FinanceandEconomicsDiscussionSeriesFederalReserveBoard,Washington,D.C.ISSN1936-2854(Print)ISSN2767-3898(Online)SpectralbacktestsunboundedandfoldedMichaelB.GordyandAlexanderJ.McNeil2024-060Pleasecitethispaperas:Gordy,MichaelB.,andAlexanderJ.McNeil(2024).“Spectralbacktestsunboundedandfolded,”FinanceandEconomicsDiscussionSeries2024-060.Washington:BoardofGover-norsoftheFederalReserveSystem,https://doi.org/10.17016/FEDS.2024.060.NOTE:StaffworkingpapersintheFinanceandEconomicsDiscussionSeries(FEDS)arepreliminarymaterialscirculatedtostimulatediscussionandcriticalcomment.TheanalysisandconclusionssetfortharethoseoftheauthorsanddonotindicateconcurrencebyothermembersoftheresearchstaffortheBoardofGovernors.ReferencesinpublicationstotheFinanceandEconomicsDiscussionSeries(otherthanacknowledgement)shouldbeclearedwiththeauthor(s)toprotectthetentativecharacterofthesepapers.Spectralbacktestsunboundedandfolded∗MichaelB.GordyFederalReserveBoard,WashingtonDCAlexanderJ.McNeilSchoolforBusinessandSociety,UniversityofYork15July2024AbstractInthespectralbacktestingframeworkofGordyandMcNeil(2020)aprobabilitymeasureontheunitintervalisusedtoweightthequantilesofgreatestinterestinthevalidationofforecastmodelsusingprobability-integraltransform(PIT)data.WeextendthisframeworktoallowgeneralLebesgue-Stieltjeskernelmeasureswithun-boundeddistri...
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