实验五异方差模型的检验

1、实验五异方差模型的检验HUASHANG COLLEGEGUANGDONG UNIVERSITV OF FINANCE & ECONOMICS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一、头验项目训练方案小组合作：是j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

2、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

3、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】中作图取自变量为GDPS来作图。模型【1】相关分析图2,4002,0001,600C 1,2008004005001,0001,5002,000CS残差散点图20,000 -16,00012,000 1E8,000 -4,000 -. 0 M11105001,0001,5002,000CS模型【2】相关分析图4,0003,500 _3,000 _2,500 _Z 2,000 ,*»1,500 _»1,000 _V500*0C5,00010,0

4、0015,00020,00025,000GDPS残差散点图GDPS模型【3】相关分析图24,00020,000 .« *16,000 .Y12,000 .甲8,000 -VV 八 n'4,000 _5,00010,00015,00020,00025,00030,000X残差散点图12,000,00010,000,000 -8,000,000 -E 6,000,000 -4,000,000-2,000,000 -*t* *W”I-|30,0005,00010,00015,00020,00025,000【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，

5、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2eii和e2i。e2为较大的残差平方和，e2i为较小的残差平方和。算统计量F*二F(g k,2 k)。判断：给定显著性水平0.05，e2i227查F分布表得临界值S 4 k)()。如果F* F(n c) k

6、 (n c) k)()，则认为模型(2 1 2 ) ( 2 , 2 )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。obsXY1 7021.94 4632.6899999999992 7220.446317.033 7299.256463.374 8241.2099999999996350.385 8842.846757.026 9214.67294.937 9867.367669.848 10097.27476.659 10908.368113.6410 11944.088296.4311 19505.66229.171215762.7712651.951

7、317680.114485.611418287.2414468.241518907.7314323.661621015.0318550.561722881.821767.781828665.2521188.84YMethod: Least SquaDate: 06/07/15iresTime:11:18Sample: 1 7Included observations: 7VariableCoefficientStd. Errort-StatisticProb.X0.7230770.2183863.3110030.0212C536.88741814.2540.2959270.7792R-squa

8、red0.686771Mean 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-sta

9、tistic)0.021217Dependent 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. d

10、ependent var3677.261S.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e； =17472943,<=1757380 F=e1 /efi =17472943/175

11、7380=9.94260945在0.05下，上式中分(5,5) =5.05,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】Heterosk

12、edasticity Test: White4.F-statistic40866Obs*R-squared7.932189Prob. F(2,25)Prob. Chi-Square(2)0.01560.0189Scaled explained SS14.57723Prob. Chi-Square(2)0.0007Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 06/07/15Time: 12:44Sample: 1978 2005Included observations: 28VariableCoeffi

13、cientStd. Errort-StatisticProb.-879.85131125.376-0.7818290.4417CS12.937204.6513282.7813980.0101CSA2-0.0066200.002964-2.2335610.0347R-squared0.283292Mean dependent var1940.891Adjusted R-squared10.225956S.D. dependent var4080.739S.E. of regression3590.225Akaike info criterion19.31077Sum squared residL

14、og likelihood3.22E+08Schwarz criterionHannan-Quinn criter.19.45351-267.350819.35441F-statisticProb(F-statistic)4.9408660.015552Durbin-Watson stat2.144291模型【2】Heteroskedasticity Test: White1.993171Prob. F(5,22)8.729438Prob. Chi-Square(5)14.67857Prob. Chi-Square(5)0.11950.12040.0118F-statisticObs*R-sq

15、uaredScaled explained SSTest Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 06/07/15Time:12:47Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.C1837.8986243.7010.2943600.7712GDPS-3.3950935.407361-0.6278650.5366GDPSA2-9.08E-050.000185-0.4895370.62

16、93GDPS*T0.1603000.3151760.5086040.6161T-491.56141982.891-0.2479010.8065TA249.08543152.98750.3208460.7514R-squared0.311766Mean dependent var3461.910Adjusted R-squared0.155349S.D. dependent var7240.935S.E. of regression6654.775Akaike info criterion20.63147Sum squared resid9.74E+08Schwarz criterion20.9

