金融计量-GARCH模型在金融大数据中地的应用

实验报告七 模型在金融数据中的应用一.实验目的理解自回归异方差（ ）模型的概念及建立的必要性和适用的场合。了解（） 模型的各种不同类型，如 模型， 模型和模型。掌握对（） 模型的识别、估计及如何运用 软件在实证研究中实现。二.实验步骤一）沪深股市收益率的波动性研究描述性统计数据选取与导入本实验选取中国上海证券市场股成分指数上证 和深圳证券市场股成分指数深证30作0为研究对象。分别从财经网站上下载了201年05月4号到20年4月19号这将近6年的上证18和0深证30的0每日收盘价，共144个8。其中，上证指数的日收盘价以下记为，深证 指数的日收盘价以下记为。将下载的数据导入 。生成收益率的数据列”，生成上证”，生成深证”，生成上证”，生成深证指数的日收益率序列，记为,输入“指数的日收益率序列，记为。观察收益率的描述性统计量利用作出的沪市收益率的描述性统计量如图所示。

利用作出的沪市收益率的描述性统计量如图所示。图沪市收益率的描述性统计量从上图可以看出，样本期内，沪市收益率的均值为0.00，3标9准5差%为1.66，偏6度9为%-0.66，左8偏2峰0度1为7.31，6远6高8于3正态分布的峰度值3，说明沪市收益率具有尖峰和厚尾特征。统计量为 ，说明在极小水平下，沪市收益率显著异于正态分布。利用 作出的深市收益率的描述性统计量如图所示。图深市收益率的描述性统计量从上图可以看出，样本期内，深市收益率的均值为0.01，2标8准%差为1.79，偏2度6为%-0.78，左1偏0峰0度7为6.07，9远5高5于7正态分布的峰度值3，说明深市收益率也具有尖峰和厚尾特征。统计量为 ，说明在极小水平下，沪市收益率也显著异于正态分布。而且深市收益率的标准差略大于沪市，说明深市的波动性更大。平稳性检验利用 软件对和进行平稳性检验。沪市收益率的检验结果如图所示；深市收益率的 检验结果如图所示。

NullHypothesis:RHhasaunitrootExogenous:ConstantLagLength:0(Automatic-basedonSIC,maxlag=10;t-StatisticProb.*AugmentedDickey-Fullerteststatistic-37.042590.0000Testcriticalvalues: 1%level-3.43466斗5%level-2.86333310%level-2.567773^MacKinnon(1996)one-sidedp-values.AugmentedDickey-FullerTestEquationDependentVariable:DfRH)Method:LeastSquares□ate:05/11/16Time:20:54Sample(adjusted}:31448Includedobservations:1446afteradjustmentsVariableCoefficientStd.Errort-StatisticProL.-0.9744620.026307-37.042590.0000C3.54E-050.0004390.0006240.9358R-squared0.487244Meandlependentvar-3.18E-06AdjustedR-squared0.406889S.D.dependentvar0.023279S.E.ofregression0.016675Akaikeinfocriterion-5.348441Sumsquaredresid0.401508Schwarzcriterion-5.341143Loglikelihood3S6S.923Hannan-Quinncriter.-5.345717F-statistic1372.154□urbin-Watsonstat1.991214Prob(F-statistic)0.000000图 的检验结果NullHypothesis:RZhasaunitrootExogenous:ConstantLagLength:0(Automatic-basedonSIC,maxlag=10)t-StatisticProb/AugmentedDickey-Fullerteststatistic35.685690.0000Testcriticalvalues: 1%level-34346645%level-2.863S3310%level-2.567773^MacKinnon(1996)one-sidedp-values.AugmentedDickey-FullerTestEquationDependentVariable:D(RZ}Method:LeastSquares□ate:05^11/16Time:20:54Sample(adjusted}:31443Includedobservations:1446afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.-0.9369900.026257-35.685690.0000C0.0001090.0004710.231174-0.8172R-squared0.463623Meandependentvar-1.20E-05AdjustedR-squared0.46B255S.D.dependentvar0.024545S.E.ofregression0.017S98Akaikeinfocriterion-5.206053Sumisquaredresid0.462578Schwarzcriterion-5.199555Loglikelihood3766.555Hannan-Quinncriter.-5.204-129F-statistic1273.469Durbin-Watsonstat1.907091Prob(F-statistic)0.000000图 的 检验结果从这两个检验结果可以看出，和的 检验值都小于临界值，说明沪市收益率和深市收益率都是平稳的。