实验14 Garch(自回归异方差模型)

1、实验14G(ARCH)模型在金融数据中的应用一、实验目的理解自回归异方差(Autoregressiveconditionalheteroscedasticity)模型的概念及建立的必要性和适用的场合。了解G(ARCH)模型的各种不同类型，如GARCH-M模型(GARCHmmean),EGARCH模型(ExponentialGARCH)和TARCH模型(又称GJR)。掌握对G(ARCH)模型的识别、估计即如何运用Eviews软件在实证研究中实现。二、实验内容及要求内容：以上证指数和深证成份指数为研究对彖，选取1997年1月2口到2002年12月31口共六年每个交易口上证指数和深证成份指数的收盘价

2、为样本，完成以下实验步骤：、对沪深股市的收益率作波动性研究、对股市收益波动作非对称性的研究、对沪深股市作波动溢出效应研究要求：深刻理解本章的概念：对实验步骤中提出的问题进行思考；熟练掌握实验的操作步骤，并得到有关结果。三、实验指导、对沪深股市的收益率作波动性研究描述性统计导入数据，建立工作组打开Eviews软件，选择“File”菜单中的“NewWorkfile选项，在“Woikfilestructuretype框中选择unstmctured/undated(思考：为什么用非规则形式)，在Daterange输入1444,如下图14-1：OOXiWorkfileCreate-DatarangeOb

3、servations:1444-Workfilestructuretype(unstructured/UndatedFIrregularDated3rdPanmlworkfilesmaybemadeFromUnstructuredworkfilesbylaterspecifyingdateand/orotheridentifierseries-Workfilenames(optional)WF:|HtestCancel图14-1单击OK，再在命令行输入datashsz,把上证综指和深幼I成指1997-1-2号到2002-12-31号数据输入。生成收益率的数据列在Eviews窗II主菜单栏下得命

4、令窗II中键入如下命令：gemrh=log(slVsh(-1),回车后即形成沪市收益率的数据序列，同样的方法可得深市收益数剧序列(gem-rz=log(sz/sz(-l)o新工作组如图14-2：图14-2观察收益率sh的描述性统计量双击选取“rh数据序列，在出现的窗II中选择view菜单下DescriptiveStatistics”菜单中的“HistogramandStats”子菜单，则可得收益率山的描述性统计量，如下图7-3：sSeries:RHWorkfile:UNTITLED:Untitled-Inix|ViewProcObjectPropertiesPrintNameFreeze1Sa

5、mpleGenrSheet|Graph5tats|IdentSeries:RHSample11444Observations1443Mean0.000270Median0.000563Maximum0.094008Minimum-0.093342Std.Dew0.016318Skewness-0.145826Kurtosis9.086901Jarque-Bera2232.768Probability0.000000n图7-3同样的步骤町得收益率iz的描述性统计量。观察这些数据，并得出有关结论。-Lag叵仃gthQAutomaticsele匚tiom:|AkaikeInfoCriterion二M

6、aximumlags:4厂Userspecified:4Cancel2平稳性检验(1)再次双击选取rh序列，选择View菜单卞的子菜单“UnitRootTest”，出现如卞窗口(图74IXlUnitRootTestTesttype(AugmentedDickey-FullerTestForunitrootin丐Level1stdifference广2nddifferenceIncludeintestequation-CInterceptIrendintercept金None对该序列进行ADF单位根检验，选择滞后4阶，带截距项而无趋势项，所以采用窗IIJLnJ凶的默认选项，结果如下图75：BSe

7、ries:RHWorkfile:UNTITLED:UntitledNameFreeze|SampleGenrSheetGraphStatsIdent|AugmentedDickey-FulleiUurtRootTestonRHViewProcObjectfropertiesprintNullHypothesis:RHhasaunitrootExogenous:NoneLagLwngth:3(AutomaticonAIC,maxlag=4)1-StatisticProb*AugmentedDickey-Fullerteststatistic-17.957920.0000Testcriticalv

