ARCH和GARCH模型建模实验报告
湖南商学院模拟实验报告课程名称计量经济学模拟实训实验项目名称ARCH和GARCH模型建模班级经济乍0902姓名卢梅香学号090110091学时32实验地点:E602时间:2012-4-20卢梅香小组成员实验目的：通过运用ARCH和GARCH模型建模，进行相关的数据分析实验步骤与内容:①计算汇率波动的回报率，Rt二l0g(P)—l0g(Pt-1Hbl=log(jpy)-log(jpy(-l))② 画出回报率的趋势图，观察是否存在ARCH效应如果存在，以Rt对常数项进行回归,即：R=B+pt0t并利用LM统计量检验随机干扰项的方差是否呈现ARCH效应?Hbl=log(jpy)-log(jpy(-l))得到下图可看出方差有内聚效应，应该存在ARCH效应构建eql:hblc得到下图ETicrs-[Egruatioit:E01forlfile:11-1]EiLe£d：i.Q.'bjtci.^V：evErocsSnicls:Ontjcois也Lwlmr应“Viar|Fra聲DLjwts:|FTnt|Hsa|Frare|Forgyt|gtHs:|Eja£id£:ARCHTest:F-filalistic92.611E6ProbabilityO.OOOCOJObs-R-squar&d0707511Prabahility□DDOIXOTestEquevIion:DspqndenLVanabio:RESIgMethod:LeastSquaresD^te.Od^D/12Time.10.43Samplefgidjusted)31427IncludedobseivaliDns:1425afteradjustingendpairrtEVariable亡口efficientStd.Errort-SlslistiePrab.CRESIDUE-1]515E-O5D.2J72D74B1EO3107CGS3U.U2EEB39.623512ooccoQ.OCCOR-squaredAdjustedR-squaredSE.ofregressionSumsquar&dresidLoglikelihoodDurbin-WatsonstatDDE11D5□.□6D44500001E9407E-D510366.012JJCO5GM&and&pandsnlwarS.D.dependentvarAhjsikeinfocriterionSchwarzcriterionF-Glali£lic：Prab(F-statistic)G.85E-C6□.□□0174-U53C64-M5231E92.G1198DDDOIXO由图看出存在ARCH效应。
③ 对回报率序列进行ARCH模型建模与估计，经反复计算，滞后阶选2；构建eq2:hblc选ARCH模型建模与估计Arch2GarchO得到下图£.114E.ditQfbj&ctzXicw^iIcIeORtiua吐ndmMeIgiVi旺|F「ou3；|〔lb_j皀1PrintMan已|Fc■亡皀re|Esti.Hl皀|PctithhIiR■亡吕idsDependentVariable:HBLMethod.ML-ARCHD31E-0Jj12Qi,12Time:10:153arnple(?idjusted]:2187IncludedcibserMations:U2BafteradjustingendpainlsCnrrrergencEachieijedafter12iteration&Coefficient^liiF-irz-Stetistic^rnh.■0LLLJJJLLLL2JJ1LLCLiJJLLLLJVariancmEquationCAEEEOS^.76367dcccoARCH(I)O.2CEOT3□.02J162B.seaag□cocoARCHP)01137140019033678220300000R-squared-0.CO17LOMeandependendrar4.16E-O5AdjustedR-squared-0CCG814SD.dependentvat0008777EE.ofregries^itinDDOB293Akaikeinfocnteno仃-EHJ^CCOSunsquaredresidO.C07783Schw^rzcritericin-G.0172c8Loglikelihood4875.216DurtairrWatsonstar1927^3④ 由于ARCH模型本身的局限性，我们对模型进行GARCH(1,1)拟合；构建eq3:hblc对模型进行GARCH(1,1)拟合,options的收敛精度改为10000.001得到下图ETievs-[Equation:E«3Voikfile:II-l]LiLe£.d:tVjcvErocaSnickOntjcoia也Lwimrfic-lj和如|已0注PLjuclsJFf5hlI展2工总|E聲tiridl.总|11Mtd!