金融数据变结构波动性模型的综述及研究进展

286Vol.28NO．6JChongqingTechnolBusinessUniv.NatSciEd201112Dec.20111672－058X201106－0594－041211．4000442．6100592010－12－172011－02－18．1986－．、ARCHARCH。GARCHTP391A。1982Engle1ARCHARCH。εt=σtztztIIDEzt=1Varzt=0σ2t=ω0+Σpi=1αiε2{t－iεtσtt。q。1986Bollerslev2ARCH———GARCH。σ2t=ω0+Σpi=1αiε2t－i+Σqj=1βjσ2t－jARCHGARCH。ARCH。。ARCH。Diebold19863LamoureuxLastrages19904。ARCH。1、。Hamilton19895Markov-SwitchingmodelMS。ytyt－μ1=φyt－1－μ1+εtyt－μ2=φyt－1－μ2+εt。Δtyt－μΔt=φyt－1－μΔt－1+εtΔt=12Δt。MSyt=μst+σstztzt～IIDEzt=1Varzt={01yt=lnPt/Pt－1PtstK∏MarkovChain。K=2yt=μ0+σ0εtst=0μ1+σ1εtst{=1∏=p1－p1[]－qqpq。。Engel＆Hamilton19906Engel19947Vigfusson19978。Vigfusson19978Frankel＆Froot19989。2ARCH。t、、PearsonIV。Clark197310。。。ytfyθ=Σkj=1pjfjy。pj≥0Σkj=1pj=1fjyNμjσ2jj=12…kkθ=μ1μ2…μkσ21σ22…σ2kp1p2…pk。。fjytt。Markovmixturemodel。1ytfytΩt－1θ。yt=Σkj=1fytΩt－1st=jθpst=jΩt－1θ。pst=jΩt－1θt－1tj。fytΩt－1θt。Timmermann200011Perez-QuirosTimmermann200112MSt。GuidonlinTimmermann200613。Alizadeh200814MSGARCH。Haas200915tVar。59563ARCHPaganSchwert199016Timmermann2000111。σ2。。HamiltonSusmel199417MS-ARCHMarkov-SwitchingARCHARCH。εt=ε～σ'sttε～=ηtσtσ2t=α0+α1ε～2t－1+…+αqε～2t－qCai199418LamoureuxLastrapes199019MS-ARCHq。εt=ηtσtσ2t=α0st+α1ε2t－1+…+αtε2{t－qGARCHCai199418GARCH。202122。HamiltonSusmel199417MS-ARCHMS-ARCH-LGARCH。Cai199418MS-ARCH。Grey199623GARCHσ2t=α0st+α1stε2t－1+β1stσ2t－12。σ2t=Σα0st－i+α1st－iε2t－1－i∏i－1j=0β1st－j+σ20∏t－1i=0β1st－iσ2tσ2tstst－1…s0。。Cai199418ARCH。Grey1996232。exanteregimeprobabilitypt－1st=j=Pst=jFt－1j=12…k。Ft－1t－1。pt－1st=jt－1tj。t－2εt－13ht－1=Σki=1pt－2st－1=jσ2jk－13σ2jt－1st－1=jεt－1。Grey19962332σ2it=α0i+α21iε2t－1+β1ht－1i=12…k。ht。Grey199623。。。Klaassen200224MSGARCHGARCH。Haas20042569528Grey199623。Brunetti200826MSGARCH、、。SatoyoshiMitsui201027MSGARCHMonteCarloMSGARCHtGARCHBlack-Scholes。1ENGLERF．AutoregressiveconditionalheteroscedasticitywithestimatesofvarianceofUnitedKingdominflationJ．Econometrica198250987-10082BOLLERSLEVT．GeneralizedautoregressiveconditionalheteroskedasticityJ．JournalofEconometrics198631307-3273DIEBOLDFX．ModelingthepersistenceofconditionalvariancesacommentJ．EconometricReview198651-504LAMOUREUXCGLASTRAPESWD．PersistenceinvariancestructuralchangeandtheGARCHmodelJ．JournalofBusinessandEconomicStatistics19908225-2345HAMILTONJD．AnewapproachtotheeconomicanalysisofnonstationarytimeseriesandthebusinesscycleJ．JournalofFinancialEconomics19964227-626ENGELCHAMILTONJD．LongSwingsintheDollarAretheyintheDataanddomarketsknowitJ．AmericanEconomicReview199080689-7137ENGELC．CantheMarkovSwitchingModelForecastExchangeRatesJ．