Bayesian Dynamic Factor Models and Portfolio Alloc

BayesianDynamicFactorModelsandPortfolioAllocationOmarAGUILARandMikeWESTWediscussthedevelopmentofdynamicfactormodelsformultivariatenancialtimeseries,andtheincorporationofstochasticvolatilitycomponentsforlatentfactorprocesses.Bayesianinferenceandcomputationisdevelopedandexploredinastudyofthedynamicfactorstructureofdailyspotexchangeratesforaselectionofinternationalcurrencies.Themodelsaredirectgeneralisationsofunivariatestochasticvolatilitymodels,andrepresentspecicvarietiesofmodelsrecentlydiscussedinthegrowingmultivariatestochasticvolatilityliterature.Wediscussmodelttingbasedonretrospectivedataandsequentialanalysisforforwardlteringandshort-termforecasting.Analysesarecomparedwithresultsfromthemuchsimplermethodofdynamicvariancematrixdiscountingthat,foroveradecade,hasbeenastandardapproachinappliednancialeconometrics.Westudythesemodelsinanalysis,forecastingandsequentialportfolioallocationforaselectedsetofinternationalexchangeratereturntimeseries.Ourgoalsaretounderstandarangeofmodellingquestionsarisinginusingthesefactormodels,andtoexploreempiricalperformanceinportfolioconstructionrelativetodiscountapproaches.Wereportonourexperiencesandconcludewithcommentsaboutthepracticalutilityofstructuredfactormodels,andonfuturepotentialmodelextensions.KEYWORDS:DynamicFactorAnalysis;DynamicLinearModels;ExchangeRatesForecast-ing;MarkovChainMonteCarlo;MultivariateStochasticVolatility;PortfolioSelection;SequentialForecasting;VarianceMatrixDiscounting1.INTRODUCTIONSincethemid-1980s,multivariatestochasticvolatilitymodelsbasedonvariance/covariancediscounting(Quin-tanaandWest1987,88)havebeenusedascomponentsofappliedBayesianforecastingmodelsinnancialeconomet-ricsettings(Quintana1992;PutnamandQuintana1994,1995;QuintanaandPutnam1996;Quintana,ChopraandPutnam1995).Thesuccessofsuchmethodsinportfo-lioconstructionisevidencedpartlybythefactthattheyhavebeenadoptedandareinvigorousday-to-dayuseascomponentsofglobalportfolioapproachesinseveralma-jorinternationalbanks.Inmorerecentyears,majorde-velopmentsinstructuredstochasticvolatility(SV)mod-ellinghaveledtotheintroductionofvariousapproachestomodellingdependenciesinvolatilityprocessesthat,inprinciple,mayleadtoimprovementsinshort-termfore-castingofmultiplenancialandeconometrictimeseries.ThereisnodoubtthatthesemorecomplexSVmodelstheoreticallyimprovethedescriptionofseveralkindsofnancialtimeseriesdata,includingexchangeratereturnseries,andholdpotentialforimprovementsinpracticalshort-termforecastingrelativetodiscountmodels.Partofourinteresthereistoempiricallyexplorethispoten-tial.Wedevelopdynamicfactor,multivariatestochasticvolatilitymodelstoaddress:MikeWestistheArtsandSciencesProfessorofStatisticsandDeci-sionSciences,andDirectoroftheInstituteofStatisticsandDecisionSciences,atDukeUniversity.TheaddressisISDS,DukeUniver-sity,Durham,NC27708-0251,USA,andthewebsiteaddressisortsoftheJBESEditor.ThisarticleisavailableinelectronicformontheISDSwebsite,questionsabouttheirpotentialtoprovidepracticalimprovementsinshort-termforecasting,andresult-ingdynamicportfolioallocations,ofinternationalex-changeratesandothernancialtimeseries;issuesofmodelstructuring,implementation,Bayesiananalysisandcomputation;andquestionsofcomparisonwiththemuchsimplermeth-odsbasedonvariance/covariancediscounting.Westudytheseissuesinconnectionwithdataanalysisandportfolioconstructionusingmultipleseriesofreturnsoninternationalexchangerates.Variantsofthebasicmethodofvariancematrixdis-counting(seeabovereferencestoQuintanaandcoauthors)haveformaltheoreticalbasesinmatrix-variate\randomwalks(Uhlig1994,97).Furtherdiscussionisgivenbelow,andmorebackgroundcanbefoundinWestandHarri-son(1997,section16.4.5).ThebasicdiscountingmethodsfollowfoundationaldevelopmentsforunivariateseriesinAmeenandHarrison(1985)andHarrisonandWest(1987),andtheformalmultivariatemodelsaredirectgeneralisa-tionsofunivariatemodelsofShephard(1994a).RelateddiscussionappearsinWestandHarrison(1997,section10.8.2).Inthegeneralmultivariatecontext,theapproachleadstotheembeddingofsmoothedestimatesof\localvariance/covariancestructurewithinaBayesianmodellingframework,andsoprovidesforadaptationtostochasticchangesastimeseriesdataareprocessed.Modicationstoallowforchangesindiscountratesinordertoadapttovaryingdegreesofchange,includingmarked/abruptchangesinvolatilitypatterns,extendthebasicapproach.Theresultingupdateequationsforsequencesofestimatedvolatilitymatriceshaveunivariatecomponentsthatrelatec???AmericanStatisticalAssociationJournalofBusiness&EconomicStatistics???12JournalofBusiness&EconomicStatistics,??????closelytovariantsofARCHandSVmodels,andsoitisnotsurprisingthattheyhaveprovenusefulinmanyappli-cations.Howe