均值方程的确定及残差序列自相关检验通过对收益率的自相关检验，可以发现沪市的收益率与其滞后7阶存在显著的自相关，而深市的收益率也与其滞后7阶存在显著的自相关，因此建立的均值方程如下：对收益率做自回归利用普通最小二乘法对和做回归，回归结果如图所示。利用普通最小二乘法对和做回归，回归结果如图所示。DependentVariable:RHMethod:LeastSquares□ate:05/14^16Time:17:34Sample(adjusted}:91448Includedobservations:1440afteradjustmentsVariableCoefficientStd.Errort-StatisticProt).C6.72E-050.0004380.1535290.87S0RH(-7}0.0478700.0262351.8246560.0683R-squared0.002310Meandependentvar6.36E-05AdjustedR-squared0.001616S.D.dependentvar0.016631S.E.ofregression0.016618Akaikeinfocriterion-5.355294Sumsquaredresid0397107Schwarzcriterion-5.347971Loglikelihood3857.812Hannan-Quinncriter.-5.352560F-statistic3.329370□urbin-Watsonstat1.945953Prob(F-statistic)0.063260图收益率的回归结果忽略常数项的不显著，的均值方程估计为再对和 做回归，回归结果如图所示。DependentVariable:RZMethod:LeastSquares□ate:05^14^16Time:17:37Sample(adjusted):9t斗4日Includedobservations:1440afteradjustmentsVariable (CoefficientStd.Error t-StatisticProb.C0.0001590.000471 0.3336320.7349RZ(-7)0.0610250.026236 2.3259630.0202R-squareo0.003743Meandependentvar0.000167AdjustedR-squared0.003055S.D.dependentvar0.017095S.E.ofregression0.017367Akaikeinfocriterion-5.210315Sumsquaredresid0.459061Schwarzcriterion-5.202993Loglikelihood3753.427Hannan-Quinncriter.-5.207582F-statistic5.410102Durbin-Watsonstat1.875428Prob(F-statistic)0.020159图收益率的回归结果同样忽略常数项的不显著，的均值方程估计为用 统计量对均值方程拟合后的残差及残差平方做自相关检验

□ate:05/14^16Time:17:42Sample:91448Includedobservations:1440AutocorrelationPartialCorrelationAC PACQ-StatProbI11110.0270.0271.04000.306(1112-0.037-0.0333.00030.223I1113-0.00B-0.0063.08370.379I]1]40.07B0.07511.4160.022I11150.0150.01011.7390.039匚1L16-0.094--0.09024.5890.000I1111-0.0040.00324.6150.001I]1]S0.0530.04829.592O.DDOI11190.03E0.03031.4480.000(11110-0.025-0.01132.3420.000(1(111-0.043-0.03735.0090.000I111120.0210.00735.6250.000I]1]130.0730.06242.7760.000[1[114-0.073-0.07351.S440.000I111150.004-0.02351.S640.000图 残差的自相关系数和值偏自相关系数显示残差不存在显著的自相关。再得到残差平方的自相关系数和值，如图所示。Dafte:05/14/16Time:1'7:MSample:91448includedobservations:144QAutocorrelationPartialCorrelationAC PACO-StatProbi□i□10.1800.18046.9390.000ii□20.2370.212125.360.000ii□30.2120.152191620.000iZli]』0.19J0.097242.400.000i□i]50.1500.051275.170.000i□i160.1240.023297.270.000i□i170.1350.0^1632S.520.000iZli130.1040.019339.170.000i1i190.09-0.010351.250.000i□i]100.12E0.06037030.000iJi1110.09-0.018386.860.000iJi1120.0920.017399.140.000i□in130.1790.119445.740.000i1i1140.0960.011459.090.000iJi1150.034-0.015469.330.000图偏自相关系数显示再做出残差和图偏自相关系数显示再做出残差和所0示。残差平方存在显著的自相关。所0示。