实验五异方差模型检验.docx

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

2、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

3、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2,4002,0001,600Z 1,200C800400005001,0001,5002,000CS残差散点图20,00016,00012,0001E8,0004,000005001,0001,5002,000CS模型【 2】相关分析图4,0003,5003,0002,500JZ2,0001,5001,000500005,00010,00015,00020,00025,000GDPS残差散点图30,00025,00020,0002E15,00010,0005,000005,00010,00015

4、,00020,00025,000GDPS模型【 3】相关分析图24,00020,00016,000Y12,0008,0004,0005,00010,00015,00020,00025,00030,000X残差散点图12,000,00010,000,0008,000,0003 6,000,000E4,000,0002,000,00005,00010,00015,00020,00025,00030,000X【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

5、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e2e1i2 为较大 的残差平方和，e2i2两个部分的残差平方为1i 和 e2i2 。为较小 的残差平方和。算统计量*e12i F (n c)( n c)k) 。判断： 给定显著性水平0.05 ，查 FF2k,2e2i2分布表得临界值F ( n c)( n c)( )。如果 F*F (n c)(n c)( ) ，则认为模型中的随机误差

6、(k,k )(k,k )2222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。obsXY17021.944632.68999999999927220.446317.0337299.256463.3748241.2099999999996350.3858842.846757.0269214.67294.9379867.367669.84810097.27476.65910908.368113.641011944.088296.43111229.179505.661215762.7712651.951317680.114485.611418287.2414468.24

7、1518907.7314323.661621015.0318550.561722881.821767.781828665.2521188.84Dependent Variable: YMethod: Least SquaresDate: 06/07/15Time: 11:18Sample: 1 7Included observations: 7VariableCoefficientStd. Errort-StatisticProb.X0.7230770.2183863.3110030.0212C536.88741814.2540.2959270.7792R-squared0.686771Mea

8、n dependent var6497.894Adjusted R-squared0.624125S.D. dependent var966.9988S.E. of regression592.8541Akaike info criterion15.84273Sum squared resid1757380.Schwarz criterion15.82728Log likelihood-53.44956Hannan-Quinn criter.15.65172F-statistic10.96274Durbin-Watson stat1.761325Prob(F-statistic)0.02121

9、7Dependent Variable: YMethod: Least SquaresDate: 06/07/15Time: 11:20Sample: 12 18Included observations: 7VariableCoefficientStd. Errort-StatisticProb.X0.7592910.1778984.2681250.0080C1243.7433707.2380.3354900.7509R-squared0.784640Mean dependent var16776.66Adjusted R-squared0.741567S.D. dependent var3

10、677.261S.E. of regression1869.382Akaike info criterion18.13956Sum squared resid17472943Schwarz criterion18.12411Log likelihood-61.48846Hannan-Quinn criter.17.94855F-statistic18.21689Durbin-Watson stat2.037081Prob(F-statistic)0.007953有上图可知e1i2=17472943，e2i2=1757380 F=e1i2/e2i2=17472943/1757380=9.9426

11、0945.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 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 Tests/White/(勾选cross terms)。摘录主要结果附在本页内。模型【 1】Heteroskedasticity

12、 Test: White4.F-statistic40866Prob. F(2,25)0.0156Obs*R-squared7.932189Prob. Chi-Square(2)0.0189Scaled explained SS14.57723Prob. Chi-Square(2)0.0007Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/07/15Time: 12:44Sample: 1978 2005Included observations: 28VariableCoefficientStd. E

13、rrort-StatisticProb.C-879.85131125.376-0.7818290.4417CS12.937204.6513282.7813980.0101CS2-0.0066200.002964-2.2335610.0347R-squared0.283292Mean dependent var1940.891Adjusted R-squared0.225956S.D. dependent var4080.739S.E. of regression3590.225Akaike info criterion19.31077Sum squared resid3.22E+08Schwa

14、rz criterion19.45351Log likelihood-267.3508Hannan-Quinn criter.19.35441F-statistic4.940866Durbin-Watson stat2.144291Prob(F-statistic)0.015552模型【 2】Heteroskedasticity Test: WhiteF-statistic1.993171Prob. F(5,22)0.1195Obs*R-squared8.729438Prob. Chi-Square(5)0.1204Scaled explained SS14.67857Prob. Chi-Sq

