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：综合性口设计性口 验证性专业班别： 123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、实验项目训练方案小组合作：是否小组成员：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

2、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勺回归模型；（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GDP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方对自变量的散点图。 模型【2

3、】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？尝试做岀来。（请对得到的图表进行处理，以上在一页内 ）2. Goldfeld-Qua nadt检验法用Goldfeld-Quanadt检验法检验模型【31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 2e2i

4、2 2计量L Je2iF（冒k.(n -c) _k)。判断：给定显着性水平:二0.05，查F分布表得临2C ）。如果F Fk）界值 F(n_c)k (n _c)2 ， 2(详见课本135页)将实验中重要的结果摘录下来,(nr) (nq C )，则认为模型中的随机误差存在异方差。( k, k)2 2附在本页。、 $为较大的残差平方和， a e2i为较小的残差平方和。算统obsXY17021.9427220.446317.0337299.256463.3746350.3858842.846757.0269214.67294.9379867.367669.84810097.27476.6591090

5、8.368113.641011944.088296.43111229.179505.661215762.7712651.951317680.114485.611418287.2414468.241518907.7314323.661621015.0318550.561722881.821767.781828665.2521188.84Dependent Variable: YMethod: Least SquaresDate: 06/07/15 Time: 11:18Sample: 1 7Included observations: 7VariableCoefficientStd. Error

6、t-StatisticProb.?X0.7230770.2183863.3110030.0212C536.88741814.2540.2959270.7792R-squared0.686771?Mean dependent var6497.894Adjusted R-squared0.624125?S.D. dependent var966.9988S.E. of regression592.8541?Akaike info criterion15.84273Sum squared resid1757380.?Schwarz criterion15.82728Log likelihood-53

7、.44956?Hannan-Quinn criter.15.65172F-statistic10.96274?Durbin-Watson stat1.761325Prob(F-statistic)0.021217Dependent Variable: YMethod: Least SquaresDate: 06/07/15Time:11:20Sample: 12 18Included observations: 7VariableCoefficientStd. Errort-StatisticProb.?X0.7592910.1778984.2681250.0080C1243.7433707.

8、2380.3354900.7509R-squared0.784640?Mean dependent var16776.66Adjusted R-squared0.741567?S.D. dependent var3677.261S.E. of regression1869.382?Akaike info criterion18.13956Sum squared resid?Schwarz criterion18.12411Log likelihood-61.48846?Hannan-Quinn criter.17.94855F-statistic18.21689?Durbin-Watson s

9、tat2.037081Prob(F-statistic)0.007953有上图可知迟 e2，迟 e2 =1757380?F=?Se2 任 efi 在 a =0.05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=?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 Tests/Wh

10、ite/勾选cross terms).摘录主要结果附在本页内。模型【1】Heteroskedasticity Test: WhiteF-statistic440866?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:Dependent Variable: RESIDA2Method: Least SquaresDate: 06/07/15Time:12:44Sample: 197

11、8 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?C-879.85131125.376-0.7818290.4417CS12.937204.6513282.7813980.0101CSA2-0.0066200.002964-2.2335610.0347R-squared0.283292?Mean dependent var1940.891Adjusted R-squared0.225956?S.D. dependent var4080.739S.E. of regression3590.22

12、5?Akaike info criterion19.31077Sum squared resid3.22E+08?Schwarz criterion19.45351Log likelihood-267.3508?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

13、?Prob. Chi-Square(5)0.1204Scaled explained SS14.67857?Prob. Chi-Square(5)0.0118Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 06/07/15Time: 12:47Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?C1837.8986243.7010.2943600.7712GDPS-3.3950935.