8、alues:1%level5%level10%level-2.566570-1.941044-1.616551MacKinnon(1996)one-sidedp-values.图7-5（2）对rz做单位根检验后，得结呆如图7-6：图7-6（3）思考：结果分别说明数据序列山、rz是稳定的还是非稳定的？3.均值方程的确定及残差序列自相关检验通过对收益率rh和rz的自相关检验（在ih序列窗II，点击viewcorrelogiam）,我们发现两市的收益率都与其滞后15阶存在显著的自相关（思考：如何通过Eviws检验），因此对两市收益率的均值就其滞后15阶做自回归，方程都采用如卞形式：+c二5+吕（1）

9、对收益率山做自回归在Eviews主菜单中选择“Quick”，并在卜拉菜单中选择“EstmiationEquationv,出现如下窗口图7-7IXlEquationEstimationSpeizifiizationOptions-EquationspecificationDependentvariableFollowedbylistofregressorsincludingARMAandPDLtermsORanexplicitequationlike学之+以51%rhcrh(-15)|EstimationsettingsMethod:|ls-LeastSquares(NLSandARMA)Sam

10、ple:t1444OKCancel图7-7在“Method”中选择LS（即普通最小二乘法），然后在“Estimationsettings上方空白处输入图示变量，单击“OKS则出现图Inl凶StatsResids曰Equation:UNTITLEDWorkfile:UNTITLED:UntitViewProcObjectPrintNameFreezeEstimateForecastDependentVariahl巴RHMethod:LeastSquaresDate:05/16/18Time:22:10Sample(adjusted):171444Includedobservations:1428

11、afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.C0.0002260.0004300.5255780.5993RH(-15)0.0939430.0262943.5728590.0004R-squared0.008872Meandependentvar0.000253AdjustedR-squared0.008177S.D.dependentvar0.016331S.E.ofregression0.016264Akaikeinfocriterion-5.398315Sumsquaredresid0.377206Schwarz

12、criterion-5.390942Loglikelihood3856.397HannanQuirincriter.-5.395562F-statistic1276532Durbin-Watsonstat2.022451Prob(F-statistic)0.000365图7-8（2）用Ljung-BoxQ统计量对均值方程拟和后的残差及残差平方做自相关检验：选择“View”菜单下“ResidualTest子菜单的项，则可得该方程残差项的自相关系数acf值和pacf值（在LagSpecification窗口中选10阶），如图7-9Date:05/16/18Time:22:15Sample:1144

13、4Includedobservations:1428Qstatisticprobabilitiesadjustedfor1dynamicregressorAutocorrelationPartialCorrelationACPACQ-StatProbi1i11-0.011-00110.186206661112-0.035-0.0351.89140.388iI*1130.0110010207270557i1140.05800576.85640144|1115-0.018-0.01e7.33790.197111160.00700107.40200285111170.0220.0208.111e0.

14、323(1(18-0.037-003910.0730260(119-0.045-0.04313.0250.1611111100.013000813.2560210图7-9Series:RE5IDO2Workfile:UNTITLED:UntitledViewProcObjectPropertiesPrintNameFreeze|SampleGenrSheetGraph5tats|IdentConeloyrainofRESID02Date:05/16/18Time:22:22Sample:11444Includedobsetvatio1428AutocorrelationPartialCorre

15、lationACPACQ-StatProbii10.1750.17543.6310.000ii320.1400.11371.7680.000iiJ30.1490.113103.650.000ii40.1200.069124.210.000i1ii50.046-0.011127.230.000ii60.0990.063141.430.000iiJ10.0760.031149.670.000i1ii80.0520.012153.550.000i1ii90.0490.012157.000.000iip100.0750.040165.070.000图7-10(3)在命令栏中输入命令：gemresl=i