■二|Ea壬白£|DepandenlVanable:HBLMethod:ML-ARCHDate:DM2M12Time:10:53阴m卩l£：(adjuGted).21427IncludEclDbearvalions:142Eafteradjustingendp口inlm匚口nvergencEachie^Bdafter27iterationsCoefficientStd.Errorz-£lslisticProb.C0OOOH90.0CO1930.7617700.^462VarianceEquati口nC763E-07175E-O74J514T7aOCCOWi..'JLLUlLU.L-Jl：JLL2JlLLLL--I'Hl'：一XFEQ006E64111Ifn.lrrrrrR-squared-D.000170Meand^pendenirar4.16E-O5AijusledR-squsrgd-00020=0SDdependentvar0000277SE.ofregressionDDDB^EAkaikeinfoeritantin-E0H993BSumsquaredreEidD.097ES9Schwarzcriterion-G.07S176Loglikelihood呵&宓Durbin-Watsonstat1930242⑤ 检验GARCH拟合后模型的残差项是否是正态分布的(用q-q图，分位数对分位数图)，如果是，说明GARCH拟合是合理，否则继续运用其他GARCH类模型来拟合；读出残差由图看出模型不是正态分布。
⑥ 从q-q图来看，残差的尾部概率显然要比标准正态要大得多，因此要尝试用其他GARCH类模型对数据进行拟合；⑦ 拟合GARCH-M(1,1)模型，观察输出结果发现*2项没有显著性，因此没有必要用GARCH-M(1,1)模型;ETicrs-[Egruatioit:£03forlfile:11-1]EiLe£d：i.Q.'bjtci.^V：evErocsSnicls:Ontjcois也Lwlmr应“yig/|F±a聲DLjwts:|FTnt|Hsq|Frare|Eg：匕iridtt：|FoaraQy11gtdts:|Lasidw：Dapandenl:Variable:HBLMethod:ML・ARCHDate.D4/2D/12Time.10:59Samplefadjusted)21427IncludEriobseivaliDns:1426aft^radjuringendp口inlseCanrerggncBachi^Bdafter33iterationsCoefficientStd.Emvz-SlalisticProb.亂口fGARCH)C■D[143043D.DODiiaj0115536O.QCttSD-Q372431Q.529857a0.5962VarianceEquation二»：'II：1弘7_||-：75DE-07□0-i：,'ii.心LAI■-~r\7iiin0ILLL-IJ-ir-??4：.'1,'H.'I11.tLGJrrrrr1LLLLR-squaredAdjustedR-squaradEE.ofregressionSumsquaredresidLoglikelihoodDurhin-WataonstatD.D0W34Meandependeni4.16E-O5-D.002cEOSildependentvar0.000277DDflezerAkaikeinfocriterian-EHH7261D.D97SOSchwarzcriterion-6.0607E9^1915.610F-giaiiGlic0ISJCTE19322E3Prab(F-ststistic)□9G12O1⑧ 下面对序列进行TARCH拟合。
在Threshold选项中设定滞后阶数为1,结果发现GARCH模型不存在新息冲击的非对称性，即不存在杠杆效应；ETicrs-[Egruatioit:餉逹Vor&file:11-1]匚]£iLcVjeytreesSriickOpIjohsS.Lnlmr¥iatf|Flra[2£Objects:|Ftriut|Hs屯|Frqrhc：|EsXiridtr|Forgoy11gtdts:|Ka巧占£：DependentVariable:HBLMethod:汕L・ARCHDate:Dd^D/12Time:11.01Samplefadjusted)21427IncludedDbseivaliDns:1435afteradjustingendp口inis!Convergencflachievedafter35iterationgCoefficientSid.Errorz-SlHli&iicProb.canaons□QOCGffiQ5ECO54□5754VarianceEqu^tianC7.60E-O71.71EO7A.A95335O.OCCOARCH(1)00373810.0C67135.657SmOOCCO(RESID 因为TARCH模型的设定是假设于对卩t的影响是二次的，过于的简单且单一，应用EGARCH模型说明°；对卩t的影响是指数的，而不是二次的°C(3)是显著的，说明存在非对称的杠杆效应；ETicrs-[Egruatioit:£03forlfile:11-1]EiLe£d：i.Q.'bjtci.