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Empiricalexchangeratemodelsofthenineties:Areanyttosurvive?Yin-WongCheung,MenzieD.ChinnAntonioGarciaPascualDepartmentofEconomics,E2,UniversityofCalifornia,SantaCruz,CA95064,USALaFolletteSchoolofPublicAairsandDepartmentofEconomics,UniversityofWisconsinandNBER,1180ObservatoryDrive,Madison,WI53706,USAInternationalMonetaryFund,70019thStreetNW,Washington,DC20431,USAWere-assessexchangeratepredictionusingawidersetofmodelsthathavebeenproposedinthelastdecade:interestrateparity,productivitybasedmodels,andacompositespecica-tion.Theperformanceofthesemodelsiscomparedagainsttworeferencespecicationschasingpowerparityandthesticky-pricemonetarymodel.Themodelsareestimatedinrst-dierenceanderrorcorrectionspecications,andmodelperformanceevaluatedatfore-casthorizonsof1,4and20quarters,usingthemeansquarederror,directionofchangemetrics,andtheconsistencytestofCheungandChinn[1998.Integration,cointegration,andtheforecastconsistencyofstructuralexchangeratemodels.JournalofInternationalMoneyandFinance17,813830].Overall,model/specication/currencycombinationsthatworkwellinoneperioddonotnecessarilyworkwellinanotherperiod.2005ElsevierLtd.Allrightsreserved.JELclassication:F31;F47Keywords:Exchangerates;Monetarymodel;Productivity;Interestrateparity;Purchasingpowerparity;Forecastingperformance *Correspondingauthor.Tel.:18314594247;fax:18314595900.E-mailaddress:cheung@ucsc.edu(Y.-W.Cheung).0261-5606/$-seefrontmatter2005ElsevierLtd.Allrightsreserved.doi:10.1016/j.jimonn.2005.08.002 JournalofInternationalMoneyandFinance24(2005)1150 www.elsevier.com/locate/econbase 1.IntroductionTherecentmovementsinthedollarandtheeurohaveappearedseeminglyinex-plicableinthecontextofstandardmodels.Whilethedollarmaynothavebeendaz-zlingasitwasdescribedinthemid-1980sithasbeencharacterizedasoverlydarling.Andtheeurosabilitytorepeatedlyconfoundpredictionsneedslittlere-emphasizing.Itisagainstthisbackdropthatseveralnewmodelshavebeenforwardedinthepastdecade.Someexplanationsaremotivatedbyndingsintheempiricalandthe-oreticalliterature,suchasthecorrelationbetweennetforeignassetpositionsandrealexchangeratesandthosebasedonproductivitydierences.Noneofthesemodels,however,havebeensubjectedtorigorousexaminationofthesortthatMeeseandRogoconductedintheirseminalwork,theoriginaltitleofwhichwehaveappro-priatedandamendedforthisstudy.Webelievethatasystematicexaminationofthesenewerempiricalmodelsislongoverdue,foranumberofreasons.First,whilethesemodelshavebecomeprominentinpolicyandnancialcircles,theyhavenotbeensubjectedtothesortsystematicout-of-sampletestingconductedinacademicstudies.Forinstance,productivitydidnotmakeanappearanceinearliercomparativestudies,buthasbeentappedasanimportantdeterminantoftheeurodollarexchangerate(Owen,2001;Rosen-berg,2000Second,mostoftherecentacademictreatmentsexchangerateforecastingperfor-mancereliesuponasinglemodelsuchasthemonetarymodelorsomeotherlimitedsetofmodelsof1970svintage,suchaspurchasingpowerparityorrealin-terestdierentialmodel.Third,thesamecriteriaareoftenused,neglectingalternativedimensionsofmodelforecastperformance.Thatis,therstandsecondmomentmetricssuchasmeaner-rorandmeansquarederrorareconsidered,whileotheraspectsthatmightbeofgreaterimportanceareoftenneglected.Wehaveinmindthedirectionofchangeperhapsmoreimportantfromamarkettimingperspectiveandotherindicatorsofforecastattributes.Inthisstudy,weextendtheforecastcomparisonofexchangeratemodelsinsev-eraldimensions.Fivemodelsarecomparedagainsttherandomwalk.Purchasingpowerparityisincludedbecauseofitsimportanceintheinternationalnanceliteratureandthe Frankel(1985)TheEconomist(2001),respectively.MeeseandRogo(1983)wasbaseduponworkinEmpiricalexchangeratemodelsoftheseventies:areanyttosurvive?InternationalFinanceDiscussionPaperNo.184(BoardofGovernorsoftheFederalReserveSystem,1981).Similarly,behavioralequilibriumexchangerate(BEER)modelsessentiallycombinationsofrealin-terestdierential,nontradedgoodsandportfoliobalancemodelshavebeenusedinestimatingtheequilibriumvaluesoftheeuro.SeeBankofAmerica(Yilmaz,2003),Bundesbank(ClostermannandSchnatz,2000),ECB(Schnatzetal.,2004),andIMF(Alberolaetal.,1999).AcorrespondingstudyforthedollarisYilmazandJen(2001)Y.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 factthattheparityconditioniscommonlyusedtogaugethedegreeofexchangeratemisalignment.Thesticky-pricemonetarymodelofDornbuschandFrankelistheonlystructuralmodelthathasbeenthesubjectofprevioussystematicanal-yses.Theothermodelsincludeoneincorporatingproductivitydierentials,aninterestrateparityspecication,andacompositespecicationincorporatinganumberofchannelsidentiedindieringtheoreticalmodels.ThebehaviorofUSdollar-basedexchangeratesoftheCanadiandollar,Britishpound,DeutschemarkandJapaneseyenareexamined.Toinsurethatourcon-clusionsarenotdrivenbydollarspecicresults,wealsoexamine(butdonotre-port)theresultsforthecorrespondingyen-basedrates.Themodelsareestimatedintwoways:inrst-dierenceanderrorcorrectionspecications.Forecastingperformanceisevaluatedatseveralhorizons(1-,4-and20-quarterhorizons)andintwosampleperiods(post-LouvreAccordandpost-1982).WeaugmenttheconventionalmetricswithadirectionofchangestatisticandtheconsistencycriterionofCheungandChinn(1998)Beforeproceedingfurther,itmayproveworthwhiletoemphasizewhywefocusonout-of-samplepredictionasourbasisofjudgingtherelativemeritsofthemodels.Itisnotthatwebelievethatwecannecessarilyout-forecastthemarketinrealtime.Indeed,ourforecastingexercisesareinthenatureofexpostsimulations,whereinmanyinstancescontemporaneousvaluesoftheright-hand-sidevariablesareusedtopredictfutureexchangerates.Rather,weconstruetheexerciseasameansofpro-tectingagainstdataminingthatmightoccurwhenrelyingsolelyonin-sampleTheexchangeratemodelsconsideredintheexercisearesummarizedinSectionSectiondiscussesthedata,theestimationmethods,andthecriteriausedtocom-pareforecastingperformance.TheforecastingresultsarereportedinSection.Sec-2.TheoreticalmodelsTheuniverseofempiricalmodelsthathasbeenexaminedovertheoatingrateperiodisenormous.Consequentlyanyevaluationofthesemodelsmustnecessarilybeselective.Ourcriteriarequirethatthemodelsare(1)prominentintheeconomicandpolicyliterature,(2)readilyimplementableandreplicable,and(3)notpreviouslyevaluatedinasystematicfashion.Weusetherandomwalkmodelasourbenchmarknaivemodel,inlinewithpreviouswork,butwealsoselectthepurchasingpowerpar-ityandthebasicDornbusch(1976)Frankel(1979)modelastwocomparatorspecications,astheystillprovidethefundamentalintuitiononhowexible Thereisanenormousliteratureondatamining.SeeInoueandKilian(2004)forsomerecentthoughtsontheusefulnessofout-of-sampleversusin-sampletests.Y.