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.
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Length: 14 pages Date of creation: May 2008 Date of revision: Publication status: Published in Journal of the Japan Statistical Society (2008), 38(1): 65-74 Handle: RePEc:cwl:cwldpp:1653
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