Forecasting-the-term-structure-of-government-bond-yields_200

JournalofEconometrics130(2006)337–364

http://doc.guandang.net/locate/jeconom

Forecastingthetermstructureofgovernment

bondyields

FrancisX.Diebolda,b,CanlinLic,Ã

DepartmentofEconomics,UniversityofPennsylvania,3718LocustWalk,Philadelphia,

PA19104-6297,USA

b

NBER,1050MassachusettsAve.,Cambridge,MA02138,USA

c

A.GaryAndersonGraduateSchoolofManagement,UniversityofCalifornia,Riverside,

CA92521,USA

Accepted21March2005Availableonline23May2005

a

Abstract

Despitepowerfuladvancesinyieldcurvemodelinginthelast20years,comparativelylittleattentionhasbeenpaidtothekeypracticalproblemofforecastingtheyieldcurve.Inthispaperwedoso.Weuseneithertheno-arbitrageapproachnortheequilibriumapproach.Instead,weusevariationsontheNelson–Siegelexponentialcomponentsframeworktomodeltheentireyieldcurve,period-by-period,asathree-dimensionalparameterevolvingdynamically.Weshowthatthethreetime-varyingparametersmaybeinterpretedasfactorscorrespondingtolevel,slopeandcurvature,andthattheymaybeestimatedwithhighef ciency.Weproposeandestimateautoregressivemodelsforthefactors,andweshowthatourmodelsareconsistentwithavarietyofstylizedfactsregardingtheyieldcurve.Weuseourmodelstoproduceterm-structureforecastsatbothshortandlonghorizons,withencouragingresults.Inparticular,ourforecastsappearmuchmoreaccurateatlonghorizonsthanvariousstandardbenchmarkforecasts.r2005PublishedbyElsevierB.V.

JELclassi cation:G1;E4;C5

Keywords:Termstructure;Yieldcurve;Factormodel;Nelson–Siegelcurve

Correspondingauthor.

E-mailaddresses:fdiebold@sas.upenn.edu(F.X.Diebold),canlin.li@ucr.edu(C.Li).0304-4076/$-seefrontmatterr2005PublishedbyElsevierB.V.doi:10.1016/j.jeconom.2005.03.005

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F.X.Diebold,C.Li/JournalofEconometrics130(2006)337–364

1.Introduction

Thelast25yearshaveproducedmajoradvancesintheoreticalmodelsofthetermstructureaswellastheireconometricestimation.Twopopularapproachestotermstructuremodelingareno-arbitragemodelsandequilibriummodels.Theno-arbitragetraditionfocusesonperfectly ttingthetermstructureatapointintimetoensurethatnoarbitragepossibilitiesexist,whichisimportantforpricingderivatives.Theequilibriumtraditionfocusesonmodelingthedynamicsoftheinstantaneousrate,typicallyusingaf nemodels,afterwhichyieldsatothermaturitiescanbederivedundervariousassumptionsabouttheriskpremium.1Prominentcontribu-tionsintheno-arbitrageveinincludeHullandWhite(1990)andHeathetal.(1992),andprominentcontributionsintheaf neequilibriumtraditionincludeVasicek(1977),Coxetal.(1985),andDuf eandKan(1996).

Interestratepointforecastingiscrucialforbondportfoliomanagement,andinterestratedensityforecastingisimportantforbothderivativespricingandriskmanagement.2Henceonewonderswhatthemodernmodelshavetosayaboutinterestrateforecasting.Itturnsoutthat,despitetheimpressivetheoreticaladvancesinthe nancialeconomicsoftheyieldcurve,surprisinglylittleattentionhasbeenpaidtothekeypracticalproblemofyieldcurveforecasting.Thearbitrage-freetermstructureliteraturehaslittletosayaboutdynamicsorforecasting,asitisconcernedprimarilywith ttingthetermstructureatapointintime.Theaf neequilibriumtermstructureliteratureisconcernedwithdynamicsdrivenbytheshortrate,andsoispotentiallylinkedtoforecasting,butmostpapersinthattradition,suchasdeJong(2000)andDaiandSingleton(2000),focusonlyonin-sample tasopposedtoout-of-sampleforecasting.Moreover,thosethatdofocusonout-of-sampleforecasting,notablyDuffee(2002),concludethatthemodelsforecastpoorly.

Inthispaperwetakeanexplicitlyout-of-sampleforecastingperspective,andweuseneithertheno-arbitrageapproachnortheequilibriumapproach.Instead,weusetheNelsonandSiegel(1987)exponentialcomponentsframeworktodistilltheentireyieldcurve,period-by-period,intoathree-dimensionalparameterthatevolvesdynamically.Weshowthatthethreetime-varyingparametersmaybeinterpretedasfactors.Unlikefactoranalysis,however,inwhichoneestimatesboththeunobservedfactorsandthefactorloadings,theNelson–Siegelframeworkimposesstructureonthefactorloadings.3Doingsonotonlyfacilitateshighlypreciseestimationofthefactors,but,asweshow,italsoletsusinterpretthefactorsaslevel,slopeandcurvature.Weproposeandestimateautoregressivemodelsforthefactors,andthenweforecasttheyieldcurvebyforecastingthefactors.Ourresultsareencouraging;in

Theempiricalliteraturethatmodelsyieldsasacointegratedsystem,typicallywithoneunderlyingstochastictrend(theshortrate)andstationaryspreadsrelativetotheshortrate,issimilarinspirit.SeeDieboldandSharpe(1990),Halletal.(1992),Shea(1992),SwansonandWhite(1995),andPaganetal.(1996).2

Forcomparativediscussionofpointanddensityforecasting,seeDieboldetal.(1998)andDieboldetal.(1999).3

ClassicunrestrictedfactoranalysesincludeLittermanandScheinkman(1991)andKnezetal.(1994).

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particular,ourmodelsproduceone-year-aheadforecaststhatarenoticeablymoreaccuratethanstandardbenchmarks.

RelatedworkincludesthefactormodelsofLitzenbergeretal.(1995),Bliss(1997a,b),DaiandSingleton(2000),deJongandSanta-Clara(1999),deJong(2000),BrandtandYaron(2001)andDuffee(2002).Particularlyrelevantarethethree-factormodelsofBalduzzietal.(1996),Chen(1996),andespeciallytheAndersenandLund(1997)modelwithstochasticmeanandvolatility,whosethreefactorsareinterpretedintermsoflevel,slopeandcurvature.Wewillsubsequentlydiscussrelatedworkingreaterdetail;fornow,suf ceittosaythatlittleofitconsidersforecastingdirectly,andthatourapproach,althoughrelated,isindeedverydifferent.

Weproceedasfollows.InSection2weprovideadetaileddescriptionofourmodelingframework,whichinterpretsandextendsearlierworkinwayslinkedtorecentdevelopmentsinmultifactortermstructuremodeling,andwealsoshowhowitcanreplicateavarietyofstylizedfactsabouttheyieldcurve.InSection3weproceedtoanempiricalanalysis,describingthedata,estimatingthemodels,andexaminingout-of-sampleforecastingperformance.InSection4weofferinterpretiveconcludingremarks.

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