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 exchangeratesbehave.Thepurchasingpowerparityconditionexaminedinthisstudyisgivenbywhereisthelogexchangerate,isthelogpricelevel(CPI),anddenotestheintercountrydierence.Strictlyspeaking,Eq.istherelativepurchasingpowerparitycondition.Therelativeversionisexaminedbecausepriceindicesratherthantheactualpricelevelsareconsidered.Thesticky-pricemonetarymodelcanbeexpressedasfollows:whereislogmoney,islogrealGDP,aretheinterestandinationrates,re-spectively,andisanerrorterm.Thecharacteristicsofthismodelarewellknown,sowewillnotdevotetimetodiscussingthetheorybehindtheequation.Wenote,however,thatthelistofvariablesincludedinEq.encompassesthoseemployedintheexiblepriceversionofthemonetarymodel,aswellasthemicro-basedgeneralequilibriummodelsofStockman(1980)Lucas(1982).Inaddition,twoobservationsareinor-der.First,thesticky-pricemodelcanbeinterpretedasanextensionofEq.suchthatthepricevariablesarereplacedbymacrovariablesthatcapturemoneydemandandovershootingeects.Second,wedonotimposecoecientrestrictionsinEq.causetheorygivesuslittleguidanceregardingtheexactvaluesofalltheparameters.Next,weassessmodelsthatareintheBalassaSamuelsonvein,inthattheyac-cordacentralroletoproductivitydierentialstoexplainingmovementsinreal,andhencealsonominal,exchangerates.RealversionsofthemodelcanbetracedtoGregorioandWolf(1994),whilenominalversionsincludeClementsandFrenkelChinn(1997).Suchmodelsdropthepurchasingpowerparityassumptionforbroadpriceindices,andallowtherealexchangeratetodependupontherelativepriceofnontradables,itselfafunctionofproductivity()dierentials.Agenericpro-ductivitydierentialexchangerateequationisAlthoughEqs.(2)and(3)bearasupercialresemblance,thetwoexpressionsem-bodyquitedierenteconomicandstatisticalimplications.ThecentraldierenceisthatEq.assumesPPPholdsinthelongrun,whiletheproductivitybasedmodelmakesnosuchpresumption.InfactthenominalexchangeratecandriftinnitelyfarawayfromPPP,althoughthepathisdeterminedinthismodelbyproductivitydierentials.Thefourthmodelisacompositemodelthatincorporatesanumberoffamiliarrelationships.Atypicalspecicationis:whereistherelativepriceofnontradables,therealinterestrate,gdebtthegov-ernmentdebttoGDPratio,totthelogtermsoftrade,andnfaisthenetforeignY.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 asset.NotethatweimposeaunitarycoecientontheintercountrylogpricelevelsothatEq.couldbere-expressedasdeterminingtherealexchangerate.Althoughthisparticularspecicationcloselyresemblesthebehavioralequilibriumexchangerate(BEER)modelofClarkandMacDonald(1999),italsosharesattrib-uteswiththeNATREXmodelofStein(1999)andtherealequilibriumexchangeratemodelofEdwards(1989),aswellasanumberofotherapproaches.Consequently,wewillhenceforthrefertothisspecicationasthecompositemodel.Again,rela-tivetoEq.,thecompositemodelincorporatestheBalassaSamuelsoneect(via),theovershootingeect(),andtheportfoliobalanceeect(gdebt,nfa).Modelsbaseduponthisframeworkhavebeenthepredominantapproachtode-terminingtherateatwhichcurrencieswillgravitatetooversomeintermediatehori-zon,especiallyinthecontextofpolicyissues.Forinstance,thebehavioralequilibriumexchangerateapproachisthemodelthatismostoftenusedtodeterminethelong-termvalueoftheeuro.Thenalspecicationassessedisnotamodelperse;ratheritisanarbitragere-uncoveredinterestrateparity:istheinterestrateofmaturity.Similartotherelativepurchasingpower,thisrelationneednotbeestimatedinordertogeneratepredictions.Theinterestrateparityisincludedintheforecastcomparisonexercisemainlybe-causeithasrecentlygatheredempiricalsupportatlonghorizons(Alexius,2001;ChinnandMeredith,2004),incontrasttothedisappointingresultsattheshorterho-rizons.MacDonaldandNagayasu(2000)havealsodemonstratedthatlong-runin-terestratesappeartopredictexchangeratelevels.Onthebasisofthesendings,weanticipatethatthisspecicationwillperformbetteratthelongerhorizonsthanatshorterhorizons.3.Data,estimationandforecastingcomparison3.1.DataTheanalysisusesquarterlydatafortheUnitedStates,Canada,UK,Japan,Ger-many,andSwitzerlandoverthe1973q2to2000q4period.Theexchangerate,money,priceandincomevariablesaredrawnprimarilyfromtheIMFsInternational Onthislatterchannel,CavalloandGhironi(2002)providearolefornetforeignassetsinthedetermi-nationofexchangeratesinthesticky-priceoptimizingframeworkofObstfeldandRogo(1995)Wedonotexamineacloselyrelatedapproach,theinternalexternalbalanceapproachoftheIMF(seeFaruqeeetal.,1999).TheIMFapproachrequiresextensivejudgmentsregardingthetrendlevelofoutput,andtheimpactofdemographicvariablesuponvariousmacroeconomicaggregates.Wedidnotbelieveitwouldbepossibletosubjectthismethodologytothesameout-of-sampleforecastingexerciseappliedtotheothers.Despitethisnding,thereislittleevidencethatlong-terminterestratedierentialsorequivalentlylong-datedforwardrateshavebeenusedforforecastingatthehorizonsweareinvestigating.Oneex-ceptionfromthenon-academicliteratureisRosenberg(2001)Y.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 FinancialStatistics.TheproductivitydatawereobtainedfromtheBankforInterna-tionalSettlements,whiletheinterestratesusedtoconducttheinterestrateparityforecastsareessentiallythesameasthoseusedinChinnandMeredith(2004).SeeAppendix1foramoredetaileddescription.Twoout-of-sampleperiodsareusedtoassessmodelperformance:1987q22000q4and1983q12000q4.Theformerperiodconformstothepost-LouvreAc-cordperiod,whilethelatterspanstheperiodaftertheendofmonetarytargetingintheUS.Theshorterout-of-sampleperiod(19872000)spansaperiodofrelativedollarstability(andappreciationinthecaseofthemark).Thelongerout-of-sampleperiodsubjectsthemodelstoamorerigoroustest,inthatthepredictiontakesplaceoveralargedollarappreciationandsubsequentdepreciation(againstthemark)andalargedollardepreciation(from250to150yenperdollar).Inotherwords,thislon-gerspanencompassesmorethanonedollarcycle.Theuseofthislongout-of-sam-pleforecastingperiodhastheaddedadvantagethatitensuresthattherearemanyforecastobservationstoconductinferenceupon.3.2.EstimationandforecastingWeadopttheconventionintheempiricalexchangeratemodelingliteratureofim-plementingrollingregressionsestablishedbyMeeseandRogo.Thatis,estimatesareappliedoveragivendatasample,out-of-sampleforecastsproduced,thenthesampleismovedup,orrolledforwardoneobservationbeforetheprocedureisre-peated.Thisprocesscontinuesuntilalltheout-of-sampleobservationsareex-hausted.Whiletherollingregressionsdonotincorporatepossibleeciencygainsasthesamplemovesforwardthroughtime,theprocedurehasthepotentialbenetofalleviatingparameterinstabilityeectsovertimewhichisacommonlycon-ceivedphenomenoninexchangeratemodeling.Twospecicationsofthesetheoreticalmodelswereestimated:(1)anerrorcorrec-tionspecication,and(2)arst-dierencespecication.Thesetwospecicationsen-taildierentimplicationsforinteractionsbetweenexchangeratesandtheirdeterminants.Itiswellknownthatboththeexchangerateanditseconomicdeter-minantsare(1).Theerrorcorrectionspecicationexplicitlyallowsforthelong-runinteractioneectofthesevariables(ascapturedbytheerrorcorrectionterm)ingeneratingforecast.Ontheotherhand,therstdierencesmodelemphasizestheeectsofchangesinthemacrovariablesonexchangerates.Ifthevariablesarecointegrated,thentheformerspecicationismoreecientthanthelatteroneandisexpectedtoforecastbetterinlonghorizons.Ifthevariablesarenotcointe-grated,theerrorcorrectionspecicationcanleadtospuriousresults.Becauseitisnoteasytodetermineunambiguouslywhetherthesevariablesarecointegratedornot,weconsiderbothspecications.Sinceimplementationoftheerrorcorrectionspecicationisrelativelyinvolved,wewilladdresstherst-dierencespecicationtobeginwith.Considerthegeneralexpressionfortherelationshipbetweentheexchangerateandfundamentals:Y.