the impact of fat-tailed distributions on some leading unit root tests

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1、JournalofAppliedStatistics,Vol.30,No.6,July,2003,635667Theimpactoffat-taileddistributionsonsomeleadingunitrootstests121K.D.PATTERSON&S.M.HERAVI,UniversityofReading,Berkshire,UK2andCardiffBusinessSchool,UniversityofWales,Cardiff,WalesThereissubstantialevidencethatmanytimeseriesassociatedwithfi

2、nancialandinsuranceclaimdataarefat-tailed,witha(much)higherprobabilityofoutlierscomparedwiththenormaldistribution.However,standardtests,orvariantsofthem,forthepresenceofunitrootsassumeanormaldistributionfortheinnovationsdrivingtheseries.Applicationoftheformertothelatterthereforeinvolvesaninconsist

3、ency.WeassesstheimpactofthisinconsistencyandprovideinformationonitsimpactoninferencewheninnovationsaredrawnfromtheCauchyandsequenceoft(v)distributions.Asimplepredictionthatfattailswilluniformlyleadtoover-sizingofstandardtests(becausethefatnessinthetailtranslatestothetestdistribution)turnsouttobein

4、correct:wefindthatsometestsareover-sizedbutsomeareunder-sized.WealsoconsidersizeretentionandthepoweroftheDickeyFullerpivotalandnormalizedbiasteststatisticsandweightedsymmetricversionsofthesetests.Tomaketheunitroottestingprocedurefeasible,wedevelopanentropy-basedtestforsomefat-taileddistributionsand

5、applyittosharepricesfromtheFTSE100.1IntroductionThisarticleisconcernedwithseveralissuesrelatedtothestandardassumptioninsimulationstoobtaincriticalvaluesforDickey–Fuller(DF)andrelatedtestsforaunitroot,thattheshocks(referredtoasinnovations)intheDGParenormallydistributed.Becauseofthewidespreadapplica

6、tionofDFteststoeconomictimeseries,thecentralquestioniswhetherthisassumptioniscritical.Theissueisimportantbecause,forseveralrelevantclassesofpotentiallynon-stationarytimeseries,theassumptionofnormalityisquestionable.Correspondence:K.D.Patterson,DepartmentofEconomics,UniversityofReading,Reading,Berk

7、shireRG66AA,UK.E-mailk.d.patterson@reading.ac.ukISSN0266-4763print;1360-0532online/03/060635-33©2003Taylor&FrancisLtdDOI:10.1080/0266476032000053736636K.D.Patterson&S.M.HeraviJustificationforanassessmentoftheimpac