第五章-异方差性(作业任务)
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5.3 为了研究中国出口商品总额EXPORT对国内生产总值GDP的影响，搜集了1990～2015年相关的指标数据，如表5.3所示。
表3 中国出口商品总额与国内生产总值（单位：亿元）
资料来源：《国家统计局网站》
(1) 根据以上数据，建立适当线性回归模型。
(2) 试分别用White检验法与ARCH检验法检验模型是否存在异方差？
(3) 如果存在异方差，用适当方法加以修正。
解：（1）
100,000
200,000300,000400,000500,000600,000700,000
X
Y
Dependent Variable: Y Method: Least Squares Date: 04/18/20 Time: 15:38 Sample: 1991 2015 Included observations: 25
Variable
Coefficient Std. Error t-Statistic Prob. C -673.0863 15354.24 -0.043837 0.9654 X
4.061131
0.201677
20.13684
0.0000
R-squared 0.946323 Mean dependent var 234690.8 Adjusted R-squared 0.943990 S.D. dependent var 210356.7 S.E. of regression 49784.06 Akaike info criterion 24.54540 Sum squared resid 5.70E+10 Schwarz criterion 24.64291 Log likelihood -304.8174 Hannan-Quinn criter. 24.57244 F-statistic 405.4924 Durbin-Watson stat 0.366228
Prob(F-statistic) 0.000000 模型回归的结果：
^
673.0863 4.0611i
X i Y =-+
()(0.043820.1368)t =-
20.9463,25
==
R n
（2）white:该模型存在异方差
Heteroskedasticity Test: White
F-statistic 4.493068 Prob. F(2,22) 0.0231 Obs*R-squared 7.250127 Prob. Chi-Square(2) 0.0266 Scaled explained SS 8.361541 Prob. Chi-Square(2) 0.0153
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 04/18/20 Time: 17:45
Sample: 1991 2015
Included observations: 25
Variable Coefficient Std. Error t-Statistic Prob.
C -1.00E+09 1.43E+09 -0.700378 0.4910
X^2 -0.455420 0.420966 -1.081847 0.2910
X 102226.2 60664.19 1.685117 0.1061 R-squared 0.290005 Mean dependent var 2.28E+09 Adjusted R-squared 0.225460 S.D. dependent var 3.84E+09 S.E. of regression 3.38E+09 Akaike info criterion 46.83295 Sum squared resid 2.51E+20 Schwarz criterion 46.97922 Log likelihood -582.4119 Hannan-Quinn criter. 46.87352 F-statistic 4.493068 Durbin-Watson stat 0.749886 Prob(F-statistic) 0.023110
ARCH检验：该模型存在异方差
Heteroskedasticity Test: ARCH
F-statistic 18.70391 Prob