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 isavectoroffundamentalvariablesunderconsideration.Therst-dier-encespecicationinvolvesthefollowingregression:Theseestimatesarethenusedtogenerateone-andmulti-quarteraheadforecasts.Sincetheseexchangeratemodelsimplyjointdeterminationofallvariablesintheequations,itmakessensetoapplyinstrumentalvariables.However,previousexperi-enceindicatesthatthegainsinconsistencyarefaroutweighedbythelossineciency,intermsofprediction(ChinnandMeese,1995).Hence,werelysolelyonOLS.Theerrorcorrectionestimationinvolvesatwo-stepprocedure.Intherststep,thelong-runcointegratingrelationimpliedbyEq.isidentiedusingtheJohansenprocedure.Theestimatedcointegratingvector()isincorporatedintotheerrorcor-rectionterm,andtheresultingequationisestimatedviaOLS.Eq.canbethoughtofasanerrorcorrectionmodelstrippedofshort-rundynamics.AsimilarapproachwasusedinMark(1995)ChinnandMeese(1995),exceptforthefactthatinthosetwocases,thecointegratingvectorwasimposedapriori.Theuseofthisspecicationismotivatedbythedicultyinesti-matingtheshort-rundynamicsinexchangerateequations.Onekeydierencebetweenourimplementationoftheerrorcorrectionspecica-tionandthatundertakeninsomeotherstudiesinvolvesthetreatmentofthecointe-gratingvector.Insomeotherprominentstudies(MacDonaldandTaylor,1993),thecointegratingrelationshipisestimatedovertheentiresample,andthenout-of-sam-pleforecastingundertaken,wheretheshort-rundynamicsaretreatedastimevaryingbutthelong-runrelationshipisnot.Whiletherearegoodreasonsforadoptingthisinparticularonewantstouseasmuchinformationaspossibletoobtainestimatesofthecointegratingrelationshipstheasymmetryinestimationapproachistroublesomeandmakesitdiculttodistinguishquasiexanteforecastsfromtrueexanteforecasts.Consequently,ourestimatesofthecointegratingrelation-shipvaryasthedatawindowmoves.Itisalsousefultostressthedierencebetweentheerrorcorrectionspecicationforecastsandtherst-dierencespecicationforecasts.Inthelatter,expostvaluesoftheright-hand-sidevariablesareusedtogeneratethepredictedexchangerate OnlycontemporaneouschangesareinvolvedinEq..Whilethisisasomewhatrestrictiveassump-tion,itisnotclearthatallowingmorelagswouldresultinimprovedprediction.Moreover,implementa-tionofaspecicationprocedurebaseduponsomelag-selectioncriterionwouldbemuchtoocumbersometoimplementinthiscontext.Weoptedtoexcludeshort-rundynamicsinEq.(8)becausea)theuseofEq.(8)yieldstrueexanteforecastsandmakesourexercisedirectlycomparablewith,forexample,Mark(1995),ChinnandMeeseGroen(2000),andb)theinclusionofshort-rundynamicscreatesadditionaldemandsonthegenerationoftheright-hand-sidevariablesandthestabilityoftheshort-rundynamicsthatcomplicatetheforecastcomparisonexercisebeyondamanageablelevel.Restrictionsonthe-parametersinEqs.(2),(3)and(4)arenotimposedbecauseinmanycaseswedonothavestrongpriorsontheexactvaluesofthecoecients.Y.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 change.Intheformer,contemporaneousvaluesoftheright-hand-sidevariablesarenotnecessary,andtheerrorcorrectionpredictionsaretrueexanteforecasts.Hence,weareaordingtherst-dierencespecicationsatremendousinformationaladvan-tageinforecasting.3.3.ForecastcomparisonToevaluatetheforecastingaccuracyofthedierentstructuralmodels,theratiobetweenthemeansquarederror(MSE)ofthestructuralmodelsandadriftlessran-domwalkisused.Avaluesmaller(larger)thanoneindicatesabetterperformanceofthestructuralmodel(randomwalk).Inferencesarebasedonaformaltestforthenullhypothesisofnodierenceintheaccuracy(i.e.intheMSE)ofthetwocompet-ingforecastsstructuralmodelversusdriftlessrandomwalk.Inparticular,weusetheDieboldMarianostatistic(DieboldandMariano,1995)whichisdenedastheratiobetweenthesamplemeanlossdierentialandanestimateofitsstandarderror;thisratioisasymptoticallydistributedasastandardnormal.Thelossdierentialisdenedasthedierencebetweenthesquaredforecasterrorofthestructuralmodelsandthatoftherandomwalk.Aconsistentestimateofthestandarddeviationcanbeconstructedfromaweightedsumoftheavailablesampleautocovariancesofthelossdierentialvector.FollowingAndrews(1991),aquadraticspectralkernelisem-ployed,togetherwithadata-dependentbandwidthselectionprocedure.Wealsoexaminethepredictivepowerofthevariousmodelsalongdierentdi-mensions.Onemightbetemptedtoconcludethatwearemerelychangingthewell-establishedrulesofthegamebydoingso.However,thereareverygoodrea-sonstouseotherevaluationcriteria.First,thereistheintuitivelyappealingrationalethatminimizingthemeansquarederror(orrelatedlymeanabsoluteerror)maynotbeimportantfromaneconomicstandpoint.Alesspedestrianmotivationisthatthetypicalmeansquarederrorcriterionmaymissoutonimportantaspectsofpredic-tions,especiallyatlonghorizons.ChristoersenandDiebold(1998)pointoutthatthestandardmeansquarederrorcriterionindicatesnoimprovementofpredictionsthattakeintoaccountcointegratingrelationshipsvisavisunivariatepredictions.Butsurely,anyreasonablecriteriawouldputsomeweightonthetendencyforpredic-tionsfromcointegratedsystemstohangtogether.Hence,ourrstalternativeevaluationmetricfortherelativeforecastperformanceofthestructuralmodelsisthedirectionofchangestatistic,whichiscomputedasthenumberofcorrectpredictionsofthedirectionofchangeoverthetotalnumberofpredictions.Avalueabove(below)50%indicatesabetter(worse)forecasting InusingtheDieboldMarianotest,wearerelyinguponasymptoticresults,whichmayormaynotbeappropriateforoursample.However,generatingnitesamplecriticalvaluesforthelargenumberofcaseswedealwithwouldbecomputationallyinfeasible.Moreimportantly,themostlikelyoutcomeofsuchanexercisewouldbetomakedetectionofstatisticallysignicantoutperformanceevenmorerare,andleavingourbasicconclusionintact.WealsoexperiencedwiththeBartlettkernelandthedeterministicbandwidthselectionmethod.Theresultsfromthesemethodsarequalitativelyverysimilar.Appendix2containsamoredetaileddiscussionoftheforecastcomparisontests.Y.