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1、AsymptoticTheoryforARCHModels:EstimationandTestingAuthor(s):AndrewA.WeissReviewedwork(s):Source:EconometricTheory,Vol.2,No.1(Apr.,1986),pp.107-131Publishedby:CambridgeUniversityPressStableURL:http://www.jstor.org/stable/3532216.Accessed:19/12/201215:03YouruseoftheJSTORarchiveindica
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3、olstoincreaseproductivityandfacilitatenewformsofscholarship.FormoreinformationaboutJSTOR,pleasecontactsupport@jstor.org..CambridgeUniversityPressiscollaboratingwithJSTORtodigitize,preserveandextendaccesstoEconometricTheory.http://www.jstor.orgThiscontentdownloadedonWed,19Dec201215:
4、03:51PMAllusesubjecttoJSTORTermsandConditionsEconometiricTheoryS,2,107-131.PrintedintheUnitedStatesofAmerica.ASYMPTOTICTHEORYFORARCHMODELS:ESTIMATIONANDTESTINGANDREWA.WEISSUniversityofSouthernCaliforniaatLosAngelesInthecontextofalineardynamicmodelwithmovingaverageerrors,wecon-sider
5、aheteroscedasticmodelwhichrepresentsanextensionoftheARCHmodelintroducedbyEngle[4].Wediscussthepropertiesofmaximumlikeli-hoodandleastsquaresestimatesoftheparametersofboththeregressionandARCHequations,andalsothepropertiesofvarioustestsofthemodelthatareavailable.Wedonotassumethattheer
6、rorsarenormallydistributed.1.INTRODUCTIONWebeginwiththesituationinwhicharesearcherwishestomodelthehet-eroscedasticityinatimeseriesregression.Forthis,Engle[4]hasintroducedtheconceptofautoregressiveconditionalheteroscedasticity(ARCH).Thisisseenasanextensionoftimeseriesbehaviorintheme
7、an,allowingthevarianceoftheerrorstochangeiftheprocesstakesintoaccountpastex-periencebutassumesitconstantifthisexperienceisnotknown.Inaprocesswithstochasticregressors,whichisthecaseinmosttimeseriesprocesses,thiscorrespondstotheusualpropertiesofthemeanoftheoutputfromtheregressionmode
8、l.Henceitismoreappealingth
