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1、ComputStatDOI10.1007/s00180-011-0290-0ORIGINALPAPERHybridbootstrapaidedunitroottestingC.Jentsch·J.-P.Kreiss·P.Mantalos·E.PaparoditisReceived:27November2009/Accepted:24October2011?Springer-Verlag2011AbstractInthispaper,weproposeahybridbootstrapprocedureforaugmentedDickey-Fuller(ADF)testsforthep
2、resenceofaunitroot.Thishybridproposalcom-binesatimedomainparametricautoregressive?ttothedataandanonparametriccorrectionappliedinthefrequencydomaintocapturefeaturesthatarepossiblynotrepresentedbytheparametricmodel.Itisknownthatconsiderablesizeandpowerproblemscanoccurinsmallsamplesforunitroottes
3、tinginthepresenceofanMAparameterusingcriticalvaluesoftheasymptoticDickey-Fullerdistribution.Theben-e?tofthesievebootstrapinthissituationhasbeeninvestigatedbyChangandPark(JTimeSerAnal24:379–400,2003).Theyshowedasymptoticvalidityaswellassubstantialimprovementsforsmallsamplesizes,buttheactualsize
4、softheirbootstraptestswerestillquitefarawayfromthenominalsize.The?nitesampleperformancesofourprocedureareextensivelyinvestigatedthroughMonteCarlosimulationsandcomparedtothesievebootstrapapproach.Regardingthesizeofthetests,ourresultsshowthatthehybridbootstrapremarkablyoutperformsthesievebootstr
5、ap.KeywordsHybridbootstrap·Sievebootstrap·Unitroottesting·ADFtestsC.JentschDepartmentofEconomics,UniversityofMannheim,L7,3-5,68131Mannheim,GermanyJ.-P.KreissInstitutfürMathematischeStochastik,TechnischeUniversit?tBraunschweig,Pockelsstra?e14,38106Braunschweig,GermanyP.Mantalos(B)DepartmentofSt
6、atistics,SwedishBusinessSchool,Universityof?rebro,70182?rebro,Swedene-mail:panagiotis.mantalos@oru.seE.PaparoditisDepartmentofMathematicsandStatistics,UniversityofCyprus,P.O.Box20537,1678Nicosia,Cyprus123C.Jentschetal.1IntroductionWhenwestudythesmallsamplepropertiesofatestprocedurebycomparingd
7、ifferenttests,twoaspectsareofprimeimportance:(a)?ndingthetestthathasactualsizeclosesttothenominalsize,and,giventhat(a)holds;(b)?ndingthetestthathasthegreatestpower.Inmostcases,however,thedistributionoftheteststatisticweuseisknownonlyasy
