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：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、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

2、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

3、。 模型【2】中作图取自变量为GDP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 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2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e1i和2e2ie2为较大的残差平方和,e

4、2i为较小的残差平方和。算统计0.05，查 F2:F k,（n C）k）。判断：给定显着性水平e2i22F (n c) (n c)()，则认为模型中 (2 k, 2 k)分布表得临界值F（n c） （n c）（）。如果F（k, k）2 2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obsXY123456789101112131415161718Dependent Variable: YMethod: Least SquaresDate: 06/07/15 Time: 11:18Sample: 1 7Included observations: 7Variabl

5、eCoefficientStd. Errort-StatisticProb.?XCR-squared?Mean dependent varAdjusted R-squared?. dependent var.of regression?Akaike info criterionSum squared resid1757380.?Schwarz criterionLog likelihood?Hannan-Quinn criter.F-statistic?Durbin-Watson statProb(F-statistic)Dependent Variable: YMethod: Least S

6、quaresDate: 06/07/15 Time: 11:20Sample: 12 18Included observations: 7VariableCoefficientStd. Errort-StatisticProb.?XCR-squared?Mean dependent varAdjusted R-squared?. dependent var.of regression?Akaike info criterionSum squared resid?Schwarz criterionLog likelihood?Hannan-Quinn criter.F-statistic?Dur

7、bin-Watson statProb(F-statistic)有上图可知e2,e2i=i757380?F=? e2/ e2i在 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（5,5 ）=，因为F=? （5,5 ）=，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） 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/White/（ 勾选cross terms）。摘录主要结果附在本页内。模型

8、【1】Heteroskedasticity Test: White4.F-statisticObs*R-squaredScaled explained SS40866?Prob. F(2,25)?Prob. Chi-Square(2)?Prob. Chi-Square(2)Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 06/07/15 Time: 12:44Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-St

9、atisticProb.?CCSCSA2R-squaredAdjusted R-squared?Mean dependent var?. dependent var.of regression Sum squared resid Log likelihood F-statisticProb(F-statistic)?Akaike info criterion +08?Schwarz criterion?Hannan-Quinn criter.?Durbin-Watson stat模型【2】Heteroskedasticity Test: WhiteF-statistic?Prob. F(5,2

10、2)Obs*R-squared?Prob. Chi-Square(5)Scaled explained SS?Prob. Chi-Square(5)Test Equation:Dependent Variable: RESIDEMethod: Least SquaresDate: 06/07/15 Time: 12:47Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?CGDPSGDPSA2GDPS*TTTA2R-squared?Mean dependent varAd

11、justed R-squared?. dependent var.of regression?Akaike info criterionSum squared resid+08?Schwarz criterionLog likelihood?Hannan-Quinn criter.F-statistic?Durbin-Watson statProb(F-statistic)模型【3】Heteroskedasticity Test: WhiteF-statistic?Prob.F(2,15)Obs*R-squared?Prob.Chi-Square(2)Scaled explained SS?P

12、rob.Chi-Square(2)Test Equation:Dependent Variable: RESIDEMethod: Least SquaresDate: 06/07/15 Time: 12:51Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.?C1865425.2810916.XXA2R-squared?Mean dependent var1232693.Adjusted R-squared?. dependent var2511199.of regression1

13、879689.?Akaike info criterionSum squared resid+13?Schwarz criterionLog likelihood?Hannan-Quinn criter.F-statistic?Durbin-Watson statProb(F-statistic)（请对得到的图表进行处理，以上在一页内 ）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 CSi、二次项CSi2，开根号项I CSi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Dep

14、endent Variable: E1Method: Least SquaresDate: 06/07/15 Time: 13:17Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?CSCR-squared?Mean dependent varAdjusted R-squared?. dependent var.of regression?Akaike info criterionSum squared resid?Schwarz criterionLog likeli

15、hood?Hannan-Quinn criter.F-statistic?Durbin-Watson statProb(F-statistic)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.?CSR-squaredAdjusted R-squared .of regressionSum squared resi

16、dLog likelihoodDurbin-Watson stat?Mean dependent var ?. dependent var ?Akaike info criterion ?Schwarz criterion ?Hannan-Quinn criter.三、二次项CS2回归Dependent Variable: E1Method: Least SquaresDate: 06/07/15 Time: 13:19Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?

17、CSA2CR-squared?Mean dependent varAdjusted R-squared?. dependent var.of regression?Akaike info criterionSum squared resid?Schwarz criterionLog likelihood?Hannan-Quinn criter.F-statistic?Durbin-Watson statProb(F-statistic)四、开根号项JCST回归Dependent Variable: E1Method: Least SquaresDate: 06/07/15 Time: 13:2

18、4Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?CSA(1/2)R-squared?Mean dependent varAdjusted R-squared?. dependent var.of regression?Akaike info criterionSum squared resid?Schwarz criterionLog likelihood?Hannan-Quinn criter.Durbin-Watson stat五、倒数项1 CSi作回归Depe

19、ndent Variable: E1Method: Least SquaresDate: 06/07/15 Time: 13:26Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?CSA(-1)CR-squared?Mean dependent varAdjusted R-squared?. dependent var.of regression?Akaike info criterionSum squared resid?Schwarz criterionLog li

