异方差检验的eviews操作

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1、异方差检验的ev i ews操作（总10页）本页仅作为文档封面，使用时可以删除This document is for reference only-rar21year.March第四章异方差性例一、参数估计进入Eviews软件包，确定时间范围，编辑输入数据；选择估计方程菜单：(1) 在 Workfile 对话框中，由路径：Quick/Estimate Equation，进入 Equation Specification 对话框，键入 Tog(y) c log(x1) log(x2)”，确认 ok，得到样本回归 估计结果；(2)直接在命令栏里输入“ ls log(y) c log(x1) lo

2、g(x2)”，按Enter，得到样 本回归估计结果；(3)在Group的当前窗口，由路径：Procs/Make Equation，进 入 Equation Specification 窗口，键入“log(y) c log(x1) log(x2)”，确认 ok，得到 样本回归估计结果。如表：表即endent Variable: LOG(Y)Method: Least SquaresDate: 05/12/11 Time: 23:50Sample: 1 31Included observations: 31VariableCoefficientStd. Error t-StatisticProb.

3、C3.2660681.0415913.1356530.0040LOG(X1)0.1502140.1085381.3839750.1773LOG(X2)0.4774530.0515%9.2538530.0000R-squared0.779878Mean dep&ndert var7.928613Adjusted R-squared0.764155S.D. dependeni var0.355750S. E. of regression0.172766Akaike info criterion-0.581995Sum squared res id0.835744Schwarz criterior-

4、0.443222Log likelihood12.02092F-st atistic49.60117Durbin-Watson stat1.780981Prob(F-st atistic)0.000000Adjjsred R-sqwared:增整后的芹本决定案教MeartvarS,以 depcndcni vai;Fl 的均值 因应量的样推差能标海携.心ike iriEo ctiteiiaT!：弄他信息量(AK)Sisit squared re&id:技差平方片Lflglikelihwd:对数f擒比DuLirin-WautMi stat:Sciiwarz cdtencin:抛瓦翅信岛量(SC)F

5、-stahstk: F检验的统计童Prob(F-statistic);相伴撕申口图估计结果为：LnY = 3.266 +0.1502LnXl + 0.4775LnX2R2= ,= F= RSS=括号内为t统计量值。二、检验模型的异方差(一)图形法(1) 生成残差平方序列。在 Workfile 的对话框中，由路径：Procs/Generate Series,进入 Generate Series by Equation对话框，键入e2=residA2”，生成残差平方项序列e2； 直接在命令栏里输入“genr e2=residA2，按Enter,得到残差平方项序列e2。(2) 绘制散点图。 直接在命

6、令框里输入“scat log(x2) e2”，按Enter，可得散点图。 选择变量名log(x2)与e2 (注意选择变量的顺序，先选的变量将在图形中 表示横轴，后选的变量表示纵轴)，再按路径view/graph/scatter/simple scatter，可得散点图。 由路径quick/graph进入series list窗口，输入“log(x2) e2”，确认并 ok，再在弹出的graph窗口把line graph换成scatter diagram，再点ok，可得散 点图。UJoClIJriIJ电OjQ rin0.250.200.150.100.050.00-a 78910L0&(X2)图

7、由图可以看出，残差平方项e2对解释变量log(X2)的散点图主要分布图形 中的下三角部分，大致看出残差平方项e2随log(X2)的变动呈增大的趋势，因 此，模型很可能存在异方差。但是否确实存在异方差还应通过更进一步的检 验。(二)Goldfeld-Quanadt检验(1)对变量取值排序(按递增或递减)。在 Workfile 窗口中，由路径：Procs/Sort Series 进入 sort workfile series 对话框，键入“X2”，如果以递增型排序，选Ascending，如果以递减型排序， 则应选Descending，点ok。本例选递增型排序，选Ascending。直接在命令栏里输

8、入“sortx2”（默认为升序），再按Enter。（2）构造子样本区间，建立回归模型。在本例中，样本容量n=31，删除中间1/4的观测值，即大约7个观测值， 余下部分平分得两个样本区间：1-12和20-31，它们的样本个数均是12个。在Sample菜单里，把sample值改为“1 12”再用OLS方法进行第一个子 样本回归估计，估计结果如表。表Dependent Variable: LOG(Y) Method: Least Squares Date: 05/13/11 Time: 03:00Sample: 1 12Included observations: 12VariableCoeffic

9、ientStd. Errort- StatisticProb.C3.1412081.12235B2.798757.0208LOG(X1)0.3963B50.07B7915.056234.0007LOG(X2)0.2347610.1097472.139009.0611R-squared0739S93Mean dependent var7.700532Adjusted R-sqjared0.681847S.D. dependent var0.156574S.E. of regression0.088316Akaike info criterian-1.803481Sum squared resid