16、esid-2,得到该方程残差平方的数据序列resl（2）同样，可得序列rz的回归方程及回归方程残差项的acf值和pacf值，如图7J1和图7-12:图7-9到7-10表明两回归方程的残差都不存在显著的自相关，但残差平方有显著的自相关。图7-11图7-12（5）对残差平方做线性图。双击选取序列resl,在新出现的窗I1中选择“View”菜单下的“LineGraph”，得到resl的线性图如图7-13图7-133同样的，rz的残差平方res2的线性图如图：图7-14观察门J以发现波动具有明显的时间可变性(tmievaiymg)和集簇性(clustermg)(6)对残差进行ARCH-LMTest依照

17、步骤(1),再对山做一次滞后15阶的回归，在出现的equation窗II中选择“View”菜单下“ResidualTest”子菜单的“Arch-LMTestw项(取滞后一阶),得如下结果(图7-15)：HeteroskedasticityTest:ARCHF-statistic44.81901Prob.F(1J425)0.0000Obs*R-squaied43.51334Prob.Clii-Square(l)0.0000TestEquation:DependentVaiiable:RESID八2Method:LeastSquaresDate:05/16/18Time:22:48Sample(a

18、djusted):181444Includedobservations:1427afteradjustmentsVariableCoefficientStd.Enort-StatisticPiob.C0.0002182.08E-0510.468990.0000RESIDA2(-1)0.1746250.0260846.6947000.0000R-squared0.030493Meandependentvar0.000264AdjustedR-squaied0.029813S.E.ofregression0.000743Sumsquaredresid0.000786S.D.dependentvar

19、AkaikeuifocriteiionSchwarzcriterion0.000754-11.57130-11.56392Loglikelihood8258.120Hamian-Qunmcriter.-11.56854F-statistic44.81901Durbm-Watsonstat2.039487Prob(F-statistic)0.000000图7-15对方程回归后的残差项同样可做Arch-LMTest,结果如图7-16：|evs-Equation：UHTITLEDlorkfile：UBTITLED-|njx|FileEditObjectsViewProcsQuickOptionsWi

20、nd.owHelp-Ifflx|View|Procs|Objects|Print|Freeze|Estimate(Forecast|Stats|Resids|ARCHTest:F-statistic47.51115Probability0.000000Obs*R-squared46.04172Probability0.000000TestEquation:DependentVariable:RESID几2Method:LeastSquaresDate:10/27/05Time:17:21Sample(adjusted):181443Includedobservations:1426aftera

21、djustingendpointsVariableCoefficientStd.Errort-StatisticProb.C0.0002622.39E-0510.973760.0000RESIDA2(-1)0.1796890.0260696.8928330.0000R-squared0.032287Meandependentvar0.000319AdjustedR-squared0.031608S.D.dependentvar0.000858S.E.ofregression0.000845Akaikeinfocriterion-11.31410Sumsquaredresid0.001016Sc

22、hwarzcriterion-11.30672Loglikelihood8068.952statistic47.51115Durbin-Watsonstat2.062131Prob(F-statistic)0.000000Path=c：eviews3DB=noiteWF=untitled图7-16得到的结果同样说明残差中ARCH效应是很显著的，因此考虑进行GARCH类模型建模。GARCH类模型建模选择“Quick”菜单下“EstimateEquation”菜单，在出现的如图7-17窗II中输入图示变量，点击“OK”键后得到山数据序列的GRACH(1,1)模型估计结果，如图7-18:。Equat

23、ionSpecificatioil)epenctentfollowedbyregressorsandARMAterms：:rhcrh(15)上J富IMeanEquationSpecification:ARCHSpecification:OrderARCH:lGARH厂F；GARCH(symmetric)TARCH(asymmetric)EGARCHComponentARCHAsymmetricComponentVarianceRegre$sor$:ARCH-Mterm:卷NoneStd.Dev./VarianceCancelMethod:jARCHAutoregressiveCondition

24、alHeteroskedastick|Sample:11443-Enterregre$or$forComponentModelintheorder:permanenttransitoryEstimationSettings:图7-17EViews-Equation：UHTITLEDVorkfile：UBTITLIDFileEditObjectsViewProcsQuick0tionsWindowHelp|(91X|View|Procs|Objacts|Frin11N：ame|Freeze|Estimate|ForesstStats|Resids|DependentVariable:RHMeth