17、1694Log likelihood-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

18、 Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 06/07/15Time: 12:51Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.C1865425.2810916.0.6636360.5170X-354.7917388.1454-0.9140690.3751XA20.0188100.0116861.6095970.1283R-squared0.505630Mean dependent var123

19、2693.Adjusted R-squared10.439714S.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

20、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。作回归。检验分别用残差的绝对值对自变量的一次项CSi、二次项CS2，开根号项（西和倒数项1/CSi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。、一次项CSi回归Method: Least SquaDate: 06/07/15Sample: 1978 2005 Included observatioiresTime: 13:17ns: 28VariableCoefficientStd. Errort-StatisticProb.CS0.0292360.0122792.3809470.024

21、9C14.159918.2594921.7143800.0984R-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.9.898858F-statistic5.6689

22、11Durbin-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 Mean dependent var27.30288Adjus

23、ted 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CS2回归Dependent Variable: E1Method: Least SquaresDate: 06/07/15Time

24、: 13:19Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.CSA21.11E-058.36E-061.3222070.1976C22.302367.5752862.9440940.0067R-squared0.063003Mean dependent var27.30288Adjusted R-squared0.026965S.D. dependent var35.20964S.E. of regression34.73168Akaike info criterio

25、n10.00193Sum squared resid31363.53Schwarz criterion10.09709Log likelihood-138.0270Hannan-Quinn criter.10.03102F-statistic1.748231Durbin-Watson stat1.203183Prob(F-statistic)0.197614四、开根号项届回归Dependent Variable: E1Method: Least SquaresDate: 06/07/15 Time: 13:24Sample: 1978 2005Included observations: 28

26、VariableCoefficientStd. Errort-StatisticProb.CSA(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 criterion9.735162Log likelihood-13

27、4.6262Hannan-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.CSA(-1)-2029.779607.7392-3.3398840.0025C46.202298.0122115.7664840.0000R-s

28、quared0.300226Mean 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-Watson stat1.566457Prob(F-

29、statistic)0.002542从四个回归的结果看冷第二个不显著，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*CSA(1/2)即异方差的形式为：a 2(1.537233* (CSA(1/2)2=2.36085CSi也即异方差的形式为:a2= a 2CS就把这个形式确定为异方差的形式。对ZJ与GDPS 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，发现根据广东数扌居CZ对CS的回归，ZJ对GDPS T的回归，消费支出与可支配收'入回归

30、都存在异方差，现在分别对它们进行处理。加权最小二乘法成为处理异方差模型的标准方法，再 Eviews中使用WL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经S来消除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。已知CZ对CS回归异方差的形式为:附在本页内。Dependent Variable: CZMethod: Least SquaresDate: 06/07/15Time: 13:32摘录主要结果Sample: 1978 2005

31、Included observations: 28Weighting series: 1/(CSA(1/2)VariableCoefficientStd. Errort-StatisticProb.CS1.2756770.01940665.736280.0000-21.243654.264097-4.9819800.0000Weighted StatisticsR-squared0.994019 Mean dependent var254.4606Adjusted R-squared0.993789 S.D. dependent var189.1988S.E. of regression22.

32、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-statistic)0.000000Unweighted StatisticsR-squaredAdjusted R-squaredS.E. of regressionDurbin-Watson stat0.99527

33、6 Mean dependent var0.995095S.D. dependent var45.74872Sum squared resid1.545575552.2429653.188154416.57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 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 是非加权方式的残差。要想检验只能自己进

34、行同方差变换， 回归以后再检验了样可resid然后进行同方差行变换，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: 28VariableCoefficient Std. Error t-StatisticProb.1/(CSA(1/2)-21.243654.264097-4.9819800.0000

35、CS/(CSA(1/2)1.2756770.01940665.736280.0000R-squared0.985934Adjusted R-squared0.985393S.E. of regression1.899444Sum squared resid93.80503Log likelihood-56.65647Mean dependent var21.13688S.D. dependent var15.71588Akaike info criterion4.189748Schwarz criterion4.284906Hannan-Quinn criter.4.218839Durbin-

36、Watson stat1.550317观察其残差趋势图Residual Actual Fitted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-19.828602.064540-9.6043680.0000C1.2625010.02721846.384560.