残差平方的自相关系数图，如图和图□ate:05/14/16Time:1746Sample:9144SIncludedobservations:*1440AutocorrelationPalialCorrelationACRACQ-StatProb1]1]10.0620.0625.59610.018(1(12-0.041-0.045799520.018111130.0150.021833470.04011140.0290.0259.53770.049111150.0160.015993120.077(1116-0.042-0.04312.5140.05111117-0.0040.00212.5410.0041]190.0440.04015.3290.0531111g0.0120.00715.5490.077[1[110-0.064-0.06121.5620.017ii11ii0.0090.01921.5S50.027111112-0.002-0.01321.6950.0411]1]130.0700.07320.3470.007(1[114-0.047-0.05232.0030.0041111150.0070.02332.0830.006图 残差的自相关系数 和值□ate:05^14^16Time:17:47Sample:914-4-8Includedobservations:1440AutocorrelationPartialCorrelationAC 3ACQ-S1atProbI■I□10.2073.20761.6320.000IIZU20.272D.240163.760.000IzzI□30.239D.162250.970.000IZlIZl40.209D.101313.980.000I□I50.200D.0S2372070.000I□II60.133D.002397.510.000I□II70.121D.000413.880.000I□I]80.147D.053450.300.000I□I190.126D.037473.330.000I□I100.176D.094513.360.000I□I]110.148D.054550.170.000I□I1120.103-D.016565.570.000IZlIZl130.207D.100627.720.000I□IJ140.1903.0906S0.440.000I□I1150.119-D.022700.950.000图 残差平方的自相关系数和值从图中可以得到与类似的结论，即的残差不存在显著的自相关，而残差平方存在显著的自相关。对残差平方做线性图对进行回归后提取残差，生成残差平方序列 ；对进行回归后提取残差，生成残差平方序列 。利用软件作出 和 的线形图，如图和图所示。

由这两个图可以看出，£的波动具有明显的时间可变性和集簇性，比如在50和0附近比较小，也就是说适合用类模型来建模。对残差进行对做回归之后的窗口中进行s选择一阶滞后，得到检验结果如图所示。同样步骤得到的检验结果，如图 所示。HeteroskedasticityTest:ARCHF-statistic 40.32412ProtJ.F(1.1437) 0.0000Obs^R-squared 斗6.S1700Prob.Chi-Squane(1) 0.0000TestEquation:□ependgm'Vmrimtiie:resideMethod:LeastSquares□ate:05/15/16Time:09:42Sample(adjusted}:131448Includedobservations:1439afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.C0.0002261.94E-0511.652620.0000RESIDA2(-1}0.1803770.0259436.9515550.0000R-squared0.03^53dMeandep@ndertwmr0.000276AdjustedR-squared0.031861S.D.dlependentvar0.000695S.E.ofregression0.000634Akaikeinfocriterion-11.73512Sumsquaredresid0.000673Schwarzcriterion-11.727S0Loglikelihood6445422Hannan-Quinncriter.-11.73239F-statistic48.32412□urbin-WatsonEtat2.066934Prob(F-statistic)0.000000图HeteroskedasticityTest:ARCHF-statistic 64.13170Prot.F(1.1437) 0.0000Obs^R-squared 61.4-7729Prob.Chi-Square(l) 0.0000TestEquation:DependentVariable:RESIDA2Method:LeastSquares□ate:05/15^16Time:09:43sample(adjuseed):101斗斗8Includedobservations:1439afteradjustmentsVariableCoefficientStdErrort-StatisticProb.c0.0D02532.04E-0512.427040.0000RESIDA2-1}0.2D6694-0.025810S.0002270.0000R-squared0.042722閘e日ndependEntvar0.000319AdjustedR-squa.red0.042056S.D.dependentvar0.000722S.E.ofregression0.0D0707Akaikeinfocriterion-11.67097Sumsquarednesid0.0D0717Schwaizcriterion-1166364Loglikelihood8399.259Hannan-Quinncriter.-11.66823F-statistic64.13170□urbin-Watsonstat2.080575Prob(F-statistic}0.0D0000图14rzARCH-LMTest检验的原假设是残差中一直到第阶都没有 现象。在这里 由检验结果可以看出，的检验统计量和检验统计量都大于临界值,因此拒绝原假设，认为残差中， 效应是显著的。对于来说也是这样，残差中的 效应也显著。

