《计量经济学》上机实验报告六

《计量经济学》上机实验报告六题目：自相关实验日期和时间:2018.531班级：16金融学类5班学号：姓名：马雨柔 实验室：202实验环境：WindowsXP;EViews3.1实验目的：掌握自相关检验及修正方法-广义差分法估计，熟悉EViews软件的相关应用实验内容：利用实例数据和EViews软件，采用有关方法对建立的回归模型进行自相关的检验及处理。第六章习题6.1,6.4实验步骤：一、建立工作义件.菜单方式.命令方式：CREATEA起始期终止期二、输入数据三、自相关检验①估计回归模型进行DW检验Isycx②高阶自相关检验-偏相关系数检验方程窗口点击view\residualtest\correlogram-Q-statistiesPAC绝对值大于0.5表明存在几阶自相关③高阶自相关检验-BG检验(布罗斯-戈弗雷检验或拉格朗日乘数检验)：方程窗口点击view\residualtest\serialCorrelationLMTest得到nR2,给定a,若nR2>/(P),表明模型存在几阶自相关四、采用广义差分法估计回归模型根据上述检验，若模型存在一、二阶自相关则广义差分法估计回归模型命令：LSYCXAR(1)AR(2)回Equation:UNTITLEDWorkfile:UNTITLED::Untitled\ _□XBreusch-GodfreySerialCorrelationLMTest:ViewProcObjectPrintNameFreezeEstimateForecastStatsResidsF-statisticObs*R-squared0.2987200.404321Prob.F(1,13)Prob.Chi-Square(l)0.59390.5249TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:06/23/18Time:17:34Sample:19801997Includedobservations:18Presamplemissingvaluelaggedresidualssettozero.VariableCoefficientStd.Errort-StatisticProb.C-4.379656102.5468 -0.0427090.9666X0.0003610.004144 0.0870900.9319AR(1)0.2079420.492755 0.4219990.6799AR(2)-0.1320090.388707 -0.3396120.7396RESID(-1)-0.2624740.480235 -0.5465520.5939R-squared0.022462Meandependentvar1.82E-08AdjustedR-squared-0.278319S.D.dependentvar144.8925S.E.ofregression163.8194Akaikeinfocriterion13.26554Sumsquaredresid348878.4Schwarzcriterion13.51286Loglikelihood-114.3899Hannan-Quinncriter.13.29964F-statistic0.074680Durbin-Watsonstat1.885849Prob(F-statistic)0.988677滞后期为2,得以下结果@Equation:UNTITLEDWorkfile:UNTTFLED::Untitled\*_nxViewProcObjectPrintNameFreezeEstimateForecastStatsResidsBreusch-GodfreySerialCorrelationLMTest:F-statistic0.159478Prob.F(2f12)0.8544Obs*R-squared0.466047Prob.Chi-Square(2)0.7921TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:06/23/18Time:17:34Sample:19801997Includedobservations:18Presamplemissingvaluelaggedresidualssettozero.R-squaredAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodF-statisticProb(F-statistic)0.025892-0.379987170.2093347654.5R-squaredAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodF-statisticProb(F-statistic)0.025892-0.379987170.2093347654.5-114.35820.0637910.996541MeandependentvarS.D.dependentvarAkaikeinfocriterionSchwarzcriterionHannan-Quinncriter.Durbin-Watsonstat1.82E-08144.892513.3731413.6699313.414061.903269VariableCoefficientStd.Errort-StatisticProb.C-6.538895107.0634-0.0610750.9523X0.0005910.0044490.1328080.8965AR⑴0.2942860.6622670.4443620.6647AR(2)-0.1430650.407434-0.3511360.7316RESID(-1)-0.3457110.642632-0.5379610.6004RESID(-2)-0.1064240.517789-0.2055350.8406从上表可知，当滞后期为1时，〃R2=0.404321,prob(nR2)=0.524866,当滞后期为2时,h/?2=0.466047,prob(nR2)=0.792135, 伴随概率均大于给定的显著性水平巾.05,并且残差滞后期的回归系数的t统计量值绝对值均小于2,这表明广义差分法估计的回归模型已消除高阶自相关性。