10、0.070197Schwarz criterion-1.682255Log likelihood13.82089F-statistic12.78726Durbin-Wats on stat1.298449Prob(F- statistic)0.002343同样地，在Sample菜单里，把sample值改为“20 31 ”再用OLS方法进行第一个子样本回归估计，估计结果如表。表Dependent VaHable: LOG(Y)Methcid: Least SquaresDate: 0M3/11 Time: 03:04Sample: 20 31Included observations: 12Va

11、riableCoefficientStd. Errort-StatisticProb.C3.9936441.3040542.11970B0.0631LOG(X1)-0.1137660.159962-0.7112050.4950LOG(X2)0.6201680.1116545.5543B00.0004R-squared0.876931Mean dependent var8.239746Adjusted R-squared0.849582S.D. dependent 倾0.375812S.E. of regression0.145754Akaike info criterion0.801478Su

12、m squared resid0.191197Schwarz criterion0.680251Log likelihood7.808868F-statistic32.06485Durbin-Watson stat2.665362Prob(F-statistic)0.000080（3）求F统计量值。基于表和表中残差平方和RSS的数据，即Sum squared resid的值，得到 RSS1=和 RSS2=，根据 Goldfeld-Quanadt 检验，F 统计量为： F= RSS2/ RSS1=。(4) 判断。在5%与10%的显著性水平下，查F分布表得：自由度为(9,9)的分布 的临界值分别为

13、二与二。因为F= (9,9)二，因此10%显著性水平下拒绝两组子样方差相同 的假设，即存在异方差。(三)White检验由表的估计结果，按路径view/residual tests/white heteroskedasticity(cross terms)，进入 White 检验，其中 cross terms 表示有交叉 乘积项。得到表的结果。表White Heteroskedasticitv Test:F-statistic9.833740Probability0.000027bs*R-squared20.55085Probability0.000986Test Equation:Depend

14、ent Variable: RESIDE Method: Lea si Squares Date; 05/13/11 Time; 01:13Sample; 1 31Included bserrations: 31VariableCoefficientStd. Errort- StatisticProb.C10.243285.4745221.8710820.0731LOG(X1)-2.3290701.116442-2.0861530.0473(LOG(X1 )-20.1491140.0581072.5661950.0167CLOG(X1)*(LOG(X2)0.0193330.0412650.46

15、85070.6435LOG(X2)-0.4573070.464020-1.0072380.3235(LOGX2)20.0211010.0133671.5796940.1267R-squared0.662931Mean deperdent var0.026969Adjusted R-sqjared0.695617S.D. dependent var0.042129S.E. of regression0.026794Akaike info triteriori-4.229312Sum squared resid0.017940Schwarz criterion-3.951766Log likeli

16、hood71.55434F-statistic9.833740Durbin-Watson stat1.462377Prob(F- statistic0.000027辅助回归结果为：e* =10.24- 0.46T.11X2 I 0.1 5(1.nXU2 + 0.02(1.11X2/ + 0.02TjiX1T.nN2由表结果得到：怀特统计量nR2=31X 二 ,查X2分布表得到在5%的显著性 水平下，自由度为5的X 2分布的临界值为乂=，因为nR2=x=，所以拒绝同方 差的原假设。由表的估计结果，按路径 view/residual tests/white heteroskedasticity （

17、no cross terms），进入 White检验，其中no cross terms表示无交叉乘积项。得到 表的结果。表White Heteroskedasticity Test:F-statistic12.61602Probability0.000008Obs*R-squared20.45911Probability0.000405Test Equation:Dependent Variable: RESIDE Method: Least Squares Date: 05/13/11 Time: 01:32 Sample: 1 31Included observations: 31Vari

18、ableCoefficientStd. Errort- StatisticProb.C77632751.3753245.6446900.0000LOG(X1)-1.8511230.446727-4.1437430.0003(LOGtX1)20.1261600.0307674.1005120.0004LOG(X2)-0.2S81660.157160-1.6426970.1125(LOGtX2)20.0172140.0103111.6695110.1070R-squared0.6S9971Mean dependent var0.026959Adjusted R-sqjared0.607659S.D

19、. dependent var0.042129S.E. of regr&ssiori0.0263B9Akaike info critericiri-4.2B50B7Sum squared resid0.018105Schwarz criterion-4.053798Log likelihood71.41日日4F-statistic12.61602Durbin-Wats on stat1.481064Prob(F- statistic)0.000008去掉交叉项后的辅助回归结果为：c2 = 7.763 - 1.1 LnXl -0.25S.n2 + 0.1 26（ ,.n 1 ? + 0.01 7

