计量经济学实验五

实 验 报 告课程名称： 计量经济学 实验项目： 实验五 异方差模型的 检验和处理 实验类型：综合性 设计性 验证性R专业班别： 13国贸10 姓 名： 陈凤妍 学 号： 实验课室： 厚德A404 指导教师： 石立 实验日期： 2016.05.27 广东商学院华商学院教务处 制 一、实验项目训练方案小组合作：是 否R小组成员：无实验目的：掌握异方差模型的检验和处理方法实验场地及仪器、设备和材料实验室：普通配置的计算机，Eviews软件及常用办公软件。实验训练内容（包括实验原理和操作步骤）：【实验原理】异方差的检验：图形检验法、Goldfeld-Quanadt检验法、White检验法、Glejser检验法；异方差的处理：模型变换法、加权最小二乘法(WLS)。【实验步骤】本实验考虑三个模型：【1】广东省财政支出CZ对财政收入CS的回归模型；（数据见附表1：附表1-广东省数据）【2】广东省固定资产折旧ZJ对国内生产总值GDPS和时间T的二元回归模型；（数据见附表1：附表1-广东省数据）【3】广东省各市城镇居民消费支出Y对人均收入X的回归模型。（数据见附表2：附表2-广东省2005年数据）（一）异方差的检验1.图形检验法分别用相关分析图和残差散点图检验模型【1】、模型【2】和模型【3】是否存在异方差。注：相关分析图是作因变量对自变量的散点图（亦可作模型残差对自变量的散点图）；残差散点图是作残差的平方对自变量的散点图。模型【2】中作图取自变量为GDPS来作图。模型【1】相关分析图 残差散点图模型【2】相关分析图 残差散点图模型【3】相关分析图 残差散点图【思考】相关分析图和残差散点图的不同点是什么？*在模型【2】中，自变量有两个，有无其他处理方法？尝试做出来。（请对得到的图表进行处理，以上在一页内）2.Goldfeld-Quanadt检验法用Goldfeld-Quanadt检验法检验模型【3】是否存在异方差。注：Goldfeld-Quanadt检验法的步骤为：排序：删除观察值中间的约1/4的，并将剩下的数据分为两个部分。构造F统计量：分别对上述两个部分的观察值求回归模型，由此得到的两个部分的残差平方为和。为较大的残差平方和，为较小的残差平方和。算统计量。判断：给定显著性水平，查F分布表得临界值。如果，则认为模型中的随机误差存在异方差。（详见课本135页）将实验中重要的结果摘录下来，附在本页。obsX1Y117021.944632.6927220.96317.0337299.256350.3848241.96463.958842.16757.0269214.67294.9379867.367476.9810097.27669.84910908.368113.11011944.088296.431112229.179505.661215762.7712651.951317680.114323.661418287.2414468.241518907.7314485.611621015.0318550.561722881.821188.841828665.2521767.78Dependent Variable: Y1Method: Least SquaresDate: 05/27/16 Time: 12:49Sample: 1 7Included observations: 7CoefficientStd. Errort-StatisticProb.X.0214C741.06461747.4610.0.6891R-squared0.Mean dependent var6470.296Adjusted R-squared0.S.D. dependent var930.0264S.E. of regression571.0279Akaike info criterion15.76771Sum squared resid.Schwarz criterion15.75226Log likelihood-53.18698Hannan-Quinn criter.15.57670F-statistic10.91575Durbin-Watson stat1.Prob(F-statistic)0.Dependent Variable: Y1Method: Least SquaresDate: 05/27/16 Time: 12:50Sample: 12 18Included observations: 7CoefficientStd. Errort-StatisticProb.X.0030C586.59523068.7330.0.8559R-squared0.Mean dependent var16776.66Adjusted R-squared0.S.D. dependent var3677.261S.E. of regression1547.415Akaike info criterion17.76151Sum squared residSchwarz criterion17.74606Log likelihood-60.16530Hannan-Quinn criter.17.57050F-statistic28.88339Durbin-Watson stat1.Prob(F-statistic)0.（请对得到的图表进行处理，以上在一页内）3.White检验法分别用White检验法检验模型【1】、模型【2】和模型【3】是否存在异方差。Eviews操作：先做模型，选view/Residual Tests/White Heteroskedasticity (no cross terms/cross terms)。摘录主要结果附在本页内。模型【1】Heteroskedasticity Test: WhiteF-statistic4.Prob. F(2,25)0.0156Obs*R-squared7.Prob. Chi-Square(2)0.0189Scaled explained SS14.57723Prob. Chi-Square(2)0.0007Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 05/27/16 Time: 13:19Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.C-879.85131125.376-0.0.4417CS12.937101CS2-0.0.-2.0.0347R-squared0.Mean dependent var1940.891Adjusted R-squared0.S.D. dependent var4080.739S.E. of regression3590.225Akaike info criterion19.31077Sum squared resid3.22E+08Schwarz criterion19.45351Log likelihood-267.3508Hannan-Quinn criter.19.35441F-statistic4.Durbin-Watson stat2.Prob(F-statistic)0.从模型结果看出，nR=7.