通过在LS命令中直接加上AR(1),AR(2),AR(3)项来检测模型的是否三阶自相关性@Equation:UNTITLEDWorkfile:UNnTLED::Untitled\ -nXDependentVariable:YViewProcObject1PrintNameFreezeEstimateForecastStatsResidsMethod:LeastSquaresDate:06/23/18Time:17:36Sample(adjusted):19811997Includedobservations:17afteradjustmentsConvergenceachievedafter7iterationsVariableCoefficientStd.Errort-StatisticProb.C846.926699.265728.5319140.0000X0.1024650.00417124.564020.0000AR(1)1.1501200.3418503.3643970.0056AR(2)-0.6626090.478437-1.3849440.1913AR(3)-0.1913740.415276•0.4608360.6532R-squared0.995686Meandependentvar3422.446AdjustedR-squared0.9942482232.947S.E.ofregression169.3462Akaikeinfocriterion13.34170Sumsquaredresid344137.6Schwarzcriterion13.58676Loglikelihood-108.4044Hannan-Quinncriter.13.36606F-statistic692.4502Durbin-Watsonstat1.899493Prob(F-statiStic)0.000000InvertedARRoots.68-.69I.68+69i-.20AR(3)回归系数的t检验不显著，表明模型确实不存在三阶自相关；上述检验表明，广义差分法估计的回归模型已消除自相关性，并且，经济意义合理，可决系数R2提高，t和F检验均显著，我们得到理想模型:Yt=837.+0.^+[AR(1)=1.,AR(2)=-0.](99.64563)(99.64563)(99.64563)(99.64563)(99.64563)(0.003988)t=(8.403449)(25.72334)(0.305204)(3.985446)(0.296827)(-2.783384)R2=0.995782,F=1101.6900,prob(F)=0.000000,DW=2.013725边际分析：模型表明国内生产总值x每增加一亿元，财政收入增加0.亿元。将其与OLS相比，(99.64563)(0.003988)t=(8.403449)(25.72334)(0.305204)(3.985446)(0.296827)(-2.783384)R2=0.995782,F=1101.6900,prob(F)=0.000000,DW=2.013725试验结果:我国1978—1997年财政收入Y和国民生产总值(GNP)X的统计资料如表1所示(单位：亿元)。表格3年份FINANCEGDP年份FINANCEGDP19781132.263624.119882357.2414922.319791146.384038.219892664.916917.819801159.934517.819902937.118598.419811175.794860.319913149.4821662.519821212.335301.819923483.3726651.919831366.955957.419934348.9534560.519841642.867206.719945218.14667019852004.828989.119956242.257494.919862122.0110201.419967404.9966850.519872199.3511954.519978651.1473452.5⑴利用DW统计量，偏相关系数和BG检验，检测模型的自相关性；⑵通过在LS命令中直接加上AR(1),AR(2)项来检测模型的自相关性，并与(1)中的检验结果进行比较；⑶分析调整自相关性之后，模型估计结果的变化情况；答：(D利用DW统计量，偏相关系数和BG检验，检测模型的自相关性DW统计量：一元线性回归模型估计IsycxDATAYXLSYCX[=]Equation:UNTITLEDWorkfile:UNTHLED::Untitled\ _HXViewProcObjectIPrintNameFreezeIEstimateForecastStatsResidsDependentVariable:YMethod:LeastSquaresDate:06/23/18Time:17:16Sample:19781997Includedobservations:20y=858.4836+0.100016%VariableCoefficientStd.Errort-StatisticProb.C858.483667.15577 12.783470.0000X0.1000160.002173 46.016780.0000R-squared0.991571Meandependentvar3081.008AdjustedR-squared0.991103S.D.dependentvar2212.282S.E.ofregression208.6715Akaikeinfocriterion13.61404Sumsquaredresid783788.0Schwarzcriterion13.71361Loglikelihood-134.1404Hannan-Quinnenter.13.63348F-statistic2117.544Durbin-Watsonstat0.861307Prob(F-statistic)0.000000(67.15577)(0.02173)t二 (46.01678)R?