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 performancethananaivemodelthatpredictstheexchangeratehasanequalchancetogoupordown.Again,DieboldandMariano(1995)provideateststatisticforthenullofnoforecastingperformanceofthestructuralmodel.Thestatisticfollowsabi-nomialdistribution,anditsstudentizedversionisasymptoticallydistributedasastan-dardnormal.NotonlydoesthedirectionofchangestatisticconstituteanalternativeLeitchandTanner(1991),forinstance,arguethatadirectionofchangecri-terionmaybemorerelevantforprotabilityandeconomicconcerns,andhenceamoreappropriatemetricthanothersbasedonpurelystatisticalmotivations.Thecriterionisalsorelatedtotestsformarkettimingability(CumbyandModest,1987Thethirdmetricweusedtoevaluateforecastperformanceistheconsistencycri-terionproposedinCheungandChinn(1998).Thismetricfocusesonthetime-seriespropertiesoftheforecast.Theforecastofagivenspotexchangerateislabeledasconsistentif(1)thetwoserieshavethesameorderofintegration,(2)theyarecoin-tegrated,and(3)thecointegrationvectorsatisestheunitaryelasticityofexpecta-tionscondition.Looselyspeaking,aforecastisconsistentifitmovesintandemwiththespotexchangerateinthelongrun.Whilethetwopreviouscriteriafocusontheprecisionoftheforecast,theconsistencyrequirementisconcernedwiththelong-runrelativevariationbetweenforecastsandactualrealizations.OnemayarguethatthecriterionislessdemandingthantheMSEanddirectionofchangemetrics.Aforecastthatsatisestheconsistencycriterioncan(1)haveanMSElargerthanthatoftherandomwalkmodel,(2)haveadirectionofchangestatisticlessthan1/2,or(3)generateforecasterrorsthatareseriallycorrelated.However,giventheproblemsrelatedtomodeling,estimation,anddataquality,theconsistencycriterioncanbeamoreexiblewaytoevaluateaforecast.CheungandChinn(1998)amoredetaileddiscussionontheconsistencycriterionanditsimplementation.Itisnotobviouswhichoneofthethreeevaluationcriteriaisbetterastheyeachhaveadierentfocus.TheMSEisastandardevaluationcriterion,thedirectionofchangemetricemphasizestheabilitytopredictdirectionalchanges,andtheconsis-tencytestisconcernedaboutthelong-runinteractionsbetweenforecastsandtheirrealizations.Insteadofarguingonecriterionisbetterthantheother,weconsidertheuseofthesecriteriaascomplementaryandprovidingamultifacetedpictureoftheforecastperformanceofthesestructuralmodels.Ofcourse,dependingonthepurposeofaspecicexercise,onemayfavoronemetricovertheother.4.Comparingtheforecastperformance4.1.TheMSEcriterionThecomparisonofforecastingperformancebasedonMSEratiosissummarizedTable1.ThetablecontainsMSEratiosandthe-valuesfromvedollar-basedcur-rencypairs,vemodelspecications,theerrorcorrectionandrst-dierencespeci-cations,threeforecastinghorizons,andtwoforecastingsamples.Eachcellinthetablehastwoentries.TherstoneistheMSEratio(theMSEsofastructuralmodeltotherandomwalkspecication).TheentryunderneaththeMSEratioisthe-valueY.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 Table1TheMSEratiosfromthedollar-basedexchangeratesSpecicationHorizonSample1:1987q22000q4Sample2:1983q1PPPS-PIRPPRODCOMPPPPS-PIRPPRODCOMPPanelA:BP/$ECM14.1651.0471.0080.9951.0855.6781.0501.0461.0421.0490.0030.4090.8830.8970.2080.0310.3100.3180.3030.44841.7501.1271.0921.0171.0991.6121.1421.1231.0851.1270.1990.5030.6200.8020.2530.2240.1710.3100.2370.225200.7821.8091.3421.0951.3400.6321.4570.8411.5452.1790.5360.0140.2400.4110.1680.1560.0710.5180.0920.057FD11.0411.0061.1911.0861.0791.0230.4340.9400.2170.1350.3370.90141.1201.1241.8811.2501.4551.4480.3150.5240.0010.1490.1760.351201.8912.5316.9533.2235.5576.0150.1770.0210.0000.1950.0190.001PanelB:CAN$/$ECM132.2051.0541.0901.1481.27831.9821.0561.0921.0411.3370.0080.1270.0480.0620.0160.0010.2790.0220.5520.00446.5041.1021.1721.1821.6036.9471.1161.1701.0171.7540.0160.1810.4520.1570.1180.0040.3340.3590.9290.018201.5690.9390.8651.0901.7601.1711.0620.8131.0971.6230.0000.5740.7600.3080.0020.0930.7270.6070.3180.000FD11.1001.1150.6141.1011.1710.6660.1790.1380.1090.2570.0470.15141.1371.1600.8991.1961.2691.1430.4610.3410.7980.3470.1920.704200.5150.5041.9241.8922.0042.2890.1930.1820.0060.1820.1430.204PanelC:DM/$ECM16.3571.0591.0301.0410.99511.1731.1051.0290.9970.9110.0060.4640.2950.5740.9550.0050.4160.3640.9610.20642.3011.0801.1361.0801.1162.6751.1041.0630.9490.8980.0160.4440.0690.2820.6420.0070.5990.4850.6260.558200.6491.0470.5961.1312.1370.4111.7710.8951.2600.6330.3630.6370.1670.1410.2160.2480.2120.6560.0390.202FD11.2681.3240.5551.1231.1960.6940.0520.1060.0010.0170.0840.02041.4021.6070.8441.0771.2811.1510.0240.0300.5710.4520.0090.612201.8141.9272.5221.7231.9643.9750.1750.1140.1400.2460.1210.003PanelD:SF/$ECM17.5951.0741.0511.024.8.6940.9951.0501.052.0.0010.1870.1380.515.0.0000.9060.1410.581.42.5371.2691.1831.184.2.1061.0021.1221.136.0.0140.0150.0590.367.0.0030.9820.2480.149.continuedonnextpage Y.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 oftheDieboldMarianostatistictestingthenullhypothesisthatthedierenceoftheMSEsofthestructuralandrandomwalkmodelsiszero(i.e.thereisnodierenceintheforecastaccuracyofthestructuralandtherandomwalkmodel).Becauseofthelackofdata,thecompositemodelisnotestimatedforthedollarSwissfrancanddol-yenexchangerates.Altogether,thereare216MSEratios,whichspreadevenlyacrossthetwoforecastingsamples.Ofthese216ratios,138arecomputedfromtheerrorcorrectionspecicationsand78fromtherst-dierenceones.Notethatinthetables,onlyerrorcorrectionspecicationentriesarereportedforthepurchasingpowerparityandinterestrateparitymodels.Infact,thetwomodelsarenotestimated;ratherthepredictedspotrateiscalculatedusingtheparityconditions.Totheextentthatthedeviationfromaparityconditioncanbeconsid-eredtheerrorcorrectionterm,webelievethiscategorizationismostappropriate. Table1(SpecicationHorizonSample1:1987q22000q4Sample2:1983q1PPPS-PIRPPRODCOMPPPPS-PIRPPRODCOMP201.1851.6211.4890.969.0.6341.3671.4891.377.0.5140.0690.0000.934.0.4310.0460.0000.011.FD11.1061.090.1.0891.067.0.1890.351.0.2370.545.41.3621.468.1.2321.332.0.0040.001.0.1530.050.202.4772.657.1.5401.870.0.0390.049.0.5210.394.PanelE:Yen/$ECM115.7131.0671.0491.073.10.5101.0081.0321.064.0.0030.3120.2510.125.0.0000.9200.3610.281.44.9731.1891.1741.239.2.5821.0151.0481.234.0.0220.2790.2470.151.0.0150.8740.6580.004.201.7970.9510.6031.011.0.8321.1750.5661.235.0.1490.6470.2270.851.0.5850.0490.1740.076.FD11.0851.048.1.1651.141.0.3210.480.0.1790.220.41.0041.023.0.9941.012.0.9780.881.0.9690.929.201.0810.973.0.9241.023.0.9120.963.0.8440.957.:Theresultsarebasedondollar-basedexchangeratesandtheirforecasts.Eachcellinthetablehastwoentries.TherstoneistheMSEratio(theMSEsofastructuralmodeltotherandomwalkspeci-cation).TheentryunderneaththeMSEratioisthe-valueofthehypothesisthattheMSEsofthestruc-turalandrandomwalkmodelsarethesame(basedonDieboldandMariano,1995,describedin).ThenotationsusedinthetableareECM:errorcorrectionspecication;FD:rst-dierencespecica-tion;PPP:purchasingpowerparitymodel;S-P:sticky-pricemodel;IRP:interestrateparitymodel;PROD:productivitydierentialmodel;andCOMP:compositemodel.Theforecastinghorizons(inquar-ters)arelistedundertheheadingHorizon.Theresultsforthepost-LouvreAccordforecastingperiodaregivenunderthelabelSample1andthoseforthepost-1983forecastingperiodaregivenunderthelabelSample2.A.indicatesthestatisticsarenotgeneratedduetounavailabilityofdata. Y.