25、od:ML-ARCHDate:10/27/05Time:17:29Sample(adjusted);171443Includedobservations:1427afteradjustingendpointsConvergenceachievedafter26iterationsCoefficientStd.Errorz-StatisticProb.C-2.21E-060.000283-0.0077950.9938RH(-15)0.0593020.0202002.9357450.0033VarianceEquationC8.72E-061.45E-066.0035430.0000ARCH(1)

26、0.1765140.01524211.580780.0000GARCH(1)0.3073910.01370358.920600.0000R-squared0.007543Meandependentvar0.000253AdjustedR-squared0.004751S.D.dependentvar0.016348S.E.ofregression0.016309Akaikeinfocriterion-5.645039Sumsquaredresid0.378216Schwarzcriterion-5.626597Loglikelihood4032.735F-statistic2.701826Du

27、rbin-Watsonstat2.023588Prob(F-statistic)0.029225Path=c：eviews3DB=noiteWF=untitled图7-18同理，iz数据序列的GRACH(1,1)模型估计结果，如图7-19：DependentVariable:RZMethod:ML-ARCHDate;10/27/D5Time;17:28Sample(adjusted):171443Includedobservations:1427afteradjustingendpointsConvergenceachievedafter28iterationsCoefficientStd.E

28、rrorz-StatisticProb.C-0.0005780.000327-1.7706770.0766RZ(-15)0.0575420.0219142.6257680.0086VarianceEquationCS.32E-061.29E-064.9065620.0000ARCH0.1221630.00978312.486960.0000GARCH(1)0.3636140.00923193.559230.0000R-squared0.005931Meandependentvar-0.000173AdjustedR-squared0.003135S.D.dependentvar0.017933

29、S.E.ofregression0.017905Akaikeinfocriterion-5.476727Sumsquaredresid0.455886Schwarzcriterion-5.458285Loglikelihood3912.645statistic2.120990Durbin-Watsonstat1.914368Prob(F-statistic)0.075965Path=c：eviews3DB=noiteWF=untitled,!x|FileEditObjectsViewProcsQuickOptionsWindowHelp一|占|X|Xiew|Procs|Objects|Frir

30、t11|Freeze|Estimate|Forcest|Stats|Resids|EViews-Equation：UBTITLEDVorkfile：U1TITLID图7-19可见，沪深股市收益率条件方差方程中ARCH项和GARCH项都是高度显著的，表明收益率/；序列具有显著的波动集簇性。GARCH-M(M)估计结果在EquationSpecification窗口的“ARCH-M”列表中选择Variance，单击OK”键后，得如下估计结果，图7-20：|evs-Equation：UHTITLEDWorkfile：UBTITLID-|njx|FileEditObjectsViewProcsQuic

31、kOptionsWindowHelp-Ifflx|View|Procs|Objects|Print|Freeze|Estimate(Forecast|Stats|Resids|DependentVariable:RHMethod:ML-ARCHDate;10/27/D5Time;17:31Sample(adjusted):171443Includedobservations:1427afteradjustingendpointsConvergenceachievedafter29iterationsCoefficientStd.Errorz-StatisticProb.GARCH5.93767

32、12.2596952.6276420.0086C-0.0010310.000450-2.2928810.0219RH(-15)0.0514680.0183492.8048810.0050VarianceEquationC1.20E-051.97E-066.1016540.0000ARCH(1)0.2151830.01860511.565640.0000GARCH(1)0.7645770.01759743.449160.0000R-squared0.014653Meandependentvar0.000253AdjustedR-squared0.011186S.D.dependentvar0.0

33、16348S.E.ofregression0.016266Akaikeinfocriterion-5.646948Sumsquaredresid0.375506Schwarzcriterion-5.623818Loglikelihood4034.384F-statistic4.226334Path=c：eviews3DB=noiteWF=untitled图7-20同理，收益率iz的GARCH-M(IJ)估计结果如卞图图7-21：|EViews-Equation：IfflTTITLEDlorkfile：UBTITLIDI口x|IJFileEditObjectsViewProcsQuickOpti