37、0000R-squared0.780115Mean dependent var1.077876Adjusted R-squared10.771658S.D. dependent var0.213378S.E. of regression0.101963Akaike info criterion-1.659667Sum squared resid0.270307Schwarz criterion-1.564510-1.630577Log likelihood25.23534Hannan-Quinncriter.F-statistic92.24388Durbin-Watsonstat1.61343

38、6Prob(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模型【2】中ZJ对GDPS和T回归异方差的处理3乘法处理异摘录主要结果已知ZJ对GDPS和T回归异方差的形式为：i22 GDPSi 4，选取权数，使用加权最小方差。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。 附在本页内。Dependent Variable:

39、ZJMethod: Least SquaresDate: 06/07/15 Time: 13:46Sample: 1978 2005Included observations: 28Weighting series: 1/(GDPSA(3/8)VariableCoefficient Std. Error t-StatisticProb.GDPS0.1669950.00256565.100680.0000T-4.3536850.881296-4.9400930.0000Weighted StatisticsR-squared0.997009Mean dependent var418.9342Ad

40、justed R-squared10.996894S.D. dependent var382.1762S.E. of regression29.59878Akaike info criterion9.682092Sum squared resid22778.28Schwarz criterion9.777250Log likelihood-133.5493Hannan-Quinn criter.9.711183Durbin-Watson stat0.668750Unweighted StatisticsR-squared0.996289Mean dependent var846.0661Adj

41、usted R-squared10.996146S.D. dependent var1014.824S.E. of regression63.00261Sum squared resid103202.6Durbin-Watson stat0.754208回归方程为 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: 06/07/15 Time

42、: 13:50Sample: 1978 2005Included observations: 28VariableGDPS/(GDPSA(3/8)T/(GDPSA(3/8)Coefficient Std. Error t-StatisticProb.0.1669950.00256565.100680.0000R-squaredAdjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat0.994224Mean dependent var27.595290.994002S.D.

43、dependent var25.174031.949678Akaike info criterion4.24195598.83235Schwarz criterion4.337112-57.38737Hannan-Quinn criter.4.2710450.668750-4.3536850.881296-4.9400930.0000观测其残差趋势图Residual Actual Fitted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 SquaDate: 06/07/15Sample

44、: 1978 2005 Included observatioiresTime: 13:52ns: 28VariableCoefficientStd. Errort-StatisticProb.C0.1619500.00346146.793580.0000T/GDPS-3.7265040.399838-9.3200440.0000R-squared0.769633Mean dependent var0.135596Adjusted R-squared0.760772S.D. dependent var0.021590S.E. of regression0.010560Akaike info c

45、riterion-6.194729Sum squared resid0.002899Schwarz criterion-6.099572Log likelihood88.72621Hannan-Quinn criter.-6.165638F-statistic86.86322Durbin-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H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：i22 Xi 3，选取权数，使用加

46、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: 06/07/15 Time: 13:56Sample: 1 18Included observations: 18Weighting series: 1/XA(2/3)VariableCoefficientStd. Errort-StatisticProb.0.0000X0.7951570.01725246.09012Weighted StatisticsR-squared0

47、.954867Mean dependent var9599.510Adjusted R-squared0.954867S.D. dependent var1867.615S.E. of regression895.7229Akaike info criterion16.48709Sum squared resid13639432Schwarz criterion16.53656Log likelihood-147.3838Hannan-Quinn criter.16.49391Durbin-Watson stat1.472431Unweighted StatisticsR-squared0.9

48、52547Mean dependent var10906.35Adjusted R-squared0.952547S.D. dependent var5381.587S.E. of regression1172.315Sum squared resid23363462Durbin-Watson stat1.419465它与存在异方差时如下方程估计明显不同Y=0.804208453455*X进行同方差性变换，然后回归实际上就是Y/(XA(21/3)和X/(XA(2/3)回归，结果如下：Dependent Variable: Y/(XA(2/3)Method: Least SquaresDate: 06/07/15Time:13:59Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.1/(XA(2/3)-495.5562520.4173-0.9522280.3551X/(XA(2/3)0.8337080.0440