14、407361-0.6278650.5366GDPSA2-9.08E-050.000185-0.4895370.6293GDPS*T0.1603000.3151760.5086040.6161T-491.56141982.891-0.2479010.8065TA249.08543152.98750.3208460.7514R-squared0.311766?Mean dependent var3461.910Adjusted R-squared0.155349?S.D. dependent var7240.935S.E. of regression6654.775?Akaike info cri

15、terion20.63147Sum squared resid9.74E+08?Schwarz criterion20.91694Log likelihood-282.8405?Hannan-Quinn criter.20.71874F-statistic1.993171?Durbin-Watson stat1.971537Prob(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

16、)0.0106Scaled explained SS14.09286?Prob.Chi-Square(2)0.0009Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 06/07/15 Time: 12:51Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.?C1865425.2810916.0.6636360.5170X-354.7917388.1454-0.9140690.3751XA20.0

17、188100.0116861.6095970.1283R-squared0.505630?Mean dependent 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-Quinn criter.31.90258F-statistic7.6708

18、26?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【11是否存在异方差。分别用残差的绝对值对自变量的一次项cSi、二次项CSi2，开根号项和倒数项1 CSi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CSi回归Dependent Variable: E1Method: Least SquaresDate: 06/07/15 Time: 13:17Sample: 1978 2005Included obs

19、ervations: 28VariableCoefficientStd. Errort-StatisticProb.?CS0.0292360.0122792.3809470.0249C14.159918.2594921.7143800.0984R-squared0.179006?Mean dependent var27.30288Adjusted R-squared0.147429?S.D. dependent var35.20964S.E. of regression32.51074?Akaike info criterion9.869767Sum squared resid27480.66

20、?Schwarz criterion9.964925Log likelihood-136.1767?Hannan-Quinn criter.9.898858F-statistic5.668911?Durbin-Watson stat1.339465Prob(F-statistic)0.024881二、去掉常数项再回归？Dependent Variable: E1Method: Least SquaresDate: 06/07/15Time: 13:22Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort

21、-StatisticProb.?CS0.0433040.0094564.5794730.0001R-squared0.086198?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?Hannan-Quinn criter.9.91

22、9981Durbin-Watson stat1.209310三、二次项cs2回归Dependent Variable: E1Method: Least SquaresDate: 06/07/15Time: 13:19Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?CSA21.11E-058.36E-061.3222070.1976C22.302367.5752862.9440940.0067R-squared0.063003?Mean dependent var27.

23、30288Adjusted R-squared0.026965?S.D. dependent var35.20964S.E. of regression34.73168?Akaike info criterion10.00193Sum squared resid31363.53?Schwarz criterion10.09709Log likelihood-138.0270?Hannan-Quinn criter.10.03102F-statistic1.748231?Durbin-Watson stat1.203183Prob(F-statistic)0.197614四、开根号项jCST回归

24、Dependent Variable: E1Method: Least SquaresDate: 06/07/15Time: 13:24Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?CSA(1/2)1.5372330.2690365.7138480.0000R-squared0.265081?Mean dependent var27.30288Adjusted R-squared0.265081?S.D. dependent var35.20964S.E. of r

25、egression30.18432?Akaike info criterion9.687583Sum squared resid24599.52?Schwarz criterion9.735162Log likelihood-134.6262?Hannan-Quinn criter.9.702128Durbin-Watson stat1.471849五、倒数项1/CSi作回归Dependent Variable: E1Method: Least SquaresDate: 06/07/15Time:13:26Sample: 1978 2005Included observations: 28Va

26、riableCoefficientStd. Errort-StatisticProb.?CSA(-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?Akaike info criterion9.710009Sum squared resid23423.14?Schwarz

27、 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，第二个不显着，其他三个显着，比较这三个回归，还是选择第三个，方程为即异方差的形式为：a2=( 1.537233*(CSA(1 /2) ) 2=2.36085CS也即异方差的形式为：ai 2= a 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

28、费支岀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，消费支岀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：G2 =2CSi，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

29、主要结果附在本页内。Dependent Variable: CZMethod: Least SquaresDate: 06/07/15 Time: 13:32Sample: 1978 2005Included observations: 28Weighting series: 1/(CSA(1/2)VariableCoefficientStd. Errort-StatisticProb.?CS1.2756770.01940665.736280.0000C-21.243654.264097-4.9819800.0000Weighted StatisticsR-squared0.994019 ?M

30、ean dependent var254.4606Adjusted R-squared0.993789 ?S.D. dependent var189.1988S.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 stat1.550317Prob(F-stati

31、stic)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回归方程为它与存在异方差的如下方程估计有所不同。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