，由White检验知，在=0.05下，查x2分布表，得临界值X0.05(2)=5.99147，比较计算的统计量与临界值，nR=7. X0.05(2)=5.99147,所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。模型【2】Heteroskedasticity Test: WhiteF-statistic1.Prob. F(5,22)0.1195Obs*R-squared8.Prob. Chi-Square(5)0.1204Scaled explained SS14.67857Prob. Chi-Square(5)0.0118Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 05/27/16 Time: 13:31Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.C1837.8986243.7010.0.7712GDPS-3.5.-0.0.5366GDPS2-9.08E-050.-0.0.6293GDPS*T.6161T-491.56141982.891-0.0.8065T249.08543152.98750.0.7514R-squared0.Mean dependent var3461.910Adjusted R-squared0.S.D. dependent var7240.935S.E. of regression6654.775Akaike info criterion20.63147Sum squared resid9.74E+08Schwarz criterion20.91694Log likelihood-282.8405Hannan-Quinn criter.20.71874F-statistic1.Durbin-Watson stat1.Prob(F-statistic)0.从模型结果看出，nR=8.，由White检验知，在=0.05下，查x2分布表，得临界值X0.05(2)=5.99147，比较计算的统计量与临界值，nR=8. X0.05(2)=5.99147,所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。模型【3】Heteroskedasticity Test: WhiteF-statistic7.Prob. F(2,15)0.0051Obs*R-squared9.Prob. Chi-Square(2)0.0106Scaled explained SS14.09286Prob. Chi-Square(2)0.0009Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 05/27/16 Time: 13:32Sample: 1 18Included observations: 18CoefficientStd. Errort-StatisticProb.C.0.0.5170X-354.7917388.1454-0.0.3751X.1283R-squared0.Mean dependent var.Adjusted R-squared0.S.D. dependent var.S.E. of regression.Akaike info criterion31.88212Sum squared resid5.30E+13Schwarz criterion32.03052Log likelihood-283.9391Hannan-Quinn criter.31.90258F-statistic7.Durbin-Watson stat2.Prob(F-statistic)0.从模型结果看出，nR=9.，由White检验知，在=0.05下，查x2分布表，得临界值X0.05(2)=5.99147，比较计算的统计量与临界值，nR=9. X0.05(2)=5.99147,所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。（请对得到的图表进行处理，以上在一页内）4.Glejser检验法用Glejser检验法检验模型【1】是否存在异方差。分别用残差的绝对值对自变量的一次项、二次项，开根号项和倒数项作回归。检验异方差是否存在，并选定异方差的最优形式。摘录主要结果附在本页内。(1)对CS回归Dependent Variable: ABS(RESID)Method: Least SquaresDate: 05/27/16 Time: 14:10Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.CS.0249C14.1599984R-squared0.Mean dependent var27.30288Adjusted R-squared0.S.D. dependent var35.20964S.E. of regression32.51074Akaike info criterion9.Sum squared resid27480.66Schwarz criterion9.Log likelihood-136.1767Hannan-Quinn criter.9.F-statistic5.Durbin-Watson stat1.Prob(F-statistic)0.(2)去掉常数项再进行回归Dependent Variable: E1Method: Least SquaresDate: 05/27/16 Time: 14:11Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.CS.0001R-squared0.Mean dependent var27.30288Adjusted R-squared0.S.D. dependent var35.20964S.E. of regression33.65794Akaike info criterion9.Sum squared resid30587.14Schwarz criterion9.Log likelihood-137.6761Hannan-Quinn criter.9.Durbin-Watson stat1.