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1、GeneralizedCpModelAveragingforHeteroskedasticModelsQingfengLiu∗†DepartmentofEconomics,OtaruUniversityofCommerceRyoOkuiInstituteofEconomicResearch,KyotoUniversityRevisedVersionJune5,2011AbstractThispaperproposesamodelaveragingmethod,thegeneralizedMallows’Cp(GC)method,w
2、hichworkswellforheteroskedasticmod-els.Undersomeregularityconditions,weprovideafeasibleformoftheGCmethodandshowthattheGCmethodhasasymptoticoptimalitynotonlyasamodelaveragingmethodbutalsoasamodelselectionmethodforheteroskedasticmodels.WeperformsomeMonteCarlostudiestoin
3、vestigatethesmallsamplepropertiesoftheGCmethod.Thesimulationresultsshowthatourmethodworkswellandperformsbetterthanalternativemethods.JELclassification:C51C52Keywords:ModelAveraging,ModelSelection,AsymptoticOpti-mality,Mallows’Cp,Heteroskedasticerror.Correspondingautho
4、r:QingfengLiu,DepartmentofEconomics,OtaruUniversityofCommerce,5-21,Midori3-chome,Otaru,Hokkaido047-8501,Japan.(Tel&Fax:+86134275312,E-mail:qliu@res.otaru-uc.ac.jp).yTheauthorswouldliketothankK.Akashi,Y.Feng,K.Hitomi,Y.Kawasaki,E.Kurozumi,K.Morimune,Y.Nishiyama,andN.Su
5、eishi,forhelpfuldiscussionsandcom-ments.11IntroductionModelselectionhelpsustochooseasingleoptimalmodelfromasetofcandi-datemodels.Inthelasttwodecades,modelaveraginghasbeenproposedasanalternativetomodelselection.Amodelaveragingestimatorisobtainedbytakingtheweightedavera
6、geoftheestimatorsobtainedfromcandidatemodels.Ascomparedtomodelselection,modelaveragingseekstoavoidselectingaverypoormodelandtoimprovetheestimatewithregardtorisk.Modelaveragingmethodscanbeseparatedintotwogroups:Bayesianmodelaveragingmethodsandfrequentist(non-Bayesian)m
7、odelaveragingmethods.Bayesianmodelaveragingmethodshavebeenadvocatedbymanyresearchers(seeDraper(1995),Hoeting,Madigan,Raftery,andVolinsky(1999),andClydeandGeorge(2004)).Ontheotherhand,frequentistmodelaveragingmethodshaveashorterhistorythantheirBayesiancoun-terparts.Int
8、heliteratureonfrequentistmodelaveragingmethods,Buck-land,Burnham,Burnham,andAugustin(1997)proposedasmoothed-AIC(SAIC)basedme