类模型建模模（型1估,计1结）果对和分别进行 建模。其均值方程形式为P其中表示和都可以。其条件方差方程为h h利用软件对进行估计，估计结果如图所利用软件对进行估计，估计结果如图所5示。□ependentVariable:RHMethod:ML-ARCH(Marquardt}-Normaldistribution□ate:05^15/16Time:09:59Sample(adjusted}:91448Includedobservations:1440afteradjustmentsConvergenceachievedafter10iterationsPresamplevariance:backcast(parameter=0.7}GARCH二C(3)+C(4rRESID(-1尸2+C(5)*GARCH(-1;R-squaredAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat0.0022420.0015480.0166-10R-squaredAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat0.0022420.0015480.0166-100.3971343998.9681.945433MeandependentvmrS.D.dependentva.rAkaikeinfocriterionSchwarzcriterionHmnnan-Quinncriter.6.86E-050.016631-5.547177-5.528870-5.540343VariableCoefficientStdError^StatisticProb.C9.57E-050.0003750.25&4530.7934RH-7}0.0559120.0256302.1772580.0295VarianceEquationC3.45E-06S.54E-074.0345070.0001RESIDM^0.0530780.00679578114190.0000GARCH0.9331620.007601122.77630.0000图 的 ，模型估计结果由估计结果可以看出，估计的模型为h h此外，除常数项外其他各系数全部显著，说明序列具有显著的波动集簇性。而且项和 项系数之和为 ，小于，也符合理论。因此对建立的 ，模型是平稳的，其条件方差表现出均值回复，即过去的波动对未来的影响是逐渐衰减的。再对进行建模，估计结果如图所示。

DependentVariable:RZMethod:ML-ARCH(Marquardt)-Normaldistribution□ate:05/15/16Time:10:07Sample(adjusted；:91448Includedobservations:1440afteradjustmentsConvergenceachievedafter15iterationsPresamplevarianc©:backcast(parameter=0.7)GARCH=C(3)+C(4rRESID(-1尸2+C(5)*GARCH[-1}R-squareaAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat0.0036990.0030060.017B68R-squareaAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat0.0036990.0030060.017B680.4590343903.2771.875473MeandependentvarS.D.dependentvarAkaikeinfocriterionSchwarzcriterionHannmn-Quinncriter.0.0001670.017S95-5.414273-5.395966-5.407439,模型估计结果估计的模型为对的数全部显著，说明,模型估计结果估计的模型为对的数全部显著，说明,模型的估计结果分析与类似,序列具有显著的波动集簇性。而且除常数项外其他各系项和项系数之和为，小于，也符合理论。因此对建立的）模之和为，小于，也符合理论。因此对建立的）模1型是平稳VariableCoefficientStd.Errorz?StatisticProb.C0.0002060.0003940.5218740.6018RZ(-7}0.0675310.0269112.5094500.0121VarianceEquationC3.20E-069.05E-073.5395100.0004-RESID(-1^20.0407090.0060917.0686370.0000GARCH(-1)0.93974-70.007006134.13220.0000的,其条件方差表现出均值回复,即过去的波动对未来的影响是逐渐衰减的。估计结果对进行 模型估计，在 项中选择方差，得到的模型估计结果如图所示。

DependentVariable:RHMethod:ML-ARCH(Marquardtj-NormaldistributionDependentVariable:RHSample(adjusteal):91448l「icli」dWdobservations；:1440afteradjustmentsConvergenceachievedafter24iterationsVariableCoefficientStd.Errorz?StatisticProb.GARCH0.1965203.0718580.0639740.9490VariableCoefficientStd.Errorz?StatisticProb.GARCH0.1965203.0718580.0639740.9490C5.53E-050.0007120.0777570.93S0RH(-7}0.0559630.0256332.1789780.0293VarianceEquationC3.45E-068.58E-074.0202610.0001RESID(-1P2O0531140.0063467.7&87450.0000GARCH[-1}0.9331180.007605122.70090.0000R-squaredAdjustedR-squaredMeandependentvarS.D.dlependE「itHaL「Presamplevariance:backcastiparameter=0.71S.E.ofregressionSumsquaredresidLoglikelihood由估计结果可以看出，均值方程中的 项的系数并不显著，说明 并不适合用模型来进行估计。