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1、NonstationaryContinuous-TimeProcesses¤FedericoM.BandiPeterC.B.PhillipsGraduateSchoolofBusiness,CowlesFoundationforResearchinEconomics,TheUniversityofChicagoYaleUniversityFirstversion:September,2001Thisversion:May14,2002¤Preliminary-Commentsarewelcome.Paperwrittenfor
2、theHandbookofFinancialEconometricseditedbyYacineA¨?t-SahaliaandLarsPeterHansen.WethankDarrellDu?e,BenoitPerronandMarkWatsonfordiscussionsandSeoyeonLeeforresearchassistance.Bandiacknowledges?nancialsupportfromtheIBMCorporationFacultyResearchFundattheUniversityofChica
3、go.PhillipsthanksfheNSFforsupportundergrantno.SES0092509.CommentsarewelcomeandcanbesenttoFedericoM.Bandiatfederico.bandi@gsb.uchicago.edu.1Contents(1)Introduction(2)IntuitionandConditions(3)ScalarDi?usionProcesses(SDP’s)(3.1)GeneralizedDensityEstimationforSDP’s(3.2)
4、KernelEstimationoftheIn?nitesimalConditionalMomentsofanSDP(3.2.1)TheChoiceoftheBandwidth(3.2.2)ExtensioninKernelEstimationforSDP’s(3.3)LocalLinearEstimationoftheIn?nitesimalConditionalMomentsofanSDP(3.4)UsingNonparametricInformationtoEstimateandTestParametricModelsf
5、orSDP’s(4)ScalarJump-Di?usionProcesses(SJDP’s)(4.1)GeneralizedDensityEstimationforSJDP’s(4.2)KernelEstimationoftheIn?nitesimalConditionalMomentsofanSJDP(5)MultivariateDi?usionProcesses(MDP’s)(5.1)GeneralizedDensityEstimationforMDP’s(5.2)KernelEstimationoftheIn?nites
6、imalConditionalMomentsofanMDP(6)Application:TheShort-EndoftheTermStructureofInterestRates(7)ConcludingRemarks(8)References(9)TablesandGraphs21IntroductionAlargebodyofrecentassetpricingtheoryiswrittenincontinuous-time,forwhichMer-ton(1990)andDu?e(1996)areclassicrefer
7、ences.Notwithstandingtheevidentbene?tofcontinuous-timetoolsformodellingpurposesandrecentadvancesintheeconometrictreatmentofcontinuous-timemodels,1theuseofstochasticprocesseswithcontinuous(intime)samplepathsstillposesremarkablechallengeswhenitcomestotheeconometrices-
8、timationandempiricalimplementationofmodernassetpricingmodels.Campbell,LoandMcKinlay(1997,CKLhenceforth)andGourierouxandJasiak(2001)arerece