20、kelihood?Hannan-Quinn criter.F-statistic?Durbin-Watson statProb(F-statistic)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：。2= (* (CS“(1/2) ) 2二也即异方差的形式为：c i 2= a 2CS就把这个形式确定为异方差的形式。对ZJ与GDP侨口 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 T的回归，消费支出

21、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寸CS回归异方差的处理已知CZ寸C泗归异方差的形式为：i22CSi，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: 13:32Sampl

22、e: 1978 2005Included observations: 28Weighting series: 1/(CSA(1/2)VariableCoefficient Std. Error t-StatisticProb.?CSCWeighted StatisticsR-squared Adjusted R-squared .of regressionSum squared resid Log likelihood F-statisticProb(F-statistic)?Mean dependent var ?. dependent var ?Akaike info criterion

23、?Schwarz criterion ?Hannan-Quinn criter. ?Durbin-Watson statUnweighted StatisticsR-squared?Mean dependent varAdjusted R-squared?. dependent var.of regression?Sum squared residDurbin-Watson stat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命令估计的序列resed不能用俩检验

24、，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/2)对1/(CS/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/(CSA(1/2)CS/(CS(/2)?Mea

25、n dependent var ?. dependent var ?Akaike info criterion ?Schwarz criterion ?Hannan-Quinn criter.R-squared Adjusted R-squared .of regressionSum squared resid Log likelihoodDurbin-Watson stat观察其残差趋势图还是存在异方差，再改为CZ/CS寸1/CS和回归，如果如下Dependent Variable: CZ/CSMethod: Least SquaresDate: 06/07/15 Time: 13:42Sa

26、mple: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?1/CSCR-squared?Mean dependent varAdjusted R-squared?. dependent var.of regression?Akaike info criterionSum squared resid?Schwarz criterionLog likelihood?Hannan-Quinn criter.F-statistic?Durbin-Watson statProb(F-stat

27、istic)观察其残差趋势图(请对得到的图表进行处理，以上在两页内)2. 模型【2】中ZJ对GDP和T回归异方差的处理3已知ZJ对GDP和T回归异方差的形式为：i22 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: 1978 2005Included observations: 28Weighting series: 1/(GDPSA

28、(3/8)VariableCoefficientStd. Errort-StatisticProb.?GDPSTWeighted StatisticsR-squaredAdjusted R-squared .of regression Sum squared resid Log likelihood?Mean dependent var ?. dependent var ?Akaike info criterion ?Schwarz criterion ?Hannan-Quinn criter.Durbin-Watson statUnweighted StatisticsR-squaredAd

29、justed R-squared.of regression?Mean dependent var?. dependent var?Sum squared residDurbin-Watson stat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/(GDPS(8/3)禾口 T/(GDPS(8/3)回归，结果如下:Dependent Variable: ZJ/(GDPSA(3/8)Method: Least SquaresDate: 06/07/15 Time: 13:50Sample: 1978 2005VariableCo

30、efficientStd. Errort-StatisticProb.?GDPS/(GDPSA(3/8)T/(GDPSA(3/8)R-squaredAdjusted R-squared .of regressionSum squared residLog likelihood?Mean dependent var ?. dependent var ?Akaike info criterion ?Schwarz criterion ?Hannan-Quinn criter.Durbin-Watson stat观测其残差趋势图 可能还存在异方差,再改为 ZJ/GDP对C和T/GDP回归，Inclu

31、ded observations: 28结果如下:Dependent Variable: ZJ/GDPSMethod: Least SquaresDate: 06/07/15 Time: 13:52Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?CT/GDPSR-squared?Mean dependent varAdjusted R-squared?. dependent var?Akaike info criterion.of regressionSum squa

32、red resid?Schwarz criterionLog likelihood?Hannan-Quinn criter.F-statistic?Durbin-Watson statProb(F-statistic)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2 2 4已知Y对X回归异方差的形式为：i 2 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。Dependent Vari

33、able: YMethod: Least SquaresDate: 06/07/15 Time: 13:56Sample: 1 18Included observations: 18Weighting series: 1/XA(2/3)VariableCoefficient Std. Error t-StatisticProb.?XWeighted StatisticsR-squared?Mean dependent varAdjusted R-squared?. dependent var.of regression?Akaike info criterionSum squared resi

34、dLog likelihood?Schwarz criterion?Hannan-Quinn criter.Unweighted StatisticsR-squaredAdjusted R-squared.of regressionDurbin-Watson stat?Mean dependent var?. dependent var?Sum squared resid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)归，结果如下：Dependent Variable: Y/(XA(2/3)Method: Least SquaresDate: 06/

35、07/15 Time: 13:59Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.?1/(XA(2/3)X/(XA(2/3)R-squared?Mean dependent varAdjusted R-squared?. dependent var.of regression?Akaike info criterionSum squared resid?Schwarz criterionLog likelihood?Hannan-Quinn criter.Durbin-Watson statDurbin-Watson stat和 X/(X(2/3)回观测其残差趋势图虽然不能够准确判断，但大致还是