同样步骤得到的 模型估计结果，如图所示。DependentVariable:RZMethod:ML-ARCH(Marquardt}-Normaldistribution□ate:05^15^16Time:10:17Sample(adjusted}:914-4-3Includedobservations:1440afteradjustmentsConvergenceachievedafter28iterationsPresampievariance:backcast(parameter=0.7)GARCH=C(4;C(5fRESID(-1f2C(6)*GARCHf-1}VariableCoefficientStd.Errorz>StatisticProb.GARCH1.4729272.3733400.5117280.6088C-0.0001300.000752-01735070.3623RZf-7)0.0602360.026874-2.5409460.0111VarianceEquationC3.25E-069.64E-07 3.3752020.0007RESID(-1^20.0492230.007125 6.9087990.0000GARCH(-1)0.9390390.007123 131.74540.0000R-squa.red0.002493Meandependent畑0.000167AdjustedR-squared0.001105S.D.dependentvar0.017B95S.E.ofregression0.017835Akaikeinfocriterion-5.413005Sumisquaredresid0.^159640Schwarzcriterion-5.391117Loglikelihood3903.421Hannan-Quinncriter.-5.404085Durbin-Watsonstat1.871200模模（型估估计计估结）果

项的系的 模型估计结果与类似，即均值方程中的项的系数并不显著，说明不适合用 模型来进行估计。二果股市收益波动非对称性的研究模型估计结果在所示。中填入1在所示。中填入1得到的，模型估计结果如图DependentVariable'RHMethod:ML-ARCH(Marquardt)-NormaldistributionDate:05/15/16Time:10:23Sample(adjusted):9U48Includedobservations:144-0afterad.ustmentsCdmergeneeadiiei/edafter15iterationsPresamplevariance:tackcastfparameter=0.7)GARCH=0(3)+Q4FREEIDf-1尸2C(5FRESI□(-1^(RESI□(-1)0)-C(6FGARCH(-1)R-squaredAdjustedR-squaredS.E.regressionSumsquaredresidLoglikelihoodDurbin-Watscnstat0.002242R-squaredAdjustedR-squaredS.E.regressionSumsquaredresidLoglikelihoodDurbin-Watscnstat0.0022420.00154300166180.3971343990.9601.945434MeandependentvarS.D.dependentvarAkaikeinfocrierorSchwarzcriterionHannar-Quinncriter.6.B6E-050.016631-5.545789-5.523320-5.537583VariableCoefficientStd.ErrorZrStatisticProb.C9.60E-050.00038J0.2505810.3D21RHf-7)0.0553090.02569B2.1749620.0296VarianceEquationC3.44E-06SU53E-O74.033S670.DDO1RESID(-1f20.0531830.003309B.339660O.ODOORESID(-1^2*(RESID(-1)<0)-0.0002730.00916D-D.0297640.9763GARCH-1)0.9332330.007599122.SD68O.ODOO图 的 ，模型估计结果估计结果显示， 的系数估计值小于，并且不显著，说明在沪市中并不存在收益波动的非对称性。同样步骤得到的 ，模型估计结果如图所示。

