实验五异方差模型的检验

1、 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： 12国 姓 名： 学 号： 412 实验课室： 厚德楼A404 指导教师： 实验日期： 2015年5月28日 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

2、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：相关分析图是作应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

3、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

4、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。obsXY17021.944632.68999999999927220.446317.0337299.256463.3748241.2099999999996350.3858842.846757.0269214.67294.9379867.367669.84810097.27476.65910908.368113.641011944.088296.43111229.179505.66

5、1215762.7712651.951317680.114485.611418287.2414468.241518907.7314323.661621015.0318550.561722881.821767.781828665.2521188.84Dependent Variable: YMethod: Least SquaresDate: 06/07/15 Time: 11:18Sample: 1 7Included observations: 7VariableCoefficientStd. Errort-StatisticProb.  X0.7230770.21838

6、63.3110030.0212C536.88741814.2540.2959270.7792R-squared0.686771    Mean dependent var6497.894Adjusted R-squared0.624125    S.D. dependent var966.9988S.E. of regression592.8541    Akaike info criterion15.84273Sum squared resid1757380. &

7、#160;  Schwarz criterion15.82728Log likelihood-53.44956    Hannan-Quinn criter.15.65172F-statistic10.96274    Durbin-Watson stat1.761325Prob(F-statistic)0.021217Dependent Variable: YMethod: Least SquaresDate: 06/07/15 Time: 11:20Sample: 12 18Included

8、 observations: 7VariableCoefficientStd. Errort-StatisticProb.  X0.7592910.1778984.2681250.0080C1243.7433707.2380.3354900.7509R-squared0.784640    Mean dependent var16776.66Adjusted R-squared0.741567    S.D. dependent var3677.261S.E. of regression1869

9、.382    Akaike info criterion18.13956Sum squared resid17472943    Schwarz criterion18.12411Log likelihood-61.48846    Hannan-Quinn criter.17.94855F-statistic18.21689    Durbin-Watson stat2.037081Prob(F-statistic)0.007953

10、有上图可知=17472943，=1757380 F=å/=17472943/1757380=9.94260945.在下，上式中分子、分母的自由度均为5，查F分布表得临界值F0.05（5,5）=5.05，因为F=9.94260945> F0.05（5,5）=5.05，所以拒接原假设，说明模型存在异方差。 （请对得到的图表进行处理，以上在一页内）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/ Heteroskedasticity Te

11、sts/White/(勾选cross terms)。摘录主要结果附在本页内。模型【1】Heteroskedasticity Test: WhiteF-statistic4.40866    Prob. F(2,25)0.0156Obs*R-squared7.932189    Prob. Chi-Square(2)0.0189Scaled explained SS14.57723    Prob. Chi-Square(2)0.0007Test Equation:Depend

12、ent Variable: RESID2Method: Least SquaresDate: 06/07/15 Time: 12:44Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.  C-879.85131125.376-0.7818290.4417CS12.937204.6513282.7813980.0101CS2-0.0066200.002964-2.2335610.0347R-squared0.283292   

13、; Mean dependent var1940.891Adjusted R-squared0.225956    S.D. dependent var4080.739S.E. of regression3590.225    Akaike info criterion19.31077Sum squared resid3.22E+08    Schwarz criterion19.45351Log likelihood-267.3508  

14、60; Hannan-Quinn criter.19.35441F-statistic4.940866    Durbin-Watson stat2.144291Prob(F-statistic)0.015552模型【2】Heteroskedasticity Test: WhiteF-statistic1.993171    Prob. F(5,22)0.1195Obs*R-squared8.729438    Prob. Chi-Square(5)0.1204Sc

15、aled explained SS14.67857    Prob. Chi-Square(5)0.0118Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/07/15 Time: 12:47Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.  C1837.8986243.7010.2943600.7712GDPS-3.39

16、50935.407361-0.6278650.5366GDPS2-9.08E-050.000185-0.4895370.6293GDPS*T0.1603000.3151760.5086040.6161T-491.56141982.891-0.2479010.8065T249.08543152.98750.3208460.7514R-squared0.311766    Mean dependent var3461.910Adjusted R-squared0.155349    S.D. dependent var

17、7240.935S.E. of regression6654.775    Akaike info criterion20.63147Sum squared resid9.74E+08    Schwarz criterion20.91694Log likelihood-282.8405    Hannan-Quinn criter.20.71874F-statistic1.993171    Durbin-Watson stat1.9

18、71537Prob(F-statistic)0.119510模型【3】Heteroskedasticity Test: WhiteF-statistic7.670826    Prob. F(2,15)0.0051Obs*R-squared9.101341    Prob. Chi-Square(2)0.0106Scaled explained SS14.09286    Prob. Chi-Square(2)0.0009Test Equation:Dependent Var