(3)对回归Dependent Variable: E1Method: Least SquaresDate: 05/27/16 Time: 14:19Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.CS21.11E-058.36E-061.0.1976C22.3023067R-squared0.Mean dependent var27.30288Adjusted R-squared0.S.D. dependent var35.20964S.E. of regression34.73168Akaike info criterion10.00193Sum squared resid31363.53Schwarz criterion10.09709Log likelihood-138.0270Hannan-Quinn criter.10.03102F-statistic1.Durbin-Watson stat1.Prob(F-statistic)0. (4)对回归Dependent Variable: E1Method: Least SquaresDate: 05/27/16 Time: 14:20Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.CS(1/2).0000R-squared0.Mean dependent var27.30288Adjusted R-squared0.S.D. dependent var35.20964S.E. of regression30.18432Akaike info criterion9.Sum squared resid24599.52Schwarz criterion9.Log likelihood-134.6262Hannan-Quinn criter.9.Durbin-Watson stat1.(5)对作回归Dependent Variable: E1Method: Least SquaresDate: 05/27/16 Time: 14:28Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.CS(-1)-2029.779607.7392-3.0.0025C46.2022000R-squared0.Mean dependent var27.30288Adjusted R-squared0.S.D. dependent var35.20964S.E. of regression30.01483Akaike info criterion9.Sum squared resid23423.14Schwarz criterion9.Log likelihood-133.9401Hannan-Quinn criter.9.F-statistic11.15483Durbin-Watson stat1.Prob(F-statistic)0.从四个回归的结果看，第二个不显著，其他三个显著，比较这三个回归，还是选择第三个，方程为ABS(RESID)=1.*CS(1/2)即异方差的形式为：=（1.*（CS(1/2)）=2.36085CS也即异方差的形式为：=CS就把这个形式确定为异方差的形式。 对ZJ与GDPS和T回归的Glejser检验可以类似进行检验，消费支出与可支配收入回归的Glejser检验可以类似进行检验。 通过前面实验的异方差模型的检验，发现根据广东数据CZ对CS的回归，ZJ对GDPS和T的回归，消费支出与可支配收入回归都存在异方差，现在分别对它们进行处理。加权最小二乘法已经成为处理异方差模型的标准方法，再Eviews中使用WLS来消除异方差，关键是权数的选取。 （请对得到的图表进行处理，以上在一页内）（二）异方差的处理1.模型【1】中CZ对CS回归异方差的处理已知CZ对CS回归异方差的形式为：，选取权数，使用加权最小二乘法处理异方差。并检验处理异方差之后模型是否仍存在异方差，若仍然存在异方差，请继续处理异方差。摘录主要结果附在本页内。Dependent Variable: CZMethod: Least SquaresDate: 05/27/16 Time: 14:32Sample: 1978 2005Included observations: 28Weighting series: 1/(CS(1/2)CoefficientStd. Errort-StatisticProb.CS36280.0000C-21.243654.-4.0.0000Weighted StatisticsR-squared0.Mean dependent var254.4606Adjusted R-squared0.S.D. dependent var189.1988S.E. of regression22.86683Akaike info criterion9.Sum squared resid13595.19Schwarz criterion9.Log likelihood-126.3240Hannan-Quinn criter.9.F-statistic4321.259Durbin-Watson stat1.Prob(F-statistic)0.Unweighted StatisticsR-squared0.Mean dependent var552.2429Adjusted R-squared0.S.D. dependent var653.1881S.E. of regression45.74872Sum squared resid54416.57Durbin-Watson stat1.回归方程为 CZ=1.*CS-21.它与存在异方差的如下方程估计有所不同。 CZ=1.*-CS-22.至于经过加权最小二乘法估计的残差项是否存在异方差，同样可以用本实验的异方差模型的检验去检验，但是若在eviews中使用wls命令估计的序列resed不能用俩检验，因为产生的序列resid是非加权方式的残差。要想检验只能自己进行同方差变换，然后回归以后再检验了。进行同方差行变换，然后回归实际上就是CZ/(CS(1/2)对1/(CS(1/2)和CS/(CS(1/2)回归，结果如下：Dependent Variable: CZ/(CS(1/2)Method: Least SquaresDate: 05/27/16 Time: 14:35Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.1/(CS(1/2)-21.243654.-4.0.0000CS/(CS(1/2)36280.0000R-squared0.Mean dependent var21.13688Adjusted R-squared0.S.D. dependent var15.71588S.E. of regression1.Akaike info criterion4.Sum squared resid93.80503Schwarz criterion4.Log likelihood-56.65647Hannan-Quinn criter.4.Durbin-Watson stat1.观察其残差趋势图还是存在异方差，再改为CZ/CS对1/CS和回归，如果如下:Dependent Variable: CZ/CSMethod: Least SquaresDate: 05/27/16 Time: 14:44Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.1/CS-19.828602.-9.0.0000C84560.0000R-squared0.Mean dependent var1.Adjusted R-squared0.S.D. dependent var0.S.E. of regression0.Akaike info criterion-1.Sum squared resid0.Schwarz criterion-1.Log likelihood25.23534Hannan-Quinn criter.