DependentVaiaUecRZMethod:ML-ARCH(Marquardt)-Normaldistribjtion□ate:05/15/16Tlrrne1026Sample(adjusted}:01449Includedobservations:1440afteradjustmentsConvergenceachievedafter16iteratonsPresamplevariance:backcast(parameter=0.7)GARCH= C(4)T尺ESIDL1『2十宣5严尺已8心曰严27尺ESID[-1卜⑴十C(6)*CARCH(-1}VariableCoefficien:Std.ErrorZrSlatisticProa.c0.35E-O50.0004090.2D42D40.0302RZ(-7)0.07220-10.026393273&6650.0062VarianceEquationc4.23E-061.06E-064.1D&7B00.0000RESIDMT20.0350250.0037014.0254720.0001RESIDt-ir2*(RE.SID(-1)<0'：0.0235400.0109232.6129420.0090GARCH(-1}0.9336600.007734120.7179U.0000R-squared0.003603Meandependentvar0.000167AdjustedR-squared0.002910S.D.dependentvar0.017895S.E.ofregression0.017863Akaikeinfocriterion-5.^115270Sumsquaredresld0.459123Schwarzcriterion-5.393302Loglikslihoodl3904.995HannanQuinncriter.-5.407069Durbin-Watsonstat1.S75496图 的 ，模型估计结果估计结果显示，的系数估计值大于）并且显著，说明在深市中存在收益波动的非对称性，即坏消息引起的波动比同等大小的好消息引起的波动要大。模型估计结果对进行估计，其估计结果如图所示。对进行估计，其估计结果如图所示。DependentVariable:RHMethod:ML-ARCH(Marquardt)-Normaldistrioution□ate:DependentVariable:RHMethod:ML-ARCH(Marquardt)-Normaldistrioution□ate:05/15/16Time:10:29Sample(adjusted}:9144SIncludedobservations:*1440alteradjustmentsConvergenceachievedafter17iterationsPresamplevariance:backcast[parameter=0.7;LOG(GARCH)=C⑶+C(4)*ABS(RESID(-1J/@S€1RT(GARCH(-1}}}+C⑸^RESID(-1}/@SQRT(GARCH㈠"+C(6fLOG[GARCH(-1}}VariableCoefficientStdErrorz-SMsficProb.C9.38E-050.0003770.2437400.3036RH(-7>0.0515050.0249112.0675630.0337VarianceEquationc⑶-0.1997730.030940-6.4560080.0000C(4)0.1276400.0138209.2359540.0000U⑶-0.0D70120.007402-0.9472990.3435C(6)0.9B73420.003301299.05920.0000R-squaredAdjustedR-squareds.E.orregressionSumsquarednesidLoglikelihood□urbin-Watsorstat0.0D22940.0D16000.0166180.3S71133996.7481.945716MeandependentvarS.D.dependentvarAKalkeinfocriterionSchwaizcriterionHannan-Quinncriter.6.86E-050.016631-5.&42705-5.520737-5.534504-图 的 ，模型估计结果估计结果中， 项的系数 为但是不能通过显著性检验，说明沪市中不存在收益波动的非对称性。同样对进行 ，模型估计，估计结果如图所示。DependentVariable:RZMethod:ML-ARCH(Marquardt}-Normaldistribution□ate:05/15/16Time:1033Sample(adjusted}:91448Includedobservations:44斗0afteradjustmentsConvergenceachievedafter24iterationsPresamplevariance:backcast[parameter=0.7;LOGtGARCHCt3)+C(4rABS(RESIDt-1}/@SClRTtGARCH(-1D)+U⑸*RE.SID(-1)i/@SaRT[GARCH(-1})+C(6)*U3G(GARCH(-1}：■VariableCoefficientStd.Errorz?StatisticProb.C-7.26E-050.00D406-0.1788530.0581RZ(-7)0.0618540.0257432.4-022690.0163VarianceEquationG⑶-0.1941480.031U9 -&2329450.00000(4}0.1207010.014052 8.1269500.00000(5)-0.0266410.00B474 -3.1438780.0017C(6)0.9876630.003426 288.26110.0000R-squared0.003579Meandependentvar0.000167AdjustedR-squared0.002886S.D.dependentvar0.017895S.E.ofregression0.017869Akaikeinfocriterion-5.410352Sumsquaredresid0.459139Schwarzcriterion-5.383834Loglikelihood39D1.813Hannan-Quinncriter.-5.402651□urbin-Watsonstat1.S75119图的, 模型估计结果估计结果中， 项的系数为并且通过了显著性检验，说明深市中存在收益波动的非对称性，这也与模型的估计结果相吻合。（三）沪深股市波动溢出效应的研究股市波动的溢出效应就是指不同资本市场之间波动的传递，接下来进行检验深沪两