34、onsWindowHelp-101x|View|Procs|Objects|Print|Freeze|Estimate(Forecast|Stats|KesidsjDependentVariable:RZMethod:ML-ARCHDate;10/27/D5Time;17:34Sample(adjusted):171443Includedobservations:1427afteradjustingendpointsConvergenceachievedafter33iterationsCoefficientStd.Errorz-StatisticProb.GARCHCRZ(-15)5.162

35、608-0.0015590.0549652.1653440.0005490.0222132.384198-2.8387312.4740050.01710.00450.0134VarianceEquationCARCH(1)GARCH(1)6.85E-060.1232680.3608481.39E-060.0095670.0093754.93939012.8846991.826440.00000.00000.0000R-squaredAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihood0.0085530.0050640.017

36、8880.4546843912.653MeandependentvarS.D.dependentvarAkaikeinfocriterionSchwarzcriterionF-statistic-0.0001730.017933-5.476337-5.4532072.451695Path=c：eviews3DB=noiteWF=untitled图7-21很明显，沪深两市均值方程中条件方差项GARCH的系数都是显著的。它们反映两市的收益与风险的正相关关系，也说明收益有正的风险溢价，而且上海股市的风险溢价要高于深圳I。这说明上海股市的投资者更加地厌恶风险(riskaverse),要求更高的风险补偿

37、。、对股市收益波动作非对称性的研究1、TARCH模型估计结果与GARCH(1,1)不同的是，在图7-17中的“ARCHSpecification下拉列表中选择TARCH”，则得ill、rz的TARCH模型估计结果，分别如下图7-22和图7-23：|evs-Equation：UHTITLEDWorkfile：UBTITLID-|njx|FileEditObjectsViewProcsQuickOptionsWindowHelp-Ifflx|View|Procs|Objects|Print|Freeze|Estimate(Forecast|Stats|Resids|DependentVariabl

38、e:RHMethod:ML-ARCHDate;10/27/D5Time;17:35Sample(adjusted):171443Includedobservations:1427afteradjustingendpointsConvergenceachievedafter26iterationsCoefficientStd.Errorz-StatisticProb.C-0.0002540.000319-0.7965900.4257RH(-15)0.0653160.0216053.0231770.0025VarianceEquationC7.2SE-061.17E-06S.2074090.000

39、0ARCH0.1106670.0136788.0908990.0000(RESIDARCH0.0852590.0184464.6220440.0000GARCH(1)0.3318560.01107075.147700.0000R-squared0.007253Meandependentvar0.000253AdjustedR-squared0.003760S.D.dependentvar0.016348S.E.ofregression0.016317Akaikeinfocriterion-5.649883Sumsquaredresid0.378326Schwarzcriterion-5.627

40、752Loglikelihood4037.191F-statistic2.076461Path=c：eviews3DB=noiteWF=untitled图7-22劉！-Equation：IfflTTITLEDlorkfile：UBTITLIDI口x|1JFileEditObjectsViewProcsQuickOptionsWindowHelp-Ifflx|View|Procs|Objects|Print|Freeze|Estimate(Forecast|Stats|Resids|DependentVariable:RZMethod:ML-ARCHDate;10/27/D5Time;17:36

41、Sample(adjusted):171443Includedobservations:1427afteradjustingendpointsConvergenceachievedafter29iterationsCoefficientStd.Errorz-StatisticProb.C-0.0007840.000355-2.2068130.0273RZ(-15)0.0562720.0222442.5297300.0114VarianceEquationC5.74E-0S1.23E-064.6717460.0000ARCH0.0968020.0097519.9273740.0000(RESID

