穩(wěn)定與不穩(wěn)定長記憶隨機(jī)過程分析：估計(jì)、應(yīng)用及預(yù)測.pdf

1、華東師范大學(xué)博士學(xué)位論文穩(wěn)定與不穩(wěn)定長記憶隨機(jī)過程分析：估計(jì)、應(yīng)用及預(yù)測姓名：陸智萍申請學(xué)位級別：博士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：周風(fēng)DominiqueGUEGAN20090301ABSTRACTInthisthesis，weconsidertwoclassesoflongmemoryprocesses：thestationarylongmemoryprocessesandthenonstationarylongmemoryprocesse

2、sWearedevotedtothestudyoftheirprobabilisticproperties，estimationmethods，forecastmethodsandthestatisticaltestsStationarylongmemoryprocesseshavebeenextensivelystudiedoverthepastdecadesIthasbeenshownthatsomelongmemoryproces

3、seshavethepropertiesofselfsimilarity，whichareimportantforparameterestimationWereviewtheselfsimilarpropertiesofcontinuoustimeanddiscretetimelongmemoryprocessesWeestablishthepropositionsthatstationarylongmemoryprocessisasy

4、mptoticallysecondorderselfsimilar，whilestationaryshortmemoryprocessisnotasymptoticallysecondorderselfsimilarThenweextendtheresultstospecificlongmemoryprocessessuchaLskfactorGARMAprocessesandkfactorGIGARCHprocessesWealsoi

5、nvestigatetheselfsimilarpropertiesofsomeheteroscedaSticmodelsandtheprocesseswithswitchesandjumpsWemakeareviewforthestationarylongmemoryprocesses’parameterestimationmethods，includingtheparametricmethods(forexample，maximum

6、likelihoodeaimation，approximatemaximumlil(elih00destimation)andthesemiparametricmethods(forexample，GPHmethod，WhittlemethodRobinsonmethod)111econsistencyandaSymptoticnormalitybehaviorsarealsoinvestigatedfortheestimatorsTe

7、stingthe丘actionallyintegratedorderofseasonalandnonseasonalunitrootsofthestochasticstationarylongmemoryprocessisquiteimportantfortheeconomicandfinancialtimeseriesmodelingThewidelyusedRobinsontest(1994)isappliedtovariouswe

8、llknownlongmemorymodelsViaMonteCarloexperiments，westudyandcomparetheperformancesofthistestusingseveralsamplesizes，whichprovideagoodreferenceforthepractitionerswhowantto，applyRobinson’StestInpractice，seasonalityandtimevar

9、yinglongrangedependencecanoftenbeobservedandthussomekindofnonstationarityexistsinsidetheeconomicandfinancialdatasetsTotakeintoaccountthiskindofphenomenawereviewtheexistingnonstationaryprocessesandweproposeanewclassofnons

10、tationarystochasticprocess：thelocallystationarykfactorGegenbauerprocessWedescribeaprocedureofestimatingconsistentlythetimevaryingparameterswiththehelpofthediscretewaveletpackettransform(DWPT)neconsistencyandasymptoticnor

11、malityoftheestimatesareproved111erobusmessofthealgorithmisinvestigatedthroughsimulationstudyWealsoproposetheforecastmethodforthisnewnonstationarylongmemoryprocessesApplicationsandforecastsbaSedontheerrorcorrectiontermint

12、heerrorcorrectionmodeloftheNikkeiStockAverage225(NSA225)indexandtheWestTexasIntermediate(WTI)crudeoilpricearefollowedKEYWORDS：Discretewaveletpackettransform，Gegenbauerprocess，Longmemoryprocesses，MonteCarlosimulations，Nik