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1、AComparisonofDirectandIteratedMultistepARMethodsforForecastingMacroeconomicTimeSeriesMassimilianoMarcellinoIstitutodiEconomiaPolitica,UniversitaBocconiandIGIERJamesH.StockDepartmentofEconomics,HarvardUniversityandtheNBERandMarkW.Watson*DepartmentofEconomicsandWoodrowWil
2、sonSchool,PrincetonUniversityandtheNBERFebruary2004(RevisedApril2005)*TheauthorsthankJin-LungLin,FrankSchorfheide,KenWest,andtworefereesforcomments.ThisresearchwasfundedinpartbyNSFgrantSBR-0214131.Abstract“Iterated”multiperiodaheadtimeseriesforecastsaremadeusingaone-per
3、iodaheadmodel,iteratedforwardforthedesirednumberofperiods,whereas“direct”forecastsaremadeusingahorizon-specificestimatedmodel,wherethedependentvariableisthemulti-periodaheadvaluebeingforecasted.Whichapproachisbetterisanempiricalmatter:intheory,iteratedforecastsaremoreef
4、ficientiftheone-periodaheadmodeliscorrectlyspecified,butdirectforecastsaremorerobusttomodelmisspecification.Thispapercomparesempiricaliteratedanddirectforecastsfromlinearunivariateandbivariatemodelsbyapplyingsimulatedout-of-samplemethodsto170U.S.monthlymacroeconomictime
5、seriesspanning1959–2002.Theiteratedforecaststypicallyoutperformthedirectforecasts,particularlyifthemodelscanselectlonglagspecifications.Therelativeperformanceoftheiteratedforecastsimproveswiththeforecasthorizon.Keywords:multistepforecasts,VARforecasts,forecastcomparison
6、sJELNumbers:C32,E37,E471.IntroductionAforecastermakingamultiperiodtimeseriesforecast–forexample,forecastingtheunemploymentratesixmonthshence–confrontsachoicebetweenusingaone-periodmodeliteratedforward,orinsteadusingamultiperiodmodelestimatedwithalossfunctiontailoredtoth
7、eforecasthorizon.Inthecaseofunivariatelinearmodelsandquadraticloss,the“iterated”forecast(sometimescalleda“plug-in”forecast)entailsfirstestimatinganautoregression,theniteratinguponthatautoregressiontoobtainthemultiperiodforecast.Incontrast,theforecastbasedonthemultiperio
8、dmodel–which,followingtheliterature,weshallcallthe“direct”forecast–entailsregressingamultiperiod-aheadvalueoft