42、ARCH0.0478690.0143873.3272750.0009GARCH(1)0.3678770.00875499.140710.0000R-squared0.005205Meandependentvar-0.000173AdjustedR-squared0.001705S.D.dependentvar0.017933S.E.ofregression0.017918Akaikeinfocriterion-5.478776Sumsquaredresid0.456219Schwarzcriterion5.456645Loglikelihood3915.106F-statistic1.4869

43、95lwnPath=c：eviews3DB=noiteVF=untitled图7-23估计结果中，(RESIDVO)*ARCH(1)的系数都人于零，而且显著，并有山方程的系数大于rz方程的系数，这说明沪深股市中坏消息引起的波动比同等人小的好消息引起的波动要大，沪深股市都存在杠杆效应。EARCH模型估计结果在图7-17的“ARCHSpecificationM下拉列表中再次选择EGARCH”，则得ill、rz的EGARCH模型估计结果，分别如下图7-24和图7-25：|evs-Equation：UHTITLEDWorkfile：UBTITLID-|njx|FileEditObjectsViewPr

44、ocsQuickOptionsWindowHelp-Ifflx|View|Procs|Objects|Print|Freeze|Estimate(Forecast|Stats|Resids|DependentVariable:RHMethod:ML-ARCHDate;10/27/D5Time;17:43Sample(adjusted):171443Includedobservations:1427afteradjustingendpointsConvergenceachievedafter57iterationsCoefficientStd.Errorz-StatisticProb.C-0.0

45、002760.000304-0.9080020.3639RH(-15)0.0543250.0209702.5906690.0096VarianceEquationC-0.5127700.057778-8.8748670.0000|RES|/SQRGARCH(10.2798140.02221812.593650.0000RES/SQRGARCH(1)-0.0518460.011154-4.6481150.0000EGARCH(1)0.9639030.005960161.71940.0000R-squared0.006390Meandependentvar0.000253AdjustedR-squ

46、ared0.002893S.D.dependentvar0.016348S.E.ofregression0.016324Akaikeinfocriterion-5.667941Sumsquaredresid0.378655Schwarzcriterion-5.645811Loglikelihood4050.076F-statistic1.827619Path=c：eviews3DB=noiteWF=untitled图7-24|evs-Equation：UHTITLEDWorkfile：UBTITLID-Inx|FileEditObjectsViewProcsQuickOptionsWindow

47、Help-Ifflx|View|Procs|Objects|Print|Freeze|Estimate(Forecast|Stats|Resids|DependentVariable:RZMethod:ML-ARCHDate;10/27/D5Time;17:41Sample(adjusted):171443Includedobservations:1427afteradjustingendpointsConvergencenotachievedafter100iterationsCoefficientStd.Errorz-StatisticProb.C-0.0007750.000340-2.2

48、776340.0227RZ(-15)0.0494520.0223732.2103260.0271VarianceEquation0-0.3713630.045840-8.1012130.0000|RES|/SQRGARCH(10.2368450.01587114.923010.0000RES/SQRGARCH(1)-0.032059.008898-3.6027780.0003EGARCH(1)0.9764660.005116190.88180.0000R-squared0.004809Meandependentvar-0.000173AdjustedR-squared0.001307S.D.d

49、ependentvar0.017933S.E.ofregression0.017922Akaikeinfocriterion-5.487199Sumsquaredresid0.456401Schwarzcriterion-5.465068Loglikelihood3921.116F-statistic1.373207Path=c：eviews3DB=noiteWF=untitled图7-25在EGARCH中，RES/SQRGARCH（1）项系数的估计值都小于零而且显著，这也说明了沪深股市中都存在杠杆效应。（三）、对沪深股市作波动溢出效应研究1.检验两市波动的因果性（1）提取条件方差重复步骤（7）,选择主菜单栏Procs下的“MakeGarchVarianceSenes”，得到残差项的条件方差数据序列GARCH01,同样的步骤得sz回归方程残差项的条件方差数据序列GARCH02。（2）检验两市波动的因果性在“Woikfile中同时选中“garchO1”和“gaich02”，右击，选择“Ope