检验和消除异方差和自相关的报告.docx

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 1983222.30 9.20 1984261.40 14.20 1985273.50 19.56 1986309.40 22.44 1987394.40 23.14 1988475.20 31.94 1989525.40 33.92 1990620.91 34.87 1991719.10 43.66 1992849.40 110.08 1993917.44 275.15 19941210.06 337.67 19951487.80 375.21 19961510.48 417.26 19971827.92 452.57 19981837.09 454.63 19991949.31 403.19 20002492.03 407.15 20012660.98 468.78 20023255.96 527.43 20034382.28 535.05 20045933.26 606.30 20057619.53 603.25 20069689.36 630.21 200712177.76 747.68 200814306.93 923.95 200912016.12 900.33 201015779.30 1057.40 201118986.00 1160.23 201220489.30 1116.16 【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=1+2X +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: 33VariableCoefficientStd. Errort-StatisticProb.C-1451.623598.2829-2.4263150.0213X15.188931.13869713.338880.0000R-squared0.851622Mean dependent var4418.315Adjusted R-squared0.846835S.D. dependent var5949.497S.E. of regression2328.409Akaike info criterion18.40245Sum squared resid1.68E+08Schwarz criterion18.49315Log likelihood-301.6404F-statistic177.9257Durbin-Watson stat0.180035Prob(F-statistic)0.000000因为残差存在负值，所以建立列函数（e=resid2),获得e=resid2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检验建立Y=1+2X +u回归模型。在窗口菜单中选择Residual Tests: White Heteroskedasticity，检验结果如下：White Heteroskedasticity Test:F-statistic3.333467Probability0.049283Obs*R-squared6.000197Probability0.049782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Y=1+2X +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-squared17.91457Probability0.000129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-statistic12.90773Probability0.000023Obs*R-squared17.94868Probability0.000451Lags to 4:ARCH Test:F-statistic8.862241Probability0.000153Obs*R-squared17.29248Probability0.0016964、Gleiser检验建立Y=1+2X +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: 33VariableCoefficientStd. Errort-StatisticProb.C1666.263252.99656.5861090.0000X0.9128950.4815221.8958530.0673R-squared0.103898Mean dependent var2019.061Adjusted R-squared0.074991S.D. dependent var1023.751S.E. of regression984.6169Akaike info criterion16.68107Sum squared resid30053586Schwarz criterion16.77177Log likelihood-273.2377F-statistic3.594258Durbin-Watson stat0.724867Prob(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/X2 ， 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: W1VariableCoefficientStd. Errort-StatisticProb.C-7316.965808.6150-9.0487620.0000X23.181690.91253425.403650.0000Weighted StatisticsR-squared0.986405Mean dependent var9398.091Adjusted R-squared0.985966S.D. dependent var16564.41S.E. of regression1962.300Akaike info criterion18.06031Sum squared resid1.19E+08Schwarz criterion18.15101Log likelihood-295.9952F-statistic645.3454Durbin-Watson stat0.949176Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.391213Mean dependent var4418.315Adjusted R-squared0.371575S.D. dependent var5949.497S.E. of regression4716.361Sum squared resid6.90E+08Durbin-Watson stat0.062636W2：Dependent Variable: YMethod: Least SquaresDate: 05/18/13 Time: 13:55Sample: 1980 2012Included observations: 33Weighting series: W2VariableCoefficientStd. Errort-StatisticProb.C187.892514.8476412.654700.0000X5.6939513.9978031.4242700.1644Weighted StatisticsR-squared0.990402Mean dependent var218.0007Adjusted R-squared0.990093S.D. dependent var598.0862S.E. of regression59.53023Akaike info criterion11.06954Sum squared resid109859.3Schwarz criterion11.16023Log likelihood-180.6474F-statistic2.028545Durbin-Watson stat1.654586Prob(F-statistic)0.164358Unweighted StatisticsR-squared0.398773Mean dependent var4418.315Adjusted R-squared0.379379S.D. dependent var5949.497S.E. of regression4686.985Sum squared resid6.81E+08Durbin-Watson stat0.055673W3：Dependent Variable: YMethod: Least SquaresDate: 05/18/13 Time: 14:11Sample: 1980 2012Included observations: 33Weighting series: W3VariableCoefficientStd. Errort-StatisticProb.C116.981796.512321.2120910.2346X11.130040.98372711.314150.0000Weighted StatisticsR-squared0.595113Mean dependent var1387.549Adjusted R-squared0.582052S.D. dependent var1231.245S.E. of regression795.9862Akaike info criterion16.25573Sum squared resid19641413Schwarz criterion16.34643Log likelihood-266.2196F-statistic128.0101Durbin-Watson stat0.126450Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.790807Mean dependent var4418.315Adjusted R-squared0.784059S.D. dependent var5949.497S.E. of regression2764.697Sum squared resid2.37E+08Durbin-Watson stat0.128599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。【实验步骤检验并消除自相关】一 检查模型是否存在自相关1、图示检验法生成新变量序列 e2=Resid(-1)作出e2关于残差的散点图，得到下图，由于大部分点落在第、象限，表明随机误差项存在着正自相关。2、回归检验法一阶回归检验：Dependent Variable: E0Method: Least SquaresDate: 05/18/13 Time: 16:39Sample (adjusted): 1981 2012Included observations: 32 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C102.7909176.70610.5817060.5651E0(-1)0.9760830.08353511.684660.0000R-squared0.819854Mean dependent var-49.34512Adjusted R-squared0.813849S.D. dependent var2310.529S.E. of regression996.8837Akaike info criterion16.70761Sum squared resid29813312Schwarz criterion16.79922Log likelihood-265.3217F-statistic136.5312Durbin-Watson stat0.950910Prob(F-statistic)0.000000 由回归结果可以知道，在0.05的显著水平之下参数的t检验均显著，可决系数较高，拟合程度较好，F检验也显著，所以该模型存在一阶自相关。3、DW检验法由OLS法的估计结果知：D.W.= 0.180035。，在5%的显著性水平下，解释变量个数为1，样本容量为33，查表得dL=,1.38，dU=1.51,即0D.W. dL,所以，误差项存在正自相关。Dependent Variable: YMethod: Least SquaresDate: 05/18/13 Time: 12:32Sample: 1980 2012Included observations: 33VariableCoefficientStd. Errort-StatisticProb.C-1451.623598.2829-2.4263150.0213X15.188931.13869713.338880.0000R-squared0.851622Mean dependent var4418.315Adjusted R-squared0.846835S.D. dependent var5949.497S.E. of regression2328.409Akaike info criterion18.40245Sum squared resid1.68E+08Schwarz criterion18.49315Log likelihood-301.6404F-statistic177.9257Durbin-Watson stat0.180035Prob(F-statistic)0.000000二 克服自相关 建立回归模型 Y C X AR(1) ，得到以下回归结果：Dependent Variable: YMethod