扩散模型中扩散系数的非参数组合估计.pdf

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1、应用概率统计第三十卷ChineseJournalofAppliedProbability第三期2014年6月andStatisticsVo1．3ONO．3Jun．2014NonparametricCombiningEstimationoftheDifusionCoeficientofDi肌sionModelsYEXUGUO1，2LINGNENGXIANG3YaoRENHAI2(DepartmentofMathematics，SoutheastUniversity，Nanjing，210096)(Sc

2、hoolofMathematicalSciences，KailiUniversity，Kaili，556011)(。SchoolofMathematics，HefeiUniversityofTechnology，Hefei，230009)AbstractInordertoimprovetheaccuracyofthedifusioncoeficientestimation，weproposeanewcombiningestimatortoestimatethedifusioncoeficientby

3、dynamicallyintegratinginformationfromthetime．domainandthestate．domain．Wefindthattheproposedestimatorcanefective．1yestimatethedifusioncoeficientofdifusionmodels，asweshowinthispaperonsimulatedtimeseries．Undercertainconditions，theasymptoticnormalityissepa

4、ratelyestablishedfortheproposednonparametricestimatorsandtheproposedtheoremprovesthatthetime-domainandstate-domainestimatorsareasymptoticallyindependent．Extensivesimulationsdemonstratetheproposedestimatoroutperformstheothertwoestimators，andalsooutperfo

5、rmstheonesintheliterature．Keywords：Nonparametricestimation，difusioncoeficient，combiningestimation，difusionmodels．AMSSubjectClassification：62G05，62G20，60J60．§1．IntroductionConsidertheproblemofestimatingthedifusioncoeficient，0．2(·)，foracontinuous—timedif

6、usionprocess五satisfyingthestochasticdiferentialequationdXt=(五)dt+(Xt)dWt，t∈[0，】，(1．1)whereWtisaWienerprocesson[0，∞】．Thefunction(·)isadriftcoeficientand(·)isreferredtoasadifusioncoeficient．Asfarasthemodel(1．1)isconcerned，weknowthatithaswideapplicationsi

7、nassetprice，yieldsofbonds，financialmarkets；seetheVasicekTheresearchwaspartlysupportedbytheGuizhouProvincialNaturMScienceFoundation(LKK[2013]30，2010076)，theProjectofKailiUniversity(Z1214，JG201313)，AnhuiProvincialNaturalScienceFoundation(11040606M03)，the

8、ProjectofScienceandResearchofMinistryofEducationofChina(309017)．ReceivedSeptember10，2011．RevisedFebruary19，2014．doi：10．3969／j．issn．1001—4268．2014．03．001226应用概率统计第三十卷mode1fVasicek，1977)，CIRmodel(Coxeta1．，1985)，CKLSmodel(Chaneta1．，1992)，t