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 Overall,theMSEresultsarenotfavorabletothestructuralmodels.Ofthe216MSEratios,151arenotsignicant(atthe10%signicancelevel)and65aresignif-icant.Thatis,forthemajoritycasesonecannotdierentiatetheforecastingperfor-mancebetweenastructuralmodelandarandomwalkmodel.Forthe65signicantcases,thereare63casesinwhichtherandomwalkmodelissignicantlybetterthanthecompetingstructuralmodelsandonlytwocasesinwhichtheoppositeistrue.Thesignicantcasesarequiteevenlydistributedacrossthetwoforecastingperiods.As10%isthesizeofthetestandtwocasesconstitutelessthan10%ofthetotalof216cases,theempiricalevidencecanhardlybeinterpretedassupportiveofthesu-periorforecastingperformanceofthestructuralmodels.InspectionoftheMSEratiosdoesnotrevealmanyconsistentpatternsintermsofoutperformance.Itappearsthattheproductivitymodeldoesnotdoparticularlybadlyforthedollarmarkrateatthe1-and4-quarterhorizons.TheMSEratiosofthepurchasingpowerparityandinterestrateparitymodelsarelessthanunity(eventhoughnotsignicant)onlyatthe20-quarterhorizonandingconsistentwiththeperceptionthattheseparityconditionsworkbetteratlongratherthanatshorthorizons.Astheyen-basedresultsfortheMSEratiosaswellastheothertwometricsdisplaythesamepattern,wedonotreportthem.Theycanbefoundintheworkingpaperversionofthisarticle(Cheungetal.,2003Consistentwiththeexistingliterature,ourresultsaresupportiveoftheassertionthatitisverydiculttondforecastsfromastructuralmodelthatcanconsistentlybeattherandomwalkmodelusingtheMSEcriterion.Thecurrentexercisefurtherstrengthenstheassertionasitcoversbothdollar-andyen-basedexchangerates,twodierentforecastingperiods,andsomestructuralmodelsthathavenotbeenex-tensivelystudiedbefore.4.2.ThedirectionofchangecriterionTable2reportstheproportionofforecaststhatcorrectlypredictthedirectionofthedollarexchangeratemovementand,underneaththesesampleproportions,thevaluesforthehypothesisthatthereportedproportionissignicantlydierentfrom1/2.Whentheproportionstatisticissignicantlylargerthan1/2,theforecastissaidtohavetheabilitytopredictthedirectionofchange.Ontheotherhand,ifthesta-tisticissignicantlylessthan1/2,theforecasttendstogivethewrongdirectionofchange.Fortradingpurposes,informationregardingthesignicanceofincorrectpredictioncanbeusedtoderiveapotentiallyprotabletradingrulebygoingagainthepredictiongeneratedbythemodel.Followingthisargument,onemightconsiderthecasesinwhichtheproportionofcorrectforecastsislargerthanorlessthan1/2containthesameinformation.However,inevaluatingtheabilityofthemodeltode-scribeexchangeratebehavior,weseparatethetwocases.Thereismixedevidenceontheabilityofthestructuralmodelstocorrectlypredictthedirectionofchange.Amongthe216directionofchangestatistics,50(23)aresig-nicantlylarger(less)than1/2atthe10%level.Theoccurrenceofthesignicantout-performancecasesishigher(23%)thantheoneimpliedbythe10%levelofthetest.Y.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 Table2Directionofchangestatisticsfromthedollar-basedexchangeratesSpecicationHorizonSample1:1987q22000q4Sample2:1983q1PPPS-PIRPPRODCOMPPPPS-PIRPPRODCOMPPanelA:BP/$ECM10.5270.5460.4640.5640.5270.5830.5690.4110.5280.5280.6860.5000.5930.3450.6860.1570.2390.1280.6370.63740.5960.5770.5000.5190.4810.6520.5220.4250.4640.5070.1660.2671.0000.7820.7820.0110.7180.1980.5470.904200.3610.3890.5360.4720.3610.6230.5090.5890.4910.3590.0960.1820.5930.7390.0960.0740.8910.1280.8910.039FD10.4550.4730.4180.4720.5000.5560.5000.6860.2250.6371.0000.34640.4810.5770.3650.5070.6670.5360.7820.2670.0520.9040.0060.547200.6390.5560.5000.4150.4530.4910.0960.5051.0000.2160.4920.891PanelB:CAN$/$ECM10.5270.4730.4290.4000.3820.5690.5140.4250.5000.4580.6860.6860.2850.1380.0800.2390.8140.1981.0000.48040.7690.4420.3390.4230.3460.7830.5360.3700.5940.3190.0000.4050.0160.2670.0270.0000.5470.0260.1180.003200.9440.5000.7320.4720.0830.9620.4720.7670.5090.1510.0001.0000.0010.7390.0000.0000.6800.0000.8910.000FD10.5090.4730.6180.5420.4440.6110.8930.6860.0800.4800.3460.05940.5390.5190.6730.4780.4930.6230.5790.7820.0130.7180.9040.041200.8890.8890.5830.5850.6040.5090.0000.0000.3170.2160.1310.891PanelC:DM/$ECM10.5450.6360.3570.4550.4910.5140.4860.4110.5000.4860.5000.0430.0330.5000.8930.8140.8140.1281.0000.81440.6540.6350.4290.4620.4620.6520.4490.4250.4490.5070.0270.0520.2850.5790.5790.0110.3990.1980.3990.904200.7780.5830.6960.3330.3330.7170.2830.5890.4340.5090.0010.3170.0030.0460.0460.0020.0020.1280.3360.891FD10.4550.4730.8000.4440.4440.7500.5000.6860.0000.3460.3460.00040.3650.4620.6730.4930.4490.6090.0520.5790.0130.9040.3990.071200.6110.6390.6670.5090.4150.4720.1820.0960.0460.8910.2160.680PanelD:SF/$ECM10.6000.4000.3390.618.0.6110.5420.3840.625.0.1380.1380.0160.080.0.0590.4800.0470.034. Y.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 Theresultsindicatethatthestructuralmodelforecastscancorrectlypredictthedirec-tionofthechange,whiletheproportionofcaseswherearandomwalkoutperformsthecompetingmodelsisonlyaboutwhatonewouldexpectiftheyoccurredrandomly.Letustakeacloserlookattheincidencesinwhichtheforecastsareintherightdirection.Approximately58%ofthe50casesareassociatedwiththeerrorcorrec-tionmodelandtheremainderwiththerstdierencespecication.Thus,theerrorcorrectionspecicationwhichincorporatestheempiricallong-runrelationshipprovidesaslightlybetterspecicationforthemodelsunderconsideration.Thefore-castingperioddoesnothaveamajorimpactonforecastingperformance,sinceexactlyhalfofthesuccessfulcasesareineachforecastingperiod. Table2(continuedSpecicationHorizonSample1:1987q22000q4Sample2:1983q1PPPS-PIRPPRODCOMPPPPS-PIRPPRODCOMP40.5580.4040.4110.539.0.6380.5800.4250.580.0.4050.1660.1820.579.0.0220.1850.1980.185.200.7500.4440.4550.583.0.8110.5280.4550.434.0.0030.5050.6700.317.0.0000.6800.6700.336.FD10.4360.400.0.4440.458.0.3450.138.0.3460.480.40.3460.308.0.4350.362.0.0270.006.0.2790.022.200.6110.611.0.7170.698.0.1820.182.0.0020.004.PanelE:Yen/$ECM10.5270.5270.3750.546.0.5970.5970.4250.514.0.6860.6860.0610.500.0.0990.0990.1980.814.40.6730.5770.4820.519.0.6810.6230.5480.406.0.0130.2670.7890.782.0.0030.0410.4130.118.200.6110.5560.6960.556.0.8110.4150.7030.340.0.1820.5050.0030.505.0.0000.2160.0010.020.FD10.5820.564.0.5830.542.0.2250.345.0.1570.480.40.6540.596.0.6520.652.0.0270.166.0.0120.012.200.6110.583.0.7550.736.0.1820.317.0.0000.001.Table3reportstheproportionofforecaststhatcorrectlypredictthedirectionofthedollarexchangeratemovement.Underneatheachdirectionofchangestatistic,the-valuesforthehypothesisthatthere-portedproportionissignicantlydierentfrom1/2islisted.Whenthestatisticissignicantlylargerthan1/2,theforecastissaidtohavetheabilitytopredictthedirectionofchange.Ifthestatisticissignicantlylessthan1/2,theforecasttendstogivethewrongdirectionofchange.ThenotationsusedinthetableareECM:errorcorrectionspecication;FD:rst-dierencespecication;PPP:purchasingpowerparitymod-el;S-P:sticky-pricemodel;IRP:interestrateparitymodel;PROD:productivitydierentialmodel;andCOMP:compositemodel.Theforecastinghorizons(inquarters)arelistedundertheheadingHorizon.Theresultsforthepost-LouvreAccordforecastingperiodaregivenunderthelabelSample1andthoseforthepost-1983forecastingperiodaregivenunderthelabelSample2.A.indicatesthestatisticsarenotgeneratedduetounavailabilityofdata. Y.