32、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/(CSA(1/2)对1/(CSA(1/2)和CS/(CSA(1/2)回归，结果如下：Dependent Variable: CZ/(CSA(1/2)Method: Least SquaresDate: 06/07/15 Time: 13:39Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?1/

33、(CSA(1/2)-21.243654.264097-4.9819800.0000CS/(CSA(1/2)1.2756770.01940665.736280.0000R-squared0.985934?Mean dependent var21.13688Adjusted R-squared0.985393?S.D. dependent var15.71588S.E. of regression1.899444?Akaike info criterion4.189748Sum squared resid93.80503?Schwarz criterion4.284906Log likelihoo

34、d-56.65647?Hannan-Quinn criter.4.218839Durbin-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-19.828602.064540-9.6043680.0000C

35、1.2625010.02721846.384560.0000R-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-1.564510Log likelihood25.23534?Hannan-Quinn criter.-1.630577F-statistic9

36、2.24388?Durbin-Watson stat1.613436Prob(F-statistic)0.000000观察其残差趋势图(请对得至U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23已知ZJ对GDPS和T回归异方差的形式为：G2 =匚2 GDPSi 4，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:

37、 1978 2005Included observations: 28Weighting series: 1/(GDPSA(3/8)VariableCoefficientStd. Errort-StatisticProb.?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.

38、of regression29.59878?Akaike info 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-squared0.996146 ?S.D. dependent var1014.824

39、S.E. of regression63.00261 ?Sum squared resid103202.6Durbin-Watson stat0.754208它与存在异方差时的如下方程估计也有所不同。进行同方差性变换，然后回归实际上就是ZJ/(GDPSA(8/3) 对GDPS/(GDPSA(8/3)和T/(GDPSA(8/3)回归，结果如下：Dependent Variable: ZJ/(GDPSA(3/8)Method: Least SquaresDate: 06/07/15Time: 13:50Sample: 1978 2005Included observations: 28Variab

40、leCoefficientStd. Errort-StatisticProb.?GDPS/(GDPSA(3/8)0.1669950.00256565.100680.0000T/(GDPSA(3/8)-4.3536850.881296-4.9400930.0000R-squared0.994224?Mean dependent var27.59529Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat0.9940021.94967898.83235-57.387370.6

41、68750?S.D. dependent var ?Akaike info criterion ?Schwarz criterion ?Hannan-Quinn criter.25.174034.2419554.3371124.271045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: 28VariableCoefficientS

42、td. Errort-StatisticProb.?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-6.194729Sum squared resid0.002899?Schwarz criterion-6.09957

43、2Log 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，其方程为变换为原方程(请对得至U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4已知丫对X回归异方差的形式为：-ic2 Xi 3，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

44、。Dependent Variable: YMethod: Least SquaresDate: 06/07/15 Time: 13:56Sample: 1 18Included observations: 18Weighting series: 1/XA(2/3)VariableCoefficient Std. Error t-Statistic Prob.?X0.7951570.01725246.090120.0000Weighted StatisticsR-squared0.954867 ?Mean dependent var9599.510Adjusted R-squared0.954

45、867 ?S.D. dependent var1867.615S.E. of regression895.7229 ?Akaike info criterion16.48709Sum squared resid?Schwarz criterion16.53656Log likelihood-147.3838 ?Hannan-Quinn criter.16.49391Durbin-Watson stat1.472431Unweighted StatisticsR-squared0.952547 ?Mean dependent var10906.35Adjusted R-squared0.9525

46、47 ?S.D. dependent var5381.587S.E. of regression1172.315 ?Sum squared residDurbin-Watson stat1.419465它与存在异方差时如下方程估计明显不同进行同方差性变换，然后回归实际上就是Y/(XA(2/3) 和X/(XA(2/3)回归，结果如下:Dependent Variable: Y/(XA(2/3)Method: Least SquaresDate: 06/07/15 Time: 13:59Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.?1/(XA(2/3)-495.5562520.4173-0.9522280.3551X/(XA(2/3)0.8337080.04402618.936730.0000R-squared0.782313?Mean dependent var18.56257Adjusted R-squared0.768707?S.D. depe