20、（ .nX2K（）（）（）（）（）R2=有怀特统计量nR2=31X二，因此，在5%的显著性水平下，仍是拒绝同方差 这一原假设，表明模型存在异方差。三、异方差性的修正（一）加权最小二乘法（WLS）（1）生成权数。按路径：Procs/Generate Series，进入Generate Series by Equation对话框，键 入“ w=1/sqr（exp或者直接在命令栏输入“ genr w=1/sqr（exp生成权数w。（2）加权最小二乘法估计（WLS）。在表的结果中，由路径：Procs/Specify/Estimate进入Equation Specification对 话框，点击Opti

21、ons按钮，在EstimationOptions对话框的weighted前面打勾并在下面输入栏处输入w,如图，连续 两次确认OK后，得到表的估计结果：Estimation Opt cn?LS and TSLS 0ptions:He teroskedasticitAJConsistent Couariance* Whiter Weighted LS/TSLS (unavailabl已 with ARMA) Weight: |wIterative procedures:It&rations：: |100Convergence: 10.001ARMA options:Starting coeffic

22、ient values|OLS/TSLS Backcast MA terms)OKJCancel表Dependent Variable: LOG(Y)Method: Least SquaresDate: 05/13/11 Time: 01:59Sample: 1 31Included observations: 31Weighting series: WVa riableCoefficientStd. Errort-St atisticProb.C2.33963207245953.2200020.0032LOG(X1)0.3170970.0033773.8031770.0007LOG(X2)0

23、.4290900.0446309.6145170.0000Weighted StatisticsR-sqjared0.998375Mean dependent war7.8S3773Adjusted P-squared0.998259S.D. dependent var2.766804S.E. of regressiori0.115025Akaike irfo criterion-1.395561Sum squared resid0.370464Schwarz criterion-1.25G7S8Log likelihciod24.63119F-statistic8602.1 S3Durbin

24、-Watson stat1.716G1GProb(F-statistic)0.000000加权最小二乘法估计（WLS）结果为:LnY = 2.34 +0.317LnXl + 0.429LnX2可以看出运用加权最小二乘法消除异方差性后，LnX1参数的t检验有了显 著的改进，这表明即使在1%显著性水平下，都不能拒绝从事农业生产带来的纯 收入对农户人均消费支出有着显著影响的假设。虽然LnX1的参数值有了较大程 度的提高，但仍没有LnX2的参数估计值大，说明其他来源的纯收入确实比来自 农业经营的纯收入对农户人均消费支出的影响更大一些。(3) 检验加权回归模型的异方差性。在命令栏中直接输入 w*log(

25、Y) w w*log(X1) w*log(X2)”，按回车键，输 出结果如表：表Dependent Variable: WLOGfV)Method: Least SquaresDate: 05/13/11 Time: 02:21Sample: 1 31Included observations: 31Va riableCoefficientStd. Error t-StatisticProb.W2.3396320.7245953.2288820.0032VTLDGpCI)0.3170970.0833773.8031770.0007WLOGpQ)0.4290980.0446309.6145170

26、.0000R-squared0.998375Mean dependent var112.9506Adjusted R-squared0.998259S.D. dependent var39.49666S.E. of regression1.647967Akaike info criterion3.928728Sum squared resid76.04228Schwarz criterion4.067501Log likelihood-57.89528F- statistic8602.183Durbin-Watsor stat1.71G616Prob(F- statistic).000000得

27、到的加权回归模型的OLS回归结果：wLnY = 2.34w + 0.317wLnXl + 0.429wLnX2对该模型进行怀特检验，得到无交叉乘积项的回归结果如表所示:表White Heteroskedasticitv Test:F-statistic1.456306Probability0.235156ObbR-SLuart!dB. 274003Prubabilil/0.21B709Test Equation:Dependent Variable: RESIDE Method: Least Squares Date: 05/13/11 Time: 02:27 Sample: 1 31Incl

28、uded observations: 31VariableCoefficientStd. Error1- StatisticProb.C6.5235482.9412442.2179550.0363WB.41515S5.773-091 .-1575720.1579WA20.2657820.1843541.4416970.1623VLOC(X10.G2C0G30.5709301.0027G20.20D7CW*LOG(X1 牌-0.0031180.002470-1.2623130.2190WLOGiX2j0.4272640.2942411.452087. 1594(W*LOG(X2)A2-0.001

29、3580.001416-0.9593130.3470R-squared0.266903Mean dependent var2.452977Adjusted W-squaredU.UbJbJyb.D. dependent var2.770135S.E. of regression2.651775Akaike info criierian4.984015Sum squared resid168.7658Schwarz criterion5.307818Loq likelihood-70.25223F- statistic1.456306Durbin-Watson stat2.142052Prob(F- statistic)0.235156辅助回归结果为：c -= 6.524 - S.41 ?w-0.627wLnX1 - (J.427wLnX2 - 0.266W- O.uO3(wLnXb；R2=怀特统计量nR2=31X二，该值小于5%显著性水平下、自由度为6的X2分 别的相应临界值x二，因此，不拒绝同方差的原假设。