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 Amongthevemodelsunderconsideration,thepurchasingpowerparityspeci-cationhasthehighestnumber(18)offorecaststhatgivethecorrectdirectionofchangeprediction,followedbythesticky-price,composite,andproductivitymodels(10,9,and8,respectively),andtheinterestrateparitymodel.Thus,atleastonthiscount,thenewerexchangeratemodelsdonotedgeouttheoldfashionedpur-chasingpowerparitydoctrineandthesticky-pricemodel.Becausetherearedieringnumbersofforecastsduetodatalimitationsandspecications,theproportionsdonotexactlymatchupwiththenumbers.Proportionately,thepurchasingpowermodeldoesthebest.Interestingly,thesuccessofdirectionofchangepredictionappearstobecurrencyspecic.Thedollaryenexchangerateyields13outof50forecaststhatgivethecor-rectdirectionofchangeprediction.Incontrast,thedollarpoundhasonlyfouroutof50forecaststhatproducethecorrectdirectionofchangeprediction.Thecasesofcorrectdirectionpredictionappeartoclusteratthelongforecastho-rizon.The20-quarterhorizonaccountsfor22ofthe50caseswhilethe4-and1-quarterhorizonshave18and10directionofchangestatistics,respectively,thataresignicantlylargerthan1/2.Sincetherehavenotbeenmanystudiesutilizingthedirectionofchangestatisticinsimilarcontexts,itisdiculttomakecompari-ChinnandMeese(1995)applythedirectionofchangestatisticto3-yearhori-zonsforthreeconventionalmodels,andndthatperformanceislargelycurrencyspecic:thenochangepredictionisoutperformedinthecaseofthedollaryenex-changerate,whileallmodelsareoutperformedinthecaseofthedollarpoundrate.Incontrast,inourstudyatthe20-quarterhorizon,thepositiveresultsappeartobefairlyevenlydistributedacrossthecurrencies,withtheexceptionofthedollarpoundrate.MirroringtheMSEresults,itisinterestingtonotethatthedirectionofchangestatisticworksforthepurchasingpowerparityatthe4-and20-quarterhorizonsandfortheinterestrateparitymodelonlyatthe20-quarterhorizon.Thispatternisentirelyconsistentwiththendingsthatthetwoparityconditionsholdbetteratlonghorizons.4.3.TheconsistencycriterionTheconsistencycriteriononlyrequirestheforecastandactualrealizationcomoveone-to-oneinthelongrun.Inassessingtheconsistency,wersttestiftheforecastandtherealizationarecointegrated.Iftheyarecointegrated,thenwetestifthe UsingMarkovswitchingmodels,Engel(1994)obtainssomesuccessalongthedirectionofchangedi-mensionathorizonsofupto1year.However,hisresultsarenotstatisticallysignicant.FloodandTaylor(1997)notedthetendencyforPPPtoholdbetteratlongerhorizons.MarkandMohdocumentthegradualcurrencyappreciationinresponsetoashort-terminterestdierential,con-trarytothepredictionsofuncoveredinterestparity.TheJohansenmethodisusedtotestthenullhypothesisofnocointegration.Themaximumeigenvaluestatisticsarereportedinthemanuscript.Resultsbasedonthetracestatisticsareessentiallythesame.Be-foreimplementingthecointegrationtest,boththeforecastandexchangerateserieswerecheckedforthe(1)property.Forbrevity,the(1)testresultsandthetracestatisticsarenotreported.Y.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 cointegratingvectorsatisesthe(1,1)requirement.Thecointegrationresultsarere-portedinTable3,whilethetestresultsforthe(1,1)restrictionarereportedinTable4Table3,67of216casesrejectthenullhypothesisofnocointegrationatthe10%signicancelevel.Thus,67forecastseries(31%ofthetotalnumber)arecointegratedwiththecorrespondingspotexchangerates.Theerrorcorrectionspecicationac-countsfor39ofthe67cointegratedcasesandtherst-dierencespecicationaccountsfortheremaining28cases.Thereissomeevidencethattheerrorcorrectionspecica-tiongivesbetterforecastingperformancethantherst-dierencespecication.These67cointegratedcasesareslightlymoreconcentratedinthelongerofthetwoforecast-ingperiods30forthepost-LouvreAccordperiodand37forthepost-1983period.Interestingly,thesticky-pricemodelgarnersthelargestnumberofcointegratedcases.Thereare60forecastseriesgeneratedunderthesticky-pricemodel.Twenty-sixofthese60series(i.e.43%)arecointegratedwiththecorrespondingspotrates.Thecompositemodelhasthesecondhighestfrequencyofcointegratedforecastseries39%of36se-ries.Thirty-sevenpercentoftheproductivitydierentialmodelforecastseries,33%ofthepurchasingpowerparitymodel,andnoneoftheinterestrateparitymodelareco-integratedwiththespotrates.Apparently,wedonotndevidencethattherecentlyde-velopedexchangeratemodelsoutperformtheoldvintagesticky-pricemodel.ThedollarpoundanddollarCanadiandollar,eachhavebetween19and17forecastseriesthatarecointegratedwiththeirrespectivespotrates.Thedollarmarkpair,whichyieldsrelativelygoodforecastsaccordingtothedirectionofchangemetric,hasonly12cointegratedforecastseries.Evidently,theforecastingperfor-manceisnotjustcurrencyspecic;italsodependsontheevaluationcriterion.Thedistributionofthecointegratedcasesacrossforecastinghorizonsispuzzling.Thefrequencyofoccurrenceisinverselyproportionaltotheforecastinghorizons.Thereare35of67one-quarteraheadforecastseriesthatarecointegratedwiththespotrates.However,thereareonly20ofthe4-quarteraheadand12ofthe20-quar-teraheadforecastseriesthatarecointegratedwiththespotrates.Onepossibleexpla-nationforthisresultisthattherearefewerobservationsinthe20-quarteraheadforecastseriesandthisaectsthepowerofthecointegrationtest.Theresultsoftestingforthelong-rununitaryelasticityofexpectationsatthe10%sig-nicancelevelarereportedinTable4.Theconditionoflong-rununitaryelasticityofex-pectationsthatisthe(1,1)restrictiononthecointegratingvectorisrejectedbythedataquitefrequently:48ofthe67cointegrationcases.Thatis28%ofthecointegratedcasesdisplaylong-rununitaryelasticityofexpectations.Takingboththecointegrationandrestrictiontestresultstogether,9%ofthe216casesofthedollar-basedexchangerateforecastseriesmeettheconsistencycriterion.Aslightlyhigherproportion(12%)meettheconsistencycriterioninthecaseoftheyen-basedexchangerates(resultsnotreported),butthepatternisessentiallythesameasforthedollar-basedexchangerates.4.4.DiscussionSeveralaspectsoftheforegoinganalysismeritdiscussion.Tobeginwith,evenatlonghorizons,theperformanceofthestructuralmodelsislessthanimpressivealongY.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 Table3Cointegrationbetweendollar-basedexchangeratesandtheirforecastsSpecicationHorizonSample1:1987q22000q4Sample2:1983q1PPPS-PIRPPRODCOMPPPPS-PIRPPRODCOMPPanelA:BP/$ECM15.257.260.776.9512.64*3.4117.09*4.6010.40*32.83*410.03*8.561.479.66*84.86*6.7512.98*3.777.8818.94*2026.64*15.84*5.3018.82*6.9510.62*3.165.034.254.72FD125.63*20.85*13.03*34.00*8.6016.91*47.306.712.216.983.023.45208.4513.00*3.443.572.792.24PanelB:CAN$/US$ECM10.7611.64*1.294.3710.35*8.4314.31*1.9013.96*19.66*42.3810.27*2.534.555.397.786.371.539.58*13.52*209.5015.02*3.9819.82*9.67*3.072.614.181.602.19FD126.34*31.53*9.1925.72*9.89*8.1243.193.873.886.998.633.892010.03*9.59*6.721.452.213.52PanelC:DM/$ECM12.173.675.193.865.232.2712.68*2.8427.29*21.03*44.755.242.745.3718.33*5.7624.06*1.816.678.492011.28*6.091.637.559.206.803.562.372.9416.60*FD120.82*4.028.2936.32*35.91*2.1844.273.1615.29*7.5610.82*2.80205.428.623.743.694.164.26PanelD:SF/$ECM15.596.753.453.80.4.5822.10*3.236.33.47.158.552.079.10.5.5810.71*2.279.68*.205.991.166.931.81.1.372.936.932.96.FD133.01*20.30*.23.55*10.38*.410.96*6.71.14.33*13.74*.209.437.51.2.272.59.PanelE:Yen/$ECM19.422.196.941.84.6.9619.44*6.4512.73*.49.013.434.133.22.10.46*10.71*3.2714.79*.206.384.672.932.19.6.762.903.485.63.FD113.35*9.79*.15.47*15.47*.45.533.77.6.025.74.201.762.15.4.943.96.:TheJohansenmaximumeigenvaluestatisticforthenullhypothesisthatadollar-basedexchangerateanditsforecastarenotcointegrated.