15、uare(5)0.0118Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/07/15Time: 12:47Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.C1837.8986243.7010.2943600.7712GDPS-3.3950935.407361-0.6278650.5366GDPS2-9.08E-050.000185-0.4895370.6293GDPS*T0.16

16、03000.3151760.5086040.6161T-491.56141982.891-0.2479010.8065T249.08543152.98750.3208460.7514R-squared0.311766Mean dependent var3461.910Adjusted R-squared0.155349S.D. dependent var7240.935S.E. of regression6654.775Akaike info criterion20.63147Sum squared resid9.74E+08Schwarz criterion20.91694Log likel

17、ihood-282.8405Hannan-Quinn criter.20.71874F-statistic1.993171Durbin-Watson stat1.971537Prob(F-statistic)0.119510模型【 3】Heteroskedasticity Test: WhiteF-statistic7.670826Prob. F(2,15)0.0051Obs*R-squared9.101341Prob. Chi-Square(2)0.0106Scaled explained SS14.09286Prob. Chi-Square(2)0.0009Test Equation:De

18、pendent Variable: RESID2Method: Least SquaresDate: 06/07/15Time: 12:51Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.C1865425.2810916.0.6636360.5170X-354.7917388.1454-0.9140690.3751X20.0188100.0116861.6095970.1283R-squared0.505630Mean dependent var1232693.Adjusted

19、R-squared0.439714S.D. dependent var2511199.S.E. of regression1879689.Akaike info criterion31.88212Sum squared resid5.30E+13Schwarz criterion32.03052Log likelihood-283.9391Hannan-Quinn criter.31.90258F-statistic7.670826Durbin-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

20、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 CSi 2 ，开根号项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Dependent Variable: E1Method: Least SquaresDate: 06/07/15Time: 13:17Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.CS0.0292360.0

21、122792.3809470.0249C14.159918.2594921.7143800.0984R-squared0.179006Mean dependent var27.30288Adjusted R-squared0.147429S.D. dependent var35.20964S.E. of regression32.51074Akaike info criterion9.869767Sum squared resid27480.66Schwarz criterion9.964925Log likelihood-136.1767Hannan-Quinn criter.9.89885

22、8F-statistic5.668911Durbin-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-StatisticProb.CS0.0433040.0094564.5794730.0001R-squared0.086198Mean dependent

23、var27.30288Adjusted R-squared0.086198S.D. dependent var35.20964S.E. of regression33.65794Akaike info criterion9.905436Sum squared resid30587.14Schwarz criterion9.953015Log likelihood-137.6761Hannan-Quinn criter.9.919981Durbin-Watson stat1.209310三、二次项 CSi 2 回归Dependent Variable: E1Method: Least Squar

24、esDate: 06/07/15Time: 13:19Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.CS21.11E-058.36E-061.3222070.1976C22.302367.5752862.9440940.0067R-squared0.063003Mean dependent var27.30288Adjusted R-squared0.026965S.D. dependent var35.20964S.E. of regression34.73168A

25、kaike info criterion10.00193Sum squared resid31363.53Schwarz criterion10.09709Log likelihood-138.0270Hannan-Quinn criter.10.03102F-statistic1.748231Durbin-Watson stat1.203183Prob(F-statistic)0.197614四、开根号项CSi 回归Dependent Variable: E1Method: Least SquaresDate: 06/07/15Time: 13:24Sample: 1978 2005Incl

26、uded observations: 28VariableCoefficientStd. Errort-StatisticProb.CS(1/2)1.5372330.2690365.7138480.0000R-squared0.265081Mean dependent var27.30288Adjusted R-squared0.265081S.D. dependent var35.20964S.E. of regression30.18432Akaike info criterion9.687583Sum squared resid24599.52Schwarz criterion9.735

27、162Log likelihood-134.6262Hannan-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: 28VariableCoefficientStd. Errort-StatisticProb.CS(-1)-2029.779607.7392-3.3398840.0025C46.202298.0

