a bootstrap cointegration rank test for panels of var models

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1、CREATESResearchPaper2010-75ABootstrapCointegrationRankTestforPanelsofVARModelsLaurentA.F.CallotSchoolofEconomicsandManagementAarhusUniversityBartholinsAllé10,Building1322,DK-8000AarhusCDenmarkABOOTSTRAPCOINTEGRATIONRANKTESTFORPANELSOFVARMODELSLAURENTA.F.CALLOT,CREATESAARHUSUNIVERSITYLCALLOT@CREATES

2、.AU.DKDecember6,2010Abstract.Thispaperproposesasequentialproceduretode-terminethecommoncointegrationrankofpanelsofcointegratedVARs.ItshowshowapanelofcointegratedVARscanbetrans-formedinasetofindependentindividualmodels.Thelikelihoodfunctionofthetransformedpanelisthesumofthelikelihoodfunc-tionsofthei

3、ndividualCointegratedVARs(CVAR)models.Abootstrapbasedprocedureisusedtocomputeempiricaldistribu-tionsofthetraceteststatisticsfortheseindividualmodels.Fromtheseempiricaldistributionstwopaneltraceteststatisticsarecon-structed.ThesatisfyingsmallsamplepropertiesofthesetestsaredocumentedbymeansofMonteCar

4、lo.Anempiricalapplicationillustratestheusefullnessofthistests.Keywords:Ranktest,Paneldata,Cointegration,Bootstrap,Crosssectiondependence.JELclassication:C12,C32,C33IwouldliketothankNielsHaldrup,MHashemPesaranandMichaelJanssonforvaluablesuggestions,andAndersBredahlKockforcommentsandhelpfulldiscus-s

5、ion.Allremainingerrorsandshortcommingsaremine.FinancialsupportbytheCenterforResearchinEconometricAnalysisofTimeSeries,CREATES,fundedbytheDanishNationalResearchFoundation,isgratefullyacknowledged.12LAURENTA.F.CALLOT1.IntroductionThispaperproposesapanelrankteststatisticbasedonabootstrapprocedureforde

6、terminationofthecointegrationrankinaPanelCoin-tegratedVectorAutoregressivve(PCVAR)models.Thecointegrationrankisanimportantelementtounderstandthedynamicsofasys-temofvariables.Thesequentiallikelihood-basedprocedureforthedeterminationofthecointegrationrankinasystemofvariableswhichareatmostI(1)(seeJoha

7、nsen(1995))isfrequentlyusedinempiricalresearch.Thetracetestisalikelihoodratiotestforthehypothesisthatthetruerankofthesystem(notedr0throughout)isequaltor(hereafterH(r))againstthehypothesisthatthesystemhasful