19、iable: RESID2Method: Least SquaresDate: 06/07/15 Time: 12:51Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.  C1865425.2810916.0.6636360.5170X-354.7917388.1454-0.9140690.3751X20.0188100.0116861.6095970.1283R-squared0.505630    Mean depe

20、ndent var1232693.Adjusted R-squared0.439714    S.D. dependent var2511199.S.E. of regression1879689.    Akaike info criterion31.88212Sum squared resid5.30E+13    Schwarz criterion32.03052Log likelihood-283.9391    Hannan-

21、Quinn criter.31.90258F-statistic7.670826    Durbin-Watson stat2.010913Prob(F-statistic)0.005074（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。一、一次项回归Dependent Variable: E1Method: Least SquaresDate: 06/

22、07/15 Time: 13:17Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.  CS0.0292360.0122792.3809470.0249C14.159918.2594921.7143800.0984R-squared0.179006    Mean dependent var27.30288Adjusted R-squared0.147429    S.D.

23、 dependent var35.20964S.E. of regression32.51074    Akaike info criterion9.869767Sum squared resid27480.66    Schwarz criterion9.964925Log likelihood-136.1767    Hannan-Quinn criter.9.898858F-statistic5.668911    Durbin-

24、Watson stat1.339465Prob(F-statistic)0.024881二、去掉常数项再回归 Dependent Variable: E1Method: Least SquaresDate: 06/07/15 Time: 13:22Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.  CS0.0433040.0094564.5794730.0001R-squared0.086198    

25、;Mean dependent var27.30288Adjusted R-squared0.086198    S.D. dependent var35.20964S.E. of regression33.65794    Akaike info criterion9.905436Sum squared resid30587.14    Schwarz criterion9.953015Log likelihood-137.6761   

26、60;Hannan-Quinn criter.9.919981Durbin-Watson stat1.209310三、二次项回归Dependent Variable: E1Method: Least SquaresDate: 06/07/15 Time: 13:19Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.  CS21.11E-058.36E-061.3222070.1976C22.302367.5752862.9440940.0067R-sq

27、uared0.063003    Mean dependent var27.30288Adjusted R-squared0.026965    S.D. dependent var35.20964S.E. of regression34.73168    Akaike info criterion10.00193Sum squared resid31363.53    Schwarz criterion10.09709Log like

28、lihood-138.0270    Hannan-Quinn criter.10.03102F-statistic1.748231    Durbin-Watson stat1.203183Prob(F-statistic)0.197614四、开根号项回归Dependent Variable: E1Method: Least SquaresDate: 06/07/15 Time: 13:24Sample: 1978 2005Included observations: 28VariableCoefficientS

29、td. Errort-StatisticProb.  CS(1/2)1.5372330.2690365.7138480.0000R-squared0.265081    Mean dependent var27.30288Adjusted R-squared0.265081    S.D. dependent var35.20964S.E. of regression30.18432    Akaike info criterion9.687583Sum

30、squared resid24599.52    Schwarz criterion9.735162Log likelihood-134.6262    Hannan-Quinn criter.9.702128Durbin-Watson stat1.471849五、倒数项作回归Dependent Variable: E1Method: Least SquaresDate: 06/07/15 Time: 13:26Sample: 1978 2005Included observations: 28VariableCo

31、efficientStd. Errort-StatisticProb.  CS(-1)-2029.779607.7392-3.3398840.0025C46.202298.0122115.7664840.0000R-squared0.300226    Mean dependent var27.30288Adjusted R-squared0.273311    S.D. dependent var35.20964S.E. of regression30.01483  

32、60; Akaike info criterion9.710009Sum squared resid23423.14    Schwarz criterion9.805167Log likelihood-133.9401    Hannan-Quinn criter.9.739100F-statistic11.15483    Durbin-Watson stat1.566457Prob(F-statistic)0.002542从四个回归的结果看，第二个不显著，其他

33、三个显著，比较这三个回归，还是选择第三个，方程为ABS(RESID)=1.53723330222*CS(1/2)即异方差的形式为：²=（1.537233*（CS(1/2)）²=2.36085CS也即异方差的形式为：²=²CS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

34、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: 06/07/15 Time: 13:32Sample: 1978 2005Included observations: 28Weighti

35、ng series: 1/(CS(1/2)VariableCoefficientStd. Errort-StatisticProb.  CS1.2756770.01940665.736280.0000C-21.243654.264097-4.9819800.0000Weighted StatisticsR-squared0.994019    Mean dependent var254.4606Adjusted R-squared0.993789    S.D. dependent var189