=0.991571F=2117.544 S.E=208.675DW=0.861307此模型的可决系数为0.991571,接近于1,表明模型对样本拟合优度高；F统计量为2117.544,其伴随概率为0.00000,接近于零，表明模型整体线性关系显著，且回归系数均显著；对样本数n为20,解释变量个数k为1,若给定的显著性水平a=0.05,查DW统计表得，为=1.201,du=1.411,而0<DW=0.861307<dL=1.201,这表明模型存在一阶正自相关。偏相关系数检验：方程窗口点击view\residualtest\correlogram-Q-statistics(=)Equation:UNTITLEDWorkfile:UNTnLED::Untitled\ _nXViewProcObjectPrintNameFreezeEstimateForecastStatsResidsCorrelogramofResidualsDate:06/23/18Time:17:20Sample:19781997Includedobservations:20AutocorrelationPartialCorrelationACPACQ-StatProbEEI匚□D匚匚□AutocorrelationPartialCorrelationACPACQ-StatProbEIEI匚□D匚匚□EI匚□D匚匚□EI匚□D匚匚□EI匚□D匚匚□=310.4370.4374.42880.035匚I20.002-0.2344.42880.109[I3-0.152-0.0655.02350.1701।4-0.0890.0265.24140.263匚I5-0.216-0.2756.60670.252□।6-0.1090.1236.98270.322匚17-0.092-0.1657.26650.402匚I8-0.230-0.2919.20780.325匚19-0.340-0.15913,8420.128E110-0.182-0.11715.3040.1211110.031-0.00115.3510.1671।120.1970.07717.4880.132BG检验：方程窗口点击view\residualtest\serialCorrelationLMTest滞后期为1,得以下结果：(=]Equation:UNTITLEDWorkfile:UNHTLED::Untitled\Breusch-GodfreySerialCorrelationLMTest:ViewProcObjectPrintNameFreezeEstimateForecastStatsResidsTestEquation:F-statistic7.518193Prob.F(1,17)0.0139Obs*R-squared6.132746Prob.Chi-Square(l)0.0133DependentVariable:RESIDMethod:LeastSquaresDate:06/23/18Time:17:23Sample:19781997Includedobservations:20Presamplemissingvaluelaggedresidualssettozero.R-squaredAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodF-statisticPrnhfP-ctQtictir\0.3066370.225065R-squaredAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodF-statisticPrnhfP-ctQtictir\0.3066370.225065178.7949543449.3-130.47843.759096MeandependentvarS.D.dependentvarAkaikeinfocriterionSchwarzcriterionHannan-Quinncriter.Durbin-Watsonstat6.54E-13203.105913.3478413.4972013,376991.110757VariableCoefficientStd.Errort-StatisticProb.C-31.9210958.70662-0.5437390.5937X0.0021400.0020191.0600190.3040RESID(-1)0.7011850.2557272.7419320.0139由上表可以看出，"A?*.132746〉/(1)=3.84146,prob(nR2)=0.013270小于给定的显著性水平a=0.05,并且e-回归系数的T统计量值绝对值均大于2,回归系数显著不为零，表明模型存在一阶自相关性。滞后期为2,得以下结果：FileEditObjectViewProcQuickOptionsAdd-insWindowHelpDATAYXLSYCXr目Equation:UNTITLEDWorkfile:UNTnLED::Untitled\-nxViewProcObjectPrintNameFreezeEstimateForecastStatsResidsBreusch-GodfreySerialCorrelationLMTest:F-statisticObs*R-squared9.46817810.84049Prob.F(2,16)Prob.Chi-Square(2)0.00190.0044TestEquation:DependentVariable:RESIDFvlethod:LeastSquaresDate:06/23/18Time:17:27Sample:19781997Includedobservations:20Presamplemissingvaluelaggedresidualssettozero.VariableCoefficientStd.Errort-StatisticProb.C-23.9874649.25821 -0.4869740.6329X0.0017700.001697 1.0432710.3123RESID(-1)1.2425910.285550 4.3515740.0005RESID(-2)-0.8075480.281604 -2.8676760.0112R-squared0.542024Meandependentvar6.54E-13AdjustedR-squared0.456154S.D.dependentvar203.1059S.E.ofregression149.7823Akaikeinfocriterion13.03310Sumsquaredresid358955.8Schwarzcriterion13,23225Loglikelihood-126.3310Hannan-Quinncriter.13,07197F-statistic6.312119Durbin-Watsonstat2.036319Prob(F-statistic)0.004971从上表可以看出，=10.84049〉/(2)=5.99147,prob(nR?)=0.004426小于给定的显著性水平a=0.05,并且ei和以一2回归系数的t统计量值绝对值均大于2,回归系数显著不为零，表明模型存在一阶、二阶自相关性。滞后期为3,得以下结果：DATAYXLSYCX国Equation:UNTITLEDWorkfile:UNTHLED::Untitled\ -nXBreusch-GodfreySerialCorrelationLMTest:ViewProcObjectPrintNameFreezeEstimateForecastStatsResidsF-statisticObs*R-squared6.14993011.03133Prob.F(3,15)Prob.Chi-Square(3)0.00610.0116TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:06/23/18Time:17:29Sample:19781997Includedobservations:20Presamplemissingvaluelaggedresidualssettozero.VariableCoefficientStd.Errort-StatisticProb.C-27.3127150.68377 -0.5388850.5979X0.0020200.001790 1.1289220.2767RESID(-1)1.1909400.305811 3.8943610.0014RESID(-2)-0.6276370.429223 -1.4622630.1643RESID(-3)-0.2099550.371623 -0.5649690.5804R-squared0.551567Meandependentvar6.54E-13AdjustedR-squared0.431984S.D.dependentvar203.1059S.E.ofregression153.0744Akaikeinfocriterion13.11204Sumsquaredresid351476.6Schwarzcriterion13.36098Loglikelihood-126.1204Hannan-Quinncriter.13.16064F-statistic4.612448Durbin-Watsonstat1.913584Prob(F-statistic)0.012544从上表可以看出，nR2=U.03133>/口3)=7.81473,prob(nR?)=0.011558小于给定的显著性水平a=0.05,et-i回归系数的t统计量值绝对值均大于2,回归系数显著不为零，但et-2、e-回归系数的t统计量其P值均大于0.05,也大于0.10,回归系数显著地为零，表明模型可能存在三阶自相关上述检验表明模型存在一阶、二阶自相关，可能存在三阶自相关，0LS估计模型中的t统计量和F统计量的结论不可信，需应用广义差分法修正模型。⑵通过在LS命令中直接加上AR(1),AR(2)项来检测模型的自相关性，并与⑴中的检验结果进行比较广义差分法估计模型LSYCXAR(1)AR(2)DATAYXLSYCXAR(1)AR(2)(=]Equation:UNTITLEDWorkfile:UNUTLEDuUntitledX _nXViewProcObjectPrintNameFreezeEstimateForecastStatsResidsDependentVariable:YMethod:LeastSquaresDate:06/23/18Time:17:31Sample(adjusted):19801997Includedobservations:18afteradjustmentsConvergenceachievedafter7iterationsR=837.+0.^+[AR(1)=1.,AR(2)=-0.]VariableCoefficientStd.Errort-StatisticProb.C837.367099.645638.4034490.0000X0.1025790.00398825.723340.0000AR(1)1.2163740.3052043.9854460.0014AR(2)-0.8261830.296827-2.7833840.0147R-squared0.995782Meandependentvar3296.751AdjustedR-squared0.9948782230.951S.E.ofregression159.6637Akaikeinfocriterion13.17715Sumsquaredresid356895.0Schwarzcriterion13.37501Loglikelihood-114.5943Hannan-Quinncriter.13.20443F-statistic1101.690Durbin-Watsonstat2.013725Prob(F-statistic)0.000000InvertedARRoots.61+681.61-.68i(99.64563)