THE COINTEGRATED VAR METHODOLOGY

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1、THECOINTEGRATEDVARMETHODOLOGYJAMESREADEAbstract.Outlineofhowtogoaboutacointegrationanalysis,asprovidedbytheSummerSchoolinEconometricsattheUniversityofCopenhagen,Summer2005.Contents1.Introduction22.AbriefmotivationforthecointegratedVARmodel23.Thevectorautoregressivemodel

2、33.1.Thesystem33.2.Conditionalfactorisationandweakexogeneity43.3.A¯rstorderautoregressivemodel43.4.Asecondorderautoregressivemodel63.5.Bi-variatesecondordervectorautorgressivemodelwithdeterministicterms83.6.Theunrestrictedvectorautoregressivemodel103.7.Estimatingtheunre

3、strictedVARinPcGive124.DiagnosticTestingontheunrestrictedVARmodel144.1.TheAssumptionsoftheVARmodel154.2.ThetestoutputfromPcGive154.3.Otherinformationfordiagnosingproblems174.4.SolvingDiagnosedProblems185.TheCointegratedVectorAutoregressiveModel245.1.TheModel245.2.Consta

4、ntandTrend285.3.Dummyvariables315.4.Estimationandrankdetermination335.5.AdditionalInformationonRankDetermination386.LimitingDistributionsoftheTracetest427.ImposingrestrictionsandIdenti¯cation437.1.¯restrictions447.2.®restrictions507.3.H-formversusR-formandinputtingrestr

5、ictionsinPcGive507.4.Usingrestrictionstounderstandthesystem51Thanksbe¯rstandforemosttoGod,withoutwhomnoneofthiswouldbepossible.Inaddition,IwouldliketothankKaterinaJuselius,SorenJohansen,HeinoBohnNielsenandAndersRahbekwhopresentedtheEconometricsSummerSchoolinCopenhagenin

6、August2005,andNickFawcettforkindlylookingoverthenotesandpointingoutnumerous(I'msure)appallingerrorsinearlierdraftsofthesenotes.ThanksalsotoDavidHendry,JennieCastleandBentNielsenamongstothersfordiscussionsinOxfordwhileformingmy`knowledge'ofthecointegratingVARmodel.12JAME

7、SREADE7.5.Identi¯cationof¯547.6.Identi¯cationof®andtheshort-runstructure588.ExtensionsoftheCVARmodel619.Data619.1.TheEconomicProblemofInterest629.2.Useofpasttheoreticalandempiricalworktoderivealistofrelevantvariablesforinclusion639.3.Otherconsiderationsforvariableselect

8、ion659.4.PreparingdatainPcGive69AppendixA.TheFrisch-WaughTheorem71References711.IntroductionThesenotesaccompan