

JEL Classification: C22