*indicates10%levelsignicance.Testsforthenullofonecoin-tegratingvectorwerealsoconductedbutinallcasesthenullwasnotrejected.ThenotationsusedinthetableareECM:errorcorrectionspecication;FD:rst-dierencespecication;PPP:purchasingpowerparitymodel;S-P:sticky-pricemodel;IRP:interestrateparitymodel;PROD:productivitydierentialmodel;andCOMP:compositemodel.Theforecastinghorizons(inquarters)arelistedundertheheadingHorizon.Theresultsforthepost-LouvreAccordforecastingperiodaregivenunderthelabelSample1andthoseforthepost-1983forecastingperiodaregivenunderthelabelSample2.A.indicatesthestatisticsarenotgeneratedduetounavailabilityofdata. Table4Resultsofthe(1,1)restrictionrest:dollar-basedexchangeratesSpecicationHorizonSample1:1987q22000q4Sample2:1983q1PPPS-PIRPPRODCOMPPPPS-PIRPPRODCOMPPanelA:BP/$ECM10.553.380.000.350.460.071.000.56410.290.981.022.590.090.000.320.310.110.762036.660.400.3615.970.000.530.550.00FD15.380.120.040.790.360.020.730.830.380.552023.20PanelB:CAN$/$ECM111.204.467.752.876.480.000.030.010.090.01424.055.364.520.000.020.032076.5982.26201.370.000.000.00FD17.816.0913.905.470.010.010.000.02204.393.500.040.06PanelC:DM/$ECM18.828.356.610.000.000.0143.206.310.070.012055827.810.000.00FD110.173.030.470.000.080.49425.217.390.000.01PanelD:SF/$ECM1.10.07..0.00.4.2.4010.96..0.120.00.20..continuedonnextpage Y.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 theMSEdimension.Thisresultisconsistentwiththoseinotherrecentstudies,al-thoughwehavedocumentedthisndingforawidersetofmodelsandspecications.Groen(2000)restrictedhisattentiontoaexiblepricemonetarymodel,whileetal.(2003)examinedaportfoliobalancemodelaswell;bothremainedwithintheMSEevaluationframework.Settingasideissuesofstatisticalsignicance,itisinterestingthatlonghorizonerrorcorrectionspecicationsareover-representedinthesetofcaseswherearandomwalkisoutperformed.Indeed,thepurchasingpowerparityandinterestrateparitymodelsatthe20-quarterhorizonaccountformanyoftheMSEratioentriesthatarelessthanunity(13of23errorcorrectiondollar-basedentries,and14of33yen-basedentries).Thefactthatoutperformanceoftherandomwalkbenchmarkoccursatthelonghorizonsisconsistentwithotherrecentwork.AsEngelandWest(2005)havenoted,ifthediscountfactorisnearunity,andatleastoneofthedrivingvariablesfollowsanearunitrootprocess,theexchangeratemayappeartobeveryclosetoarandomwalk,andexhibitverylittlepredictabilityatshorthorizons.Butatlon-gerhorizons,thischaracterizationmaybelessapt,especiallyifitisthecase Table4(SpecicationHorizonSample1:1987q22000q4Sample2:1983q1PPPS-PIRPPRODCOMPPPPS-PIRPPRODCOMPFD120.1720.82.4.574.79.0.000.00.0.030.03.420.87.8.848.40.0.00.0.000.00.20..PanelE:Yen/$ECM1.3.222.47..0.070.12.4.3500.555.71..0.000.460.02.20..FD16.765.40.0.450.71.0.010.02.0.500.40.4..20..:Thelikelihoodratioteststatisticfortherestrictionof(1,1)onthecointegratingvectoranditsvaluearereported.ThetestisonlyappliedtothecointegrationcasespresentinTable3.ThenotationsusedinthetableareECM:errorcorrectionspecication;FD:rst-dierencespecication;PPP:purchas-ingpowerparitymodel;S-P:sticky-pricemodel;IRP:interestrateparitymodel;PROD:productivitydif-ferentialmodel;andCOMP:compositemodel.Theforecastinghorizons(inquarters)arelistedundertheheadingHorizon.Theresultsforthepost-LouvreAccordforecastingperiodaregivenunderthelabelSample1andthoseforthepost-1983forecastingperiodaregivenunderthelabelSample2.A.indicatesthestatisticsarenotgeneratedduetounavailabilityofdata. Y.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 thatexchangeratesarenotweaklyexogenouswithrespecttothecointegratingvector.Expandingthesetofcriteriadoesyieldsomeinterestingsurprises.Inparticular,thedirectionofchangestatisticsindicatesmoreevidencethatstructuralmodelscanoutperformarandomwalk.However,thebasicconclusionthatnospeciceco-nomicmodelisconsistentlymoresuccessfulthantheothersremainsintact.This,webelieve,isanewnding.Evenifwecannotgleanfromthisanalysisaconsistentwinner,itmaystillbeofinteresttonotethebestandworstperformingcombinationsofmodel/specication/currency.Ofthereportedresults,theinterestrateparitymodelatthe20-quarterho-rizonforthedollaryenexchangerate(post-1982)performsbestaccordingtotheMSEcriterion,withanMSEratioof0.57(-valueof0.17).(Thecorrespondingre-sultsfortheCanadiandollaryenexchangerateareevenbetter,witharatioof0.48-valueof0.04);seeCheungetal.,2003Table2Note,however,thatthesuperiorperformanceofaparticularmodel/specication/currencycombinationdoesnotnecessarilycarryoverfromoneout-of-sampleperiodtotheother.Thatisthelowestdollar-basedMSEratioduringthe1987q2periodisfortheDeutschemarkcompositemodelinrstdierences,whilethecor-respondingentryforthe1983q12000q4periodisfortheyeninterestparitymodel.Asidefromthepurchasingpowerparityspecication,theworstperformancesareassociatedwithrst-dierencespecications;inthiscasethehighestMSEratioisfortherst-dierencespecicationofthecompositemodelatthe20-quarterhorizonforthepounddollarexchangerateoverthepost-Louvreperiod.However,theothercatastrophicfailuresinpredictionperformancearedistributedacrossthevariousmod-elsestimatedinrstdierences,so(takingintoaccountthefactthatthesepredictionsutilizeexpostrealizationsoftheright-hand-sidevariables)thekeydeterminantinthispatternofresultsappearstobethedicultyinestimatingstableshort-rundynamics.Thatbeingsaid,wedonotwishtooverplaythestabilityofthelong-runestimatesweobtain.Inacompanionstudy(Cheungetal.,2005),wedonotndadenitere-lationshipbetweenin-sampletandout-of-sampleforecastperformance.Moreover,theestimatesexhibitwidevariationovertime.Evenincaseswherethestructuralmodeldoesreasonablywell,thereisquitesubstantialtime-variationintheestimateoftherateatwhichtheexchangeraterespondstodisequilibria.Asimilarobserva-tionappliestothecoecientestimatesoftheparametersofthecointegratingvector.Thus,aninterestingfutureresearchtopicistofurtherinvestigatetheeectofimpos-ingparameterrestrictionsandtheinteractionbetweenparameterinstabilityandforecastperformance. EngelandWest(2005)useGrangercausalityteststoconducttheirinference.Sincetheyfailtondcointegrationoftheexchangeratewiththemonetaryfundamentals,theydonotconducttestsforweakexogeneity.However,otherstudies,spanningdierentsampleperiodsandmodels,havedetectedbothco-integration;seeforinstanceMacDonaldandMarsh(1999)Chinn(1997),amongothers.Aninterestingresearchtopic,assuggestedbyareferee,istoinvestigatewhethertheforecastsofthesemodelscangenerateprotabletradingstrategies.Theissue,whichisbeyondthescopeofthecurrentex-ercise,wouldinvolveobtainingdierentvintagesofmacrodatatouseasfuturevariablesingeneratingY.