^V：evErocsSnicls:Ontjcois也Lwlmr应“yig/|F±a聲DLjwts:|FTnt|Hsq|Frare|Eg：匕iridtt：|FoaraQy11gtdts:|Lasidw：Dapandenl:Variable:HBLMethod:ML・ARCHDate:D4/2D/12Time.11.02Samplefadjusted)21427IncludEriobseivaliDns:1426aft^radjuringendp口inlseCanrerggncBachi^Bdsrfter1S9iterati口nsCoefficientStd.Errorz-SlalisticProb.CDDODIES00003X1aaiSEiaJ161VarianceEquation?0051335-lIT.1：MLLLLL|r叩013896700135401026233rrrrrRES^OR[GARCH](H-□D2I2E3□DDB4S・2514ml□0119*'、卜:l-.l..r--ILLGlILI.'J.'LLL.L-JlLLLLR-squared-D.D00215Meandependeni■/ar4.16E-O5AdjustedR-squarad-D.OOcCzOS.D.dependent^ar0.0002772E.ofr&t|ressiQndDoezeaAksikeirrfh亡riteritin-EHH9383SumsquaredreEid□.□97643Schwarzcriterion■6.07OSGOLoglikelihood^1917.13)Durbin-Watsonstat19301S6⑩ 进一步用成分ARCH模型拟合，再观察残差是否还存在ARCH效应。 ETicws-[Eqroi^tzoii:EQ3Torkfile:11-11£ile£d:ts也刊Erpcs£juirk[iRtiran肚口日口Help¥ig/|Flra聲ObjectFrSn±|ffana|Fir总屯zr|Fs:li「dtR|Fraranyt.呂RgsidsDependentVariable:HBLMethod:h1L・ARCHDate;04^20/12Time:11;03S：3rnple(adjusted)21427IncludedDbseivalicins:1426afteradjustingendpointsCanrerggncHachievedlifter16i2「ati口nsCoefficientStd.Etokz-StatisticProb.C□0IXQ93DC001®1D.193SVarianceEquationPerm.C6.66EJ351.D3EJ356.J77427o.canP■■■■I[Cl099^430002233432.9422o.conPerm:[ARCH-GAF!CH|□030690DD0E4344.7E37O]o.DoaaIkii.1；I.'4iJ]L092624ILLLUj-■l.L-yj-,-L.LUJJTran:[GARCH-Q]04853950150723「「nvR-equarod0OOOE69Meandependentv^r■■-kzJbAdjUEt&dR-^qusretl-0004213SD.dependenti>ar0me2773.E.ufregre^sian0.0C6234Akaikeinh匚nlenon-E..E93629SumsquaredresitlO.O970MSchurzcriterian-6877433LoglikelihoodJ925.43SDurbin-Watsonatat1929240实验结果与分析：1、由图1可看出方差有内聚效应，应该存在ARCH效应2、看残差的ARCH检验，可看出存在ARCH效应。 3、从q-q图来看，残差的尾部概率显然要比标准正态要大得多，因此要尝试用其他GARCH类模型对数据进行拟合4、拟合GARCH-M(1,1)模型，观察输出结果发现2f项没有显著性，因此没有必要用GARCH-M(1,1)模型5、对序列进行TARCH拟合在Threshold选项中设定滞后阶数为1,结果发现GARCH模型不存在新息冲击的非对称性，即不存在杠杆效应；6、拟合EGARCH模型因为TARCH模型的设定是假设a；对卩t的影响是二次的，过于的简单且单一，应用EGARCH模型说明&；对"t的影响是指数的，而不是二次的C⑶是显著的，说明存在非对称的杠杆效应；讨论与心得：1、通过运用ARCH和GARCH模型建模，进行相关的数据分析2、当残差的尾部概率显然要比标准正态要大得多，要尝试用其他GARCH类模型对数据进行拟合成绩评定评阅教师评阅时间。