36、.1988S.E. of regression22.86683    Akaike info criterion9.166001Sum squared resid13595.19    Schwarz criterion9.261159Log likelihood-126.3240    Hannan-Quinn criter.9.195092F-statistic4321.259    Durbin-Watson stat1.5503

37、17Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.995276    Mean dependent var552.2429Adjusted R-squared0.995095    S.D. dependent var653.1881S.E. of regression45.74872    Sum squared resid54416.57Durbin-Watson stat1.545575回归方程为 CZ

38、=1.2756769685*CS-21.2436468305它与存在异方差的如下方程估计有所不同。 CZ=1.27887365026*-CS-22.6807299594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/(C

39、S(1/2)Method: Least SquaresDate: 06/07/15 Time: 13:39Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.  1/(CS(1/2)-21.243654.264097-4.9819800.0000CS/(CS(1/2)1.2756770.01940665.736280.0000R-squared0.985934    Mean dependent var21.136

40、88Adjusted R-squared0.985393    S.D. dependent var15.71588S.E. of regression1.899444    Akaike info criterion4.189748Sum squared resid93.80503    Schwarz criterion4.284906Log likelihood-56.65647    Hannan-Quinn criter.4.

41、218839Durbin-Watson stat1.550317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: 06/07/15 Time: 13:42Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.  1/CS-19.828602.064540-9.6043680.0000C1.2625010.02721846.384

42、560.0000R-squared0.780115    Mean dependent var1.077876Adjusted R-squared0.771658    S.D. dependent var0.213378S.E. of regression0.101963    Akaike info criterion-1.659667Sum squared resid0.270307    Schwarz criterion-1.

43、564510Log likelihood25.23534    Hannan-Quinn criter.-1.630577F-statistic92.24388    Durbin-Watson stat1.613436Prob(F-statistic)0.000000观察其残差趋势图应该不存在异方差了，其方程为CZ/CS=-19.8286033657*1/CS+1.26250140483变换为原方程为CZ=-19.8286033657+1.26250140483*CS（请对得到的图表进行处理，以上在两页内）2.模

44、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: 06/07/15 Time: 13:46Sample: 1978 2005Included observations: 28Weighting series: 1/(GDPS(3/8)VariableCoefficientStd. Errort-StatisticProb

45、.  GDPS0.1669950.00256565.100680.0000T-4.3536850.881296-4.9400930.0000Weighted StatisticsR-squared0.997009    Mean dependent var418.9342Adjusted R-squared0.996894    S.D. dependent var382.1762S.E. of regression29.59878    Akaike i

46、nfo criterion9.682092Sum squared resid22778.28    Schwarz criterion9.777250Log likelihood-133.5493    Hannan-Quinn criter.9.711183Durbin-Watson stat0.668750Unweighted StatisticsR-squared0.996289    Mean dependent var846.0661Adjusted R-squar

47、ed0.996146    S.D. dependent var1014.824S.E. of regression63.00261    Sum squared resid103202.6Durbin-Watson stat0.754208回归方程为ZJ=0.166994775675*GDPS-4.35368534692*T它与存在异方差时的如下方程估计也有所不同。ZJ=0.163625595483*GDPS-2.83149724876*T进行同方差性变换，然后回归实际上就是ZJ/(GDPS(8/3)对GDPS/

48、(GDPS(8/3)和T/(GDPS(8/3)回归，结果如下：Dependent Variable: ZJ/(GDPS(3/8)Method: Least SquaresDate: 06/07/15 Time: 13:50Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.  GDPS/(GDPS(3/8)0.1669950.00256565.100680.0000T/(GDPS(3/8)-4.3536850.881296-4.9400930.0000R

49、-squared0.994224    Mean dependent var27.59529Adjusted R-squared0.994002    S.D. dependent var25.17403S.E. of regression1.949678    Akaike info criterion4.241955Sum squared resid98.83235    Schwarz criterion4.337112Log l

50、ikelihood-57.38737    Hannan-Quinn criter.4.271045Durbin-Watson stat0.668750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: 06/07/15 Time: 13:52Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb

51、.  C0.1619500.00346146.793580.0000T/GDPS-3.7265040.399838-9.3200440.0000R-squared0.769633    Mean dependent var0.135596Adjusted R-squared0.760772    S.D. dependent var0.021590S.E. of regression0.010560    Akaike info criterion-6.1

52、94729Sum squared resid0.002899    Schwarz criterion-6.099572Log likelihood88.72621    Hannan-Quinn criter.-6.165638F-statistic86.86322    Durbin-Watson stat0.439676Prob(F-statistic)0.000000观测其残差趋势图应该不存在异方差了，其方程为ZJ/GDPS=0.161949825215-3.72650431798*T/GDPS变换为原方程ZJ=0.161949825215*-3.72650431798T（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