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 Onequestionthatmightoccurtothereaderiswhetherourresultsaresensitivetotheout-of-sampleperiodwehaveselected.Infact,itispossibletotheper-formanceofthemodelsaccordingtoanMSEcriterionbyselectingashorterout-of-sampleforecastingperiod.Inanothersetofresults(Cheungetal.,2005),weimple-mentedthesameexercisesfora1993q12000q4forecastingperiod,andfoundsome-whatgreatersuccessfordollar-basedratesaccordingtotheMSEcriterion,andsomewhatlesssuccessalongthedirectionofchangedimension.Webelievethatthedierenceinresultsisanartifactofthelongupswinginthedollarduringthe1990sthatgivesanadvantagetostructuralmodelsovertheno-changeforecastem-bodiedintherandomwalkmodelwhenusingthemostrecent8yearsoftheoatingrateperiodasthepredictionsample.Thisconjectureisbuttressedbythefactthattheyen-basedexchangeratesdidnotexhibitasimilarpatternofresults.Thus,inusingfairlylongout-of-sampleperiods,aswehavedone,wehavegivenmaximumadvan-tagetotherandomwalkcharacterization.5.ConcludingremarksThispaperhassystematicallyassessedthepredictivecapabilitiesofmodelsdevel-opedduringthe1990s.Thesemodelshavebeencomparedalonganumberofdimen-sions,includingeconometricspecication,currencies,out-of-samplepredictionperiods,anddieringmetrics.Thedierencesinforecastevaluationsfromdierentevaluationcriteria,forinstance,illustratethepotentiallimitationofusingasinglecriterionsuchasthepopularMSEmetric.Clearly,theevaluationcriteriacouldhavebeenexpandedfurther.Forinstance,recentlyAbhyankaretal.(2005)haveproposedautility-basedmetricbasedupontheportfolioallocationproblem.Theyndthattherelativeperformanceofthestructuralmodelincreaseswhenusingthismetric.Totheextentthatthisisageneralnding,onecaninterpretourap-proachasbeingconservativewithrespecttondingsuperiormodelperformance.Atthisjuncture,itmayalsobeusefultooutlinetheboundariesofthisstudywithrespecttomodelsandspecications.Firstly,wehaveonlyevaluatedlinearmodels,eschewingfunctionalnonlinearities(MeeseandRose,1991;KilianandTaylor,2003andregimeswitching(EngelandHamilton,1990;CheungandErlandsson,2005Norhaveweemployedpanelregressiontechniquesinconjunctionwithlong-runre-lationships,despitethefactthatrecentevidencesuggeststhepotentialusefulnessofsuchapproaches(MarkandSul,2001).Further,wedidnotundertakesystems-basedestimationthathasbeenfoundincertaincircumstancestoyieldsuperiorforecastperformance,evenatshorthorizons(e.g.,MacDonaldandMarsh,1997).Suchamethodologywouldhaveprovenmuchtoocumbersometoimplementinthecross-currencyrecursiveframeworkemployedinthisstudy.Finally,thecurrentstudyexaminestheforecastingperformanceandtheresultsarenotnecessarilyindic-ativeoftheabilitiesofthesemodelstoexplainexchangeratebehavior.Forinstance, McCrackenandSapp(2005)forwardanencompassingtestfornestedmodels.Sincenotallofourmodelscanbenestedinageneralspecication,wedonotimplementthisapproach.Y.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 ClementsandHendry(2001)showthatanincorrectbutsimplemodelmayoutper-formacorrectmodelinforecasting.Consequently,onecouldviewthisexerciseasarstpassexaminationofthesenewerexchangeratemodels.Insummarizingtheevidencefromthisextensiveanalysis,weconcludethatthean-swertothequestionposedinthetitleofthispaperisaboldperhaps.Thatis,theresultsdonotpointtoanygivenmodel/specicationcombinationasbeingverysuc-cessful.Ontheotherhand,somemodelsseemtodowellatcertainhorizons,forcer-taincriteria.Andindeed,itmaybethatonemodelwilldowellforoneexchangerate,andnotforanother.Forinstance,theproductivitymodeldoeswellforthemarkyenratealongthedirectionofchangeandconsistencydimensions(althoughnotbytheMSEcriterion);butthatsameconclusioncannotbeappliedtoanyotherex-changerate.Perhapsitisinthissensethattheresultsfromthisstudysetthestageforfutureresearch.AcknowledgementsWethank,withoutimplicating,twoanonymousreferees,MarioCrucini,CharlesEngel,JeFrankel,FabioGhironi,JanGroen,LutzKilian,EdLeamer,RonaldMacDonald,NelsonMark,MikeMelvin(Co-Editor),DavidPapell,RobertoRigo-bon,JohnRogers,LucioSarno,TorstenSløk,MarkTaylor,FrankWestermann,seminarparticipantsatAcademicaSinica,theBankofEngland,BostonCollege,UCLA,UniversityofHouston,UniversityofWisconsin,BrandeisUniversity,theECB,Kiel,FederalReserveBankofBoston,andconferenceparticipantsattheNBERSummerInstitute,theCES-ifoVeniceSummerInstituteconferenceonEx-changeRateModelingandthe2003IEFSpaneloninternationalnanceforhelpfulcommentsandsuggestions.JeannineBailliu,GabrieleGalatiandGuyMeredithgra-ciouslyprovideddata.ThenancialsupportoffacultyresearchfundsoftheUniver-sityofCalifornia,SantaCruzisgratefullyacknowledged.TheviewscontainedhereindonotnecessarilyrepresentthoseoftheIMForanyotherorganizationstheauthorsareassociatedwith.Appendix1.DataUnlessotherwisestated,weuseseasonallyadjustedquarterlydatafromtheIMFInternationalFinancialStatisticsrangingfromthesecondquarterof1973tothelastquarterof2000.Theexchangeratedataareend-of-periodexchangerates.Theout-putdataaremeasuredinconstant1990prices.Theconsumerandproducerpricein-dicesalsouse1990asbaseyear.Inationratesarecalculatedas4-quarterlogdierencesoftheCPI.Realinterestratesarecalculatedbysubtractingthelaggedin-ationratefromthe3-monthnominalinterestrates.The3-month,annualand5-yearinterestratesareend-of-periodconstantmaturityinterestrates,andareobtainedfromtheIMFcountrydesks.SeeChinnandMeredith(2004)fordetails.Five-yearinterestratedatawereunavailableforY.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 JapanandSwitzerland;hencedatafromGlobalFinancialDatahttp://www.global-ndata.com/wereused,specically,5-yeargovernmentnoteyieldsforSwitzerlandand5-yeardiscountedbondsforJapan.Theproductivityseriesarelaborproductivityindices,measuredasrealGDPperemployee,convertedtoindices(1995100).ThesedataaredrawnfromtheBankforInternationalSettlementsdatabase.Thenetforeignasset(NFA)seriesiscomputedasfollows.Usingstockdataforyear1995onNFA(LaneandMilesi-Ferretti,2001)athttp://econserv2.bess.tcd.ie/plane/data.html,andowquarterlydatafromtheIFSstatisticsonthecurrentac-count,wegeneratedquarterlystocksfortheNFAseries(withtheexceptionofJa-pan,forwhichthereisnoquarterlydataavailableonthecurrentaccount).Togeneratequarterlygovernmentdebtdatawefollowasimilarstrategy.WeuseannualdebtdatafromtheIFSstatistics,combinedwithquarterlygovernmentdecit(surplus)data.ThedatasourceforCanadiangovernmentdebtistheBankofCan-ada.FortheUK,theIFSdataareupdatedwithgovernmentdebtdatafromthepub-licsectoraccountsoftheUKStatisticalOce(forJapanandSwitzerlandwehaveveryincompletedatasets,andhencenocompositemodelsareestimatedforthesetwocountries).Appendix2.EvaluatingforecastaccuracyTheDieboldMarianostatistics(DieboldandMariano,1995)areusedtoevalu-atetheforecastperformanceofthedierentmodelspecicationsrelativetothatofrandomwalk.Giventheexchangerateseriesandtheforecastseriesthelossfunctionforthemeansquareerrorisdenedas:Testingwhethertheperformanceoftheforecastseriesisdierentfromthatofthenaiverandomwalkforecast,itisequivalenttotestingwhetherthepopulationmeanofthelossdierentialseriesiszero.ThelossdierentialisdenedasUndertheassumptionsofcovariancestationarityandshort-memoryfor,thelarge-samplestatisticforthenullofequalforecastperformanceisdistributedasastandardnormal,andcanbeexpressedasisthelagwindow,)isthetruncationlag,andisthenumberofobservations.Dierentlag-windowspecicationscanbeapplied,suchastheBarlettY.-W.Cheungetal./JournalofInternationalMoneyandFinance24(2005)1150 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