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）1980181.19 3.54 1981220.10 3.54 1982223.20 3.54 1983222.309.20 1984261.4014.20 1985273.5019.56 1986309.4022.44 1987394.4023.14 1988475.2031.94 1989525.4033.92 1990620.9134.87 1991719.1043.66 1992849.40110.08 1993917.44275.15 19941210.06337.67 19951487.80375.21 19961510.48417.26 19971827.92452.57 19981837.09454.63 19991949.31403.1920002492.03407.1520012660.98468.7820023255.96527.4320034382.28535.0520045933.26606.3020057619.53603.2520069689.36630.21200712177.76747.68200814306.93923.95200912016.12900.33201015779.301057.40201118986.001160.23201220489.301116.16【实验步骤——检验并消除异方差】一检查模型是否存在异方差性1、图形分析检验（1）散点相关图分析做出外商直接投资X与出口贸易总额Y的散点图（SCAT X Y）。
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；Y=β1+β2X +u，使resid中存放最后一次回归的残差。
Dependent Variable: YMethod: Least SquaresDate: 05/18/13 Time: 12:32Sample: 1980 2012Included observations: 33Variable CoefficientStd.Error t-Statistic Prob.C-1451.623598.2829-2.4263150.0213 X15.188931.13869713.338880.0000R-squared0.851622 Mean dependentvar4418.315Adjusted R-squared0.846835 S.D. dependentvar5949.497S.E. of Akaike inforegression2328.409criterion18.40245Sum squaredresid 1.68E+08 Schwarz criterion18.49315Log likelihood-301.6404 F-statistic177.9257Durbin-Watsonstat0.180035 Prob(F-statistic)0.000000因为残差存在负值，所以建立列函数（e=resid^2),获得e=resid^2的数列，建立e关于X的散点图，可以发现随着X增加，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+β2X +u回归模型。
建立Y=β1在窗口菜单中选择Residual Tests: White Heteroskedasticity，检验结果如下：White Heteroskedasticity Test:F-statistic 3.333467 Probability0.049283Obs*R-squared6.000197 Probability0.049782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Y=β+β2X +u回归模型。
1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-statistic19.16665 Probability0.000006Obs*R-squared17.91457 Probability0.000129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检验，取得同样的检验结果：Lags to 3:ARCH Test:F-statistic12.90773 Probability0.000023Obs*R-squared17.94868 Probability0.000451Lags to 4:ARCH Test:F-statistic8.862241 Probability0.000153Obs*R-squared17.29248 Probability0.0016964、Gleiser检验建立Y=β1+β2X +u回归模型。
生成新变量序列： 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。
Dependent Variable: E1Method: Least SquaresDate: 05/18/13 Time: 13:28Sample: 1980 2012Included observations: 33Variable CoefficientStd.Error t-Statistic Prob.C1666.263252.99656.5861090.0000 X0.9128950.4815221.8958530.0673R-squared0.103898 Mean dependentvar2019.061Adjusted R-squared0.074991 S.D. dependentvar1023.751S.E. ofregression984.6169 Akaike infocriterion16.68107Sum squaredresid30053586 Schwarzcriterion16.77177Log likelihood-273.2377 F-statistic 3.594258Durbin-Watsonstat0.724867 Prob(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W1=1/X ，W2=1/X^2 ， 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:Dependent Variable: YMethod: Least SquaresDate: 05/18/13 Time: 13:52Sample: 1980 2012Included observations: 33Weighting series: W1Variable CoefficientStd.Error t-Statistic Prob.C-7316.965808.6150-9.0487620.0000 X23.181690.91253425.403650.0000Weighted StatisticsR-squared0.986405 Mean dependentvar9398.091Adjusted R-squared 0.985966 S.D. dependentvar16564.41S.E. ofregression1962.300 Akaike infocriterion18.06031Sum squaredresid 1.19E+08 Schwarz criterion18.15101 Log likelihood-295.9952 F-statistic645.3454 Durbin-Watsonstat0.949176 Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.391213 Mean dependentvar4418.315Adjusted R-squared0.371575 S.D. dependentvar5949.497S.E. ofregression4716.361 Sum squaredresid 6.90E+08Durbin-Watsonstat0.062636W2：Dependent Variable: YMethod: Least Squares Date: 05/18/13 Time: 13:55 Sample: 1980 2012 Included observations: 33 Weighting series: W2Variable CoefficientStd.Error t-Statistic Prob.C187.892514.8476412.654700.0000 X 5.6939513.9978031.4242700.1644Weighted StatisticsR-squared0.990402 Meandependent var218.0007Adjusted R-squared0.990093 S.D. dependentvar598.0862S.E. ofregression59.53023 Akaike infocriterion11.06954Sum squaredresid109859.3 Schwarzcriterion11.16023Log likelihood-180.6474 F-statistic 2.028545Durbin-Watsonstat1.654586 Prob(F-statistic)0.164358UnweightedStatisticsR-squared0.398773 Meandependent var4418.315Adjusted R-squared0.379379 S.D. dependentvar5949.497S.E. ofregression4686.985 Sum squaredresid 6.81E+08Durbin-Watsonstat0.055673W3：Dependent Variable: YMethod: Least SquaresDate: 05/18/13 Time: 14:11Sample: 1980 2012Included observations: 33Weighting series: W3Variable Coefficient Std.Errort-Statistic Prob.C116.981796.512321.2120910.2346 X11.130040.98372711.314150.0000Weighted StatisticsR-squared0.595113 Meandependent var1387.549Adjusted R-squared0.582052 S.D. dependentvar1231.245S.E. ofregression795.9862 Akaike infocriterion16.25573Sum squaredresid19641413 Schwarzcriterion16.34643Log likelihood-266.2196 F-statistic128.0101 Durbin-Watsonstat0.126450 Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.790807 Meandependent var4418.315Adjusted R-squared0.784059 S.D. dependentvar5949.497S.E. ofregression2764.697 Sum squaredresid 2.37E+08Durbin-Watsonstat0.128599经比较，以W1=1/W作为权数的模型消除异方差性效果最好，参数的t检验均显著，可决系数大幅提高（R2=0.986405）,拟合程度较好，F检验也显著，并说明外商直接投资每增加1亿美元，平均说来将增加11.13004亿美元出口贸易总额，而不是原模型的15.18893亿美元出口贸易总额。