gjrgarch模型的弱收敛及层论研究-research on weak convergence and stratification of gjrgarch model.docx

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2018-06-04 发布于上海
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gjrgarch模型的弱收敛及层论研究-research on weak convergence and stratification of gjrgarch model.docx

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gjrgarch模型的弱收敛及层论研究-research on weak convergence and stratification of gjrgarch model

AbstractInthestudyofdynamicpropertiesin theeconomicandfinancialphenomenon, the researchofriskorinstabilityplaysaveryimportantrole.Discretetime autoregressive conditionalheteroskedasticitymodels(ARCHmodel)areeffectivemeansastothese research.Theyareveryimportantinthepracticalapplication.GeneralizedARCH models(GARCHmodel)areeasilyusedtodoforecasting,estimationandtestingabout timeseries.Whilestochasticdifferentialequationsandcontinuoustimediffusion processesoccupy animportantpositioninthetheoreticalresearch.Theoreticalresults aboutthemhavebeenveryrich.Sheafcohomologytheorysynthesizesvarious cohomologyclassesfromalgebra,topologyandgeometrybackground.Itisan effectivemeansastotheresearchofgeometricobjects.Smoothmanifoldisakind of topologicalspaceswithgoodtopologicalandgeometricalproperties.Whenthesheaf cohomology theoryisappliedtosmoothmanifold,theresultscangetbetter.Thus,this papermainlystudiesGJR-GARCHmodelanditslimitation asdiffusionprocessesand sheafversionofgeneralized Mayer-Vietorissequence.Chapter1mainlyintroducestheresearchbackgroundofweaklyconverging theoryofdiscretetimemodelsandsheafversion,analysesandsummarizesthe research statusofthemathome and abroad.Besides,themain contentsofthispaperis gived out.Chapter2mainlyintroducessomenecessarybasicsknowledge,includingthe basicdefinitionsandrelatedknowledgeincoursesofprobabilityandmeasure, stochasticprocessandalgebraictopology. Itlaysafoundationfortheoreticalresearch and practicalapplicationin subsequentchapters.Chapter3discussesthe theoryofdiscrete timeGJR-GARCH model weaklyconvergingtocontinuoustimediffusionprocessthroughaconcreteGARCHmodel: theGJR-GARCHmodel.ThenabridgeisbuiltbetweentheGARCHmodelandthe diffusionprocess.When doingestimationandtesting,GARCHmodelscan beusedas adiffusionprocess approximation.On thecontrary,whendiffusionprocessmodelsare asGARCHmodelsapproximation,theirplentifultheoreticalresultsmaybeappliedto GARCHmodels.Chapter4investigatesthesheavesofgermsofdifferentialformsonasmooth manifold are soft.