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1、QEDQueen’sEconomicsDepartmentWorkingPaperNo.1227CriticalValuesforCointegrationTestsJamesG.MacKinnonQueen’sUniversityDepartmentofEconomicsQueen’sUniversity94UniversityAvenueKingston,Ontario,CanadaK7L3N61-2010CriticalValuesforCointegrationTestsJamesG.MacKinnonDepartmentofEconomicsQue
2、en’sUniversityKingston,Ontario,CanadaK7L3N6jgm@econ.queensu.cahttp://www.econ.queensu.ca/faculty/mackinnon/AbstractThispaperprovidestablesofcriticalvaluesforsomepopulartestsofcointegrationandunitroots.Althoughthesetablesarenecessarilybasedoncomputersimulations,theyaremuchmoreaccura
3、tethanthosepreviouslyavailable.Theresultsofthesimulationexperimentsaresummarizedbymeansofresponsesurfaceregressionsinwhichcriticalvaluesdependonthesamplesize.Fromtheseregressions,asymptoticcriticalvaluescanbereadoffdirectly,andcriticalvaluesforanyfinitesamplesizecaneasilybecomputedwi
4、thahandcalculator.Addedin2010version:Anewappendixcontainsadditionalresultsthataremoreaccurateandcovermorecasesthantheonesintheoriginalpaper.January1990ReissuedJanuary2010withadditionalresultsThispaperoriginallyappearedasUniversityofCaliforniaSanDiegoDiscussionPaper90-4,whichisappar
5、entlynolongeravailableontheweb.ItwaswrittenwhileIwasvisitingUCSDinthefallof1989andearly1990andsupported,inpart,bygrantsfromtheSocialSciencesandHumanitiesResearchCouncilofCanada.IamgratefultoalloftheeconometriciansatUCSDforprovidingahospitableresearchenvironmentandtoRobEngleandthela
6、teCliveGrangerforcommentsonanearlierversion.ForwardIspenttheacademicyearof1989-1990onsabbaticalattheUniversityofCaliforniaSanDiego.SinceRobertEngleandCliveGrangerweretherepermanently,andDavidHendry,SørenJohansen,andTimoTer¨asvirtawerealsovisiting,therewasinevitablymuchdiscussionabo
7、utcointegration.Iwassurprisedtofindthat,formostofthetests,accuratecriticalvaluesdidnotthenexist.IthereforesetouttocalculatethemfortheDickey-FullerandEngle-Grangertests,andtheresultwasthispaper.ThepaperoriginallyappearedasUniversityofCaliforniaSanDiegoDiscussionPaperNo.90-4.Formanyye
8、ars,abitmappedPDFofitthatw
