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1、消除异方差和自相关的实验报告【实验内容】通过查询中国统计局的2012年中国统计年鉴及新浪财经 数据网，获得1980年-2012年各项指标的数据，如下表所示年份Y-出口贸易总额（亿美元）X-外商直接投资（亿美元）1980181.193.541981220.103.541982223.203.541983222.309.201984261.4014.201985273.5019.561986309.4022.441987394.4023.141988475.2031.941989525.4033.921990620.9134.871991719.1043.661992849.40110.08199
2、3917.44275.1519941210.06337.6719951487.80375.2119961510.48417.2619971827.92452.5719981837.09454.6319991949.31403.1920002492.03407.1520012660.98468.7820023255.96527.4320034382.28535.0520045933.26606.3020057619.53603.2520069689.36630.21200712177.76747.68200814306.93923.95200912016.12900.33201015779.30
3、1057.40201118986.001160.23201220489.301116.16【实验步骤 检验并消除异方差】1检查模型是否存在异方差性1、图形分析检验 Group! GROUP01 Workfil! UIVTITLEDUfttitled(1 )散点相关图分析駆Pti创忖目胡Sample| Shsat | 彳血| Spm|24OD0q20000- 1600012000D_u200X6BOO 1DQ0 12 DO0000-做出外商直接投资X与出口贸易总额丫的散点图（SCAT X 丫）。观察相关图可以看出，随着外商直接投资的增加，出口 贸易总额的平均水平不断提高，但离散程度也逐步扩大。这
4、说 明变量之间可能存在递增的异方差性。（2）残差图分析建立一元线性回归；丫=念+佥X +u,使resid中存放最后一次 回归的残差。Depe ndent Variable: YMethod: Least SquaresDate: 05/18/13 Time: 12:32Sample: 1980 2012In cluded observati ons: 33VariableCoefficie ntStd.Errort-StatisticProb.C-1451.623598.2829-2.4263150.0213X15.188931.13869713.338880.0000Mean depe nd
5、entR-squared0.851622var4418.315Adjusted R-S.D. depe ndentsquared0.846835var5949.497S.E. ofAkaike inforegressi on2328.409criteri on18.40245Sum squaredresid1.68E+08Schwarz criteri on18.49315Log likelihood-301.6404F-statistic177.9257Durbi n-Wats onstat0.180035Prob(F-statistic)0.000000获得X增 Group: UNTITL
6、ED Workfile: UNTtTLEDUntitfed .OE+OO3.00IE+07-2.50E+07-2.00IE+07-1.00E+07-5.DOE+06-X百訴Hintiii 1.5QE+Q7-2D0400300100D 1200因为残差存在负值，所以建立列函数( e=residA2), e=residA2的数列，建立e关于X的散点图，可以发现随着 加，残差呈现明显的扩大趋势，表明存在递增的异方差。2、White 检验建立丫 =悅+血X +u回归模型。Tests:White在窗口菜单中选择ResidualHeteroskedasticity，检验结果如下:White Heteros
7、kedasticity Test:F-statistic3.333467Probability0.049283Obs*R-squared 6.000197Probability0.049782取显著水平，由于 Probability (Obs*R-squared ) 0.05 的显著 水平，认为存在异方差性。3、ARCH检验建立丫=悅+琳+u回归模型。在窗口菜单中选择Residual Tests: ARCH Test，阶数为 2，检验结果如下：Lags to 2:ARCH Test:F-statistic19.16665Probability0.000006Obs*R-squared 17.9
8、1457Probability0.000129取显著水平，由于 Probability(Obs*R-squared ) 0.05 的显著水平，认为存在异方差性。同理，分别作3阶，4阶的ARCH佥验，取得同样的检验结果：Lags to 3:ARCH Test:Obs*R-squared 17.94868 Probability0.000451Lags to 4:ARCH Test:F-statistic8.862241Probability0.000153Obs*R-squared 17.29248Probability0.0016964、Gleiser 检验建立丫 =优+伎X +u回归模型。生
9、成新变量序列：GENR E1 = ABS(Resid)建立新残差序列E1对解释变量X的回归模型，回归结果如图 所示。Depe ndent Variable: E1Method: Least SquaresDate: 05/18/13 Time: 13:28Sample: 1980 2012In eluded observati ons: 33Std.VariableCoefficie ntError t-Statistic Prob.C1666.263252.9965 6.5861090.0000X0.9128950.481522 1.8958530.0673Mean depe ndentR-
10、squared0.103898var2019.061Adjusted R-S.D. depe ndentsquared0.074991var1023.751S.E. ofAkaike inforegressi on984.6169criteri on16.68107Sum squaredSchwarzresid30053586criteri on16.77177Log likelihood-273.2377F-statistic3.594258Durbi n-Wats onstat0.724867Prob(F-statistic)0.067335由上述回归结果可知，回归模型中解释变量的系数估计
11、值 显著不为0，通过10%显著性检验。所以认为存在异方差性。二克服异方差1、确定权数变量W仁1/X ，W2=1/XA2 ，W3=1/SQR(X)其中RESID为最初回归模型LS Y C X的残差序列。2、利用加权最小二乘法估计模型在Eviews命令窗口中键入命令 LS= Y C X，在回归的权数 变量栏里依次输入 W1、W2、W3、W4，得到回归结果。并对 所估计的模型再分别进行 White检验，观察异方差的调整情 况。W1:Depe ndent Variable: YMethod: Least SquaresDate: 05/18/13 Time: 13:52Sample: 1980 201
12、2In cluded observati ons: 33Weight ing series: W1Std.VariableCoefficientError t-Statistic Prob.C-7316.965 808.6150 -9.0487620.0000X23.18169 0.912534 25.403650.0000Weighted StatisticsMean depe ndentR-squared0.986405 var9398.091Adjusted R-0.985966S.D. depe ndent16564.41squaredvarS.E. ofAkaike inforegr
13、essi on1962.300criteri on18.06031Sum squaredresid1.19E+08Schwarz criteri on18.15101Log likelihood-295.9952F-statistic645.3454Durbi n-Wats onstat0.949176Prob(F-statistic)0.000000Un weightedStatisticsMean depe ndentR-squared0.391213var4418.315Adjusted R-S.D. depe ndentsquared0.371575var5949.497S.E. ofSum squaredregressi on4716.361resid6.90E+08Durbi n-Wats onstat0.062636W2 :Depe ndent Variable: YMethod: Least SquaresDate: 05/18/13 Time: 13:55Sample: 1980 2012In eluded observati ons: 33Weighti ng series: W2Variable