28、122115.7664840.0000R-squared0.300226Mean dependent var27.30288Adjusted R-squared0.273311S.D. dependent var35.20964S.E. of regression30.01483Akaike info criterion9.710009Sum squared resid23423.14Schwarz criterion9.805167Log likelihood-133.9401Hannan-Quinn criter.9.739100F-statistic11.15483Durbin-Wats

29、on stat1.566457Prob(F-statistic)0.002542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)=1.53723330222*CS(1/2)即异方差的形式为：2=（ 1.537233* （ CS(1/2) ） 2=2.36085CSi也即异方差的形式为：i 2= 2CSi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，

30、 ZJ 对 GDPS和归，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。T 的回（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：法处理异方差。2 2i CSi ，选取权数，使用加权最小二乘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 SquaresD

31、ate: 06/07/15Time: 13:32Sample: 1978 2005Included observations: 28Weighting series: 1/(CS(1/2)VariableCoefficientStd. Errort-StatisticProb.CS1.2756770.01940665.736280.0000C-21.243654.264097-4.9819800.0000Weighted StatisticsR-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihoodF

32、-statisticProb(F-statistic)R-squaredAdjusted R-squaredS.E. of regressionDurbin-Watson stat0.994019Mean dependent var254.46060.993789S.D. dependent var189.198822.86683Akaike info criterion9.16600113595.19Schwarz criterion9.261159-126.3240Hannan-Quinn criter.9.1950924321.259Durbin-Watson stat1.5503170

33、.000000Unweighted Statistics0.995276Mean dependent var552.24290.995095S.D. dependent var653.188145.74872Sum squared resid54416.571.545575回归方程为CZ=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

34、 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: 06/07/15Time: 13:39Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.1/(CS(1/2

35、)-21.243654.264097-4.9819800.0000CS/(CS(1/2)1.2756770.01940665.736280.0000R-squared0.985934Mean dependent var21.13688Adjusted R-squared0.985393S.D. dependent var15.71588S.E. of regression1.899444Akaike info criterion4.189748Sum squared resid93.80503Schwarz criterion4.284906Log likelihood-56.65647Han

36、nan-Quinn criter.4.218839Durbin-Watson stat1.550317观察其残差趋势图6050403042021000-2-4-6198019851990199520002005ResidualActualFitted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: 06/07/15Time: 13:42Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-

37、StatisticProb.1/CS-19.828602.064540-9.6043680.0000C1.2625010.02721846.384560.0000R-squared0.780115Mean dependent var1.077876Adjusted R-squared0.771658S.D. dependent var0.213378S.E. of regression0.101963Akaike info criterion-1.659667Sum squared resid0.270307Schwarz criterion-1.564510Log likelihood25.

38、23534Hannan-Quinn criter.-1.630577F-statistic92.24388Durbin-Watson stat1.613436Prob(F-statistic)0.0000001.61.41.2.31.0.20.8.10.6.0-.1-.2-.3198019851990199520002005ResidualActualFitted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

39、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：权最小二乘法处理异方差。232 GDPS i 4，选取权数，使用加i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: 06/07/15Time: 13:46Sample: 1978 2005Included observations: 28Weighting series: 1/(GDPS(3/8)VariableCoefficient

40、Std. Errort-StatisticProb.GDPS0.1669950.00256565.100680.0000T-4.3536850.881296-4.9400930.0000Weighted StatisticsR-squared0.997009Mean dependent var418.9342Adjusted R-squared0.996894S.D. dependent var382.1762S.E. of regression29.59878Akaike info criterion9.682092Sum squared resid22778.28Schwarz crite

41、rion9.777250Log likelihood-133.5493Hannan-Quinn criter.9.711183Durbin-Watson stat0.668750Unweighted StatisticsR-squared0.996289Mean dependent var846.0661Adjusted R-squared0.996146S.D. dependent var1014.824S.E. of regression63.00261Sum squared resid103202.6Durbin-Watson stat0.754208回归方程为ZJ=0.16699477

42、5675*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/(GDPS(8/3) 和T/(GDPS(8/3) 回归，结果如下：Dependent Variable: ZJ/(GDPS(3/8)Method: Least SquaresDate: 06/07/15Time: 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-squared0.994224Mean dependent var27.59529Adjusted R-squared0.994002S.D. dependent var25.17403S.E. of regression1.949678Akaike info criterion4.241955Sum squar