JournalofInternationalEconomics199436151-1658VIGFUSSONR．SwitchingbetweenChartistsandFundamentalistsAMarkovRegime-SwitchingApprochJ．InternationalJournalofFinanceandEconomics19972291-3059FRANKELJAFROOTKA．ChartistsfundamentalistsandthedemandfordollarsJ．GreekEconomicReview19881049-10210CLARKPK．AsubordinatedstochasticprocessmodelwithfinitevarianceforspeculativepricesJ．JRStatSocB1977391-3811TIMMERMANNA．MomentsofmarkovswitchingmodelsJ．JournalofEconometrics20009675-11112PEREZ-QUIROSGTIMMERMANNA．BusinesscycleasymmetriesinstockreturnsEvidencefromhigherordermomentsandconditionaldensities．JJournalofEconometrics2001103259-30613GUIDOLINMTIMMERMANNA．TermstructureofriskunderalternativeeconometricspecificationsJ．JournalofEconometrics2006131285-30814ALIZADEHNOMIKOSPOULIASIS．AmarkovregimeswitchingapproachforhedgingenergycommoditiesJ．JournalofBanking＆Finance2008321970-198315HAASM．Value-at-RiskviamixturedistributionsreconsideredJ．AppliedMathematicsandComputation20092152103-211916PAGANARSCHWERGW．AlternativemodelsforconditionalstockvolatilityJ．JournalofEconometrics199045267-29017HAMILTONJDSUSMELR．AutoregressiveconditionalheteroskedasticityandchangesinregimeJ．JournalofEconometrics199464307-33318CAIJ．Amarkovmodelofswitching-regimeARCHJ．JournalofBusinessandEconomicStatistics199412309-31619LAMOUREUXCGLASTRAPESWD．PersistenceinvariancestructuralchangeandtheGARCHmodelJ．JournalofBusinessandEconomicStatistics19908225-23420．GARCHJ．200321686-9121．ARCHJ．2004193270-27722．GARCH———J．2009284637-64523GRAYSF．Modelingtheconditionaldistributionofinterestratesasaregime-switchingprocessJ．JournalofFinancialEconomics19964227-6224KLAASSENF．ImprovingGARCHvolatilityforecastswithregimeswitchingGARCHJ．EmpiricalEconomics200227363-39425HAASMMITTNIKSPAOLELLAM．Anewapproachtomarkov-switchingGARCHmodelsEB/OL．http//．uni-tuebingen．de/dgf/program/CPaper115．pdf2004-03-3126BRUNETTICSCOTTICMARIANORetal．MarkovswitchingGARCHmodelsofcurrencyturmoilinsouthestAsiaJ．EmergingMarketsReview20089104-1286137956TheStudyofRWAinWDMOpticalNetworksWANGYing-yingSchoolofInformationScienceandTechnologyYanchengTeachersUniversityJiangsuYancheng224002ChinaAbstractTheintelligentopticalnetworkisconsideredasthemostcompetitivecandidatefornextgenerationhigh－speedbackbonenetworkandrepresentsthedevelopmentdirectionofnextgenerationopticalnetwork．RWAisakeytechnologyintheintelligentopticalnetworkwhichaimstofindthepathfromoriginalnodetoobjectivenodeandtoassignwavelengthonthispathwhenrequestisestablishedbylightpathbetweenapairnodesofanetwork．Thecorequestionfornetworkd