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GARCH康建林,朱开永,周圣武,韩 苗(, 221008) :大量的实证研究表明诸如股票价格等经济类时间序列具有方差随时间变化即异方差的特点.目前被认为最集中地反映了方差变化特点而被广泛地应用在金融时间序列上的模型为广义自回归条件异方差(GARCH)模型.应用GARCH模型对我国股票波动率进行应用预测分析,结果表明模型对波动率进行了很好的预测.这对股票投资者尤其短期交易者具有指导意义.:GARCH;波动率;预测:F830.91 :A :1004-8332(2005)03-0029-04,,.,(volatilityclustering),,.,.,、ARMA,.,,,.,GARCH(GeneralizedAutoregressiveConditionHeteroskedastic).,.,..,,.:Ri=InPiPi-1(1).:S=1n-1∑ni=1(Ri-R)2/τ(2)τ[1].1 GARCH,(Engle)1982(AutoregressiveConditionalHeteroskedastic),ARCH[2]..ARCH(q)“”,“”,q.Bollerslev(1986)ARCH,GARCH(GeneralizedARCH).GARCHεt-i,ht-j.GARCH(p,q)(3):2005 №.3 JournalofGannanTeachersCollege June.2005:2004-10-17 :(1981—),,2003,:.DOI:10.13698/j.cnki.cn36-1037/c.2005.03.009yt=X′tβ+εtεt=htvtht=k0+∑qi=1αiεt-i2+…+∑pj=1ρjht-j2p≥0,q≥0,k0≥0,αi≥0,ρj≥0,i=1,…,q,j=1,…,p(3)yt,Xt,φt-1tt-1,vti.i.dN(0,1).εtφt-1~N(0,ht),εt,.3[3] (3)hiGARCH(p,q):∑qi=1αi+∑pj=1ρj12 H0:α1=α2=…αq=0,H1αi0,,[4]:ξ=TF0′Z0(Z0′Z0)-1Z0′F0F0′F0,Z0=Z10(β),Z20(β),…,ZT0(β),F0=ei2h0-1,e22h0-1,…,eT2h0-1,h0、εt0Zt0(β)ht、εtZt(β).ξ,Ft0=et2h0-1Zt0=1,et-12,…,et-q21,R2,ξTR2.3 GARCH,:.,,.,,ARCH.,,.,,.,[4].,2002.04.112003.04.30252,“”.GARCH,BHHH,Matlab6.5.θi+1θi+1,θi+1[5]:θi+1=θi+λi(∑Tt=1lti(θ)θ·lti(θ)θ′)-1∑Tt=1lti(θ)θlt(θ)=-12In(2Π)-12In(ht)-12εt2ht,lti(θ)θ,θi;hi.4 “(AkaikeInformationCriteria,AIC)”“Bayesian(BIC)”,BIC.BIC:BIC=(-2×LLF)+(NumParams×Log(NumObs)),,LLF,NumParams,NumObs.Ljung-BoxQ.5 ,“”.:Rt=-0.0017-0.0003Rt-1,Rtt,(2).130 2005LM.1 LMOrderqLMTestStochasticCriticalValueχ2(q)SignificanceLevelαOrderqLMTestStochasticCriticalValueχ2(q)SignificanceLevelα423.75849.48770.051024.753618.30700.05523.633311.07050.051124.642919.67510.05623.592212.59160.051225.540121.02610.05723.674814.06710.051325.424322.36200.05823.843415.50730.051425.515523.68480.05924.841116.91900.051525.370424.99580.052 BICBicpq1231-1.3136e+003-1.3081e+003-1.3065e+0032-1.3082e+003-1.3119e+003-1.3009e+0033-1.3031e+003-1.3064e+003-1.2953e+003,ARCH,GARCH.GARCH,,Rt=C+εt.p、q=1、2、3,BIC2.BIC,GARCH(1),0.0525Ljung-BoxQ28.851537.6525,GARCH(1),GARCH(1).:Rt=C+εtht=k0+αεt-12+ρht-1(4):Rt=-0.001999+εt (-1.6255)ht=2.9599×10-5+0.078017εt-12+0.83239ht-1 (1.6181) (2.2210) (9.9964)(5)1 (2003.05.14~2003.06.11) :`·',`-'(4)、(5)ρ0.7,α0.25,[3].,.12003.05.142003.06.11.2002.04.182003.05.13249.,,,0.013%.GARCH(1),.6 GARCH,.,,GARCH.313 ,,, GARCH GARCH,,GARCH(1),ARCH,LM,;,GARCH(1)ARCH(∞),GARCHARCH.,GARCH,.,GARCH,.:[1] JohnC.Hull.options,futures,andotherderivatives(4)[M].:,2001.368~385.[2] RosarioN.MantegnaandH.EugeneStanley.AnIntroductiontoEconophysics:CorrelationsandComplexityinFinance[M].U.K.:Cambridgeu-niversitypress,2000.76~87,113~129.[3] .[M].:,1999.8,(1).[4] .[M].:,2001.2,(1).ApplyingGARCHModeltoForecastChineseStockVolatilityKANGJian-lin,ZHUKai-yong,ZHOUSheng-wu,HANMiao(DepartmentofAppliedMathematics,ChinaUniversityofMining&Technology,Xuzhou221008,China)Abstract:Alotofresearchindicatesthateconomictimeseries,suchasstockpriceetc,havevarianceuptotimechangei.e.het-eroskedastic.Atpresent,themodelthatisthinkedtoreflectvariancechangecharacteristicsbroadlyisgeneralizedautoregressivecon-ditionalheteroskedastic(GARCH),whichhasbeenwidelyusedinfinancialtimeseries.ThepaperappliesGARCHmodeltoforecaststockvolatilityinChinesestockmarkets.Theconclusionrevealsthatthemodelpredictswell.Ithasdirectivesignificancetothestockinvestorsespeciallyshort-termtraders.Keywords:GARCH;volatility;forecast(CEPS)《》20051———(CEPS)。———,:。,《》2005。,《》CEPS,,(CEPS)、;,。《》32 2005
本文标题:GARCH模型在中国股票波动预测中的应用-康建林
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