4.8 BUGS for a Bayesian analysis of stochastic volatility models

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1、EconometricsJournal(2000),volume3,pp.198–215.BUGSforaBayesiananalysisofstochasticvolatilitymodelsRENATEMEYER†,JUNYU‡†DepartmentofStatistics,UniversityofAuckland,PrivateBag92019,Auckland,NewZealandE-mail:meyer@stat.auckland.ac.nz‡DepartmentofEconomics,UniversityofAuckland,Priv

2、ateBag92019,Auckland,NewZealandE-mail:j.yu@auckland.ac.nzReceived:April2000SummaryThispaperreviewsthegeneralBayesianapproachtoparameterestimationinstochasticvolatilitymodelswithposteriorcomputationsperformedbyGibbssampling.ThemainpurposeistoillustratetheeasewithwhichtheBayesi

3、anstochasticvolatilitymodelcannowbestudiedroutinelyviaBUGS(BayesianinferenceusingGibbssampling),arecentlydeveloped,user-friendly,andfreelyavailablesoftwarepackage.Itisanidealsoftwaretoolfortheexploratoryphaseofmodelbuildingasanymodificationsofamodelincludingchangesofpriorsands

4、amplingerrordistributionsarereadilyrealizedwithonlyminorchangesofthecode.However,duetothesinglemoveGibbssampler,convergencecanbeslow.BUGSautomatesthecalculationofthefullconditionalposteriordistributionsusingamodelrepresentationbydirectedacyclicgraphs.Itcontainsanexpertsystemf

5、orchoosinganeffectivesamplingmethodforeachfullconditional.Furthermore,softwareforconvergencediagnosticsandstatisticalsummariesisavailablefortheBUGSoutput.TheBUGSimplementationofastochasticvolatilitymodelisillustratedusingatimeseriesofdailyPound/Dollarexchangerates.Keywords:St

6、ochasticvolatility,Gibbssampler,BUGS,Heavy-taileddistributions,Non-Gaussiannonlineartimeseriesmodels,Leverageeffect.1.IntroductionThestochasticvolatility(SV)modelintroducedbyTauchenandPitts(1983)andTaylor(1982)isusedtodescribefinancialtimeseries.ItoffersanalternativetotheARCH-

7、typemodelsofEngle(1982)andBollerslev(1986)forthewell-documentedtime-varyingvolatilityexhibitedinmanyfinancialtimeseries.TheSVmodelprovidesamorerealisticandflexiblemodellingoffinancialtimeseriesthantheARCH-typemodels,sinceitessentiallyinvolvestwonoiseprocesses,onefortheobservatio

8、ns,andoneforthelatentvolatilities.Theso-calledobservationerrorsaccou