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1、InternationalJournalofForecasting6(1990)503-508503North-HollandTheuseofpriorinformationinforecastcombination*FrancisX.DieboldDepartmentofEconomics,UniversityofPennsylvania,Philadelphia,PA191046297,USAPeterPaulyDepartmentofEconomics,UniversityofToronto,On
2、tario,CanadaM5SIA1Abstract:Simpleaveragesoften,butnotalways,outperformmoresophisticated“optimal”forecastcomposites.WeusedBayesianshrinkagetechniquestoallowtheincorporationofpriorinformationintotheestimationofcombiningweights;theestimatedcombiningweightsw
3、erecoaxedor“shrunken”towardequalitybutwerenotforcedtobeexactlyequal.Theleast-squaresandprior(i.e.,arithmeticaverage)weightsthenemergedaspolarcasesfortheposteriormean;theexactlocationdependedonpriorprecision,whichwasestimatedfromthedata.Inasimpleexamplein
4、volvingU.S.GNPforecasts,alargeamountofshrinkagewasfoundtobeoptimal.Keywords:Bayesian,Pooling,Prediction,Shrinkage.1.Introductionscience,mathematicalstatistics(classicalandBayesian),operationsresearchandpsychology.ANumerousforecastsbasedonpartiallyoverlap
5、-surveyandcomprehensiveannotatedbibliographypinginformationsetsareavailabletodecision-isgivenbyClemen(1989).makers;thepossibilityofcombiningsuchprimaryThispaper,likemostoftheliterature,iscon-forecastsintoanoptimalpooledforecastim-cernedwiththeformationof
6、minimummean-mediatelyarises.Whilepoolingofforecastsissquared-error(MSE)combinedforecastsbypro-suboptimalrelativetopoolingofinformationsets,jectingrealizationsintothespacespannedbytheitmustberecognizedthatinmanyforecastingprimaryforecasts.Itiswellknowntha
7、t,undersituations,particularlyinrealtime,poolingofcertainconditions,linearcompositeforecastsusinginformationsetsiseitherimpossibleorprohibi-weightsconstructedinthisfashionmusthavetivelycostly.ThispragmaticobservationhasasymptoticMSElessthanorequaltothato
8、fthespurredalargeliterature,withcontributionsfrombestprimaryforecast.Infinitesamplesofthesizediverseareasincludingeconomics,managementtypicallyavailableineconometricforecasting,however,samplingerrorcontaminatesthecombin-in