-1.F-statistic92.24388Durbin-Watson stat1.Prob(F-statistic)0.观察其残差趋势图应该不存在异方差了，其方程为CZ/CS=-19.*1/CS+1.变换为原方程为CZ=-19.+1.*CS（请对得到的图表进行处理，以上在两页内）2.模型【2】中ZJ对GDPS和T回归异方差的处理已知ZJ对GDPS和T回归异方差的形式为：，选取权数，使用加权最小二乘法处理异方差。并检验处理异方差之后模型是否仍存在异方差，若仍然存在异方差，请继续处理异方差。摘录主要结果附在本页内。Dependent Variable: ZJMethod: Least SquaresDate: 05/27/16 Time: 14:47Sample: 1978 2005Included observations: 28Weighting series: 1/(GDPS(3/8)CoefficientStd. Errort-StatisticProb.GDPS00680.0000T-4.0.-4.0.0000Weighted StatisticsR-squared0.Mean dependent var418.9342Adjusted R-squared0.S.D. dependent var382.1762S.E. of regression29.59878Akaike info criterion9.Sum squared resid22778.28Schwarz criterion9.Log likelihood-133.5493Hannan-Quinn criter.9.Durbin-Watson stat0.Unweighted StatisticsR-squared0.Mean dependent var846.0661Adjusted R-squared0.S.D. dependent var1014.824S.E. of regression63.00261Sum squared resid.6Durbin-Watson stat0.回归方程为ZJ=0.5*GDPS-4.*T它与存在异方差时的如下方程估计也有所不同。ZJ=0.3*GDPS-2.*T进行同方差性变换，然后回归实际上就是ZJ/(GDPS(8/3)对GDPS/(GDPS(8/3)和T/(GDPS(8/3)回归，结果如下：Dependent Variable: ZJ/(GDPS(3/8)Method: Least SquaresDate: 05/27/16 Time: 14:49Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.GDPS/(GDPS(3/8)00680.0000T/(GDPS(3/8)-4.0.-4.0.0000R-squared0.Mean dependent var27.59529Adjusted R-squared0.S.D. dependent var25.17403S.E. of regression1.Akaike info criterion4.Sum squared resid98.83235Schwarz criterion4.Log likelihood-57.38737Hannan-Quinn criter.4.Durbin-Watson stat0.观测其残差趋势图可能还存在异方差，再改为ZJ/GDPS对C和T/GDPS回归，结果如下：Dependent Variable: ZJ/GDPSMethod: Least SquaresDate: 05/27/16 Time: 14:51Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.T/GDPS-3.0.-9.0.0000C93580.0000R-squared0.Mean dependent var0.Adjusted R-squared0.S.D. dependent var0.S.E. of regression0.Akaike info criterion-6.Sum squared resid0.Schwarz criterion-6.Log likelihood88.72621Hannan-Quinn criter.-6.F-statistic86.86322Durbin-Watson stat0.Prob(F-statistic)0.观测其残差趋势图应该不存在异方差了，其方程为ZJ/GDPS=0.5-3.*T/GDPS变换为原方程ZJ=0.5*-3.T（请对得到的图表进行处理，以上在两页内）3.模型【3】中消费支出Y对可支配收入X回归异方差的处理已知Y对X回归异方差的形式为：，选取权数，使用加权最小二乘法处理异方差。并检验处理异方差之后模型是否仍存在异方差，若仍然存在异方差，请继续处理异方差。摘录主要结果附在本页内。Dependent Variable: YMethod: Least SquaresDate: 05/27/16 Time: 14:56Sample: 1 18Included observations: 18Weighting series: 1/X(2/3)CoefficientStd. Errort-StatisticProb.X90120.0000Weighted StatisticsR-squared0.Mean dependent var9599.510Adjusted R-squared0.S.D. dependent var1867.615S.E. of regression895.7229Akaike info criterion16.48709Sum squared residSchwarz criterion16.53656Log likelihood-147.3838Hannan-Quinn criter.16.49391Durbin-Watson stat1.Unweighted StatisticsR-squared0.Mean dependent var10906.35Adjusted R-squared0.S.D. dependent var5381.587S.E. of regression1172.315Sum squared residDurbin-Watson stat1.它与存在异方差时如下方程估计明显不同Y=0.5*X进行同方差性变换，然后回归实际上就是Y/(X(2/3)和X/(X(2/3)回归，结果如下：Dependent Variable: Y/(X(2/3)Method: Least SquaresDate: 05/27/16 Time: 14:58Sample: 1 18Included observations: 18CoefficientStd. Errort-StatisticProb.1/(X(2/3)-495.5562520.4173-0.0.3551X/(X(2/3)36730.0000R-squared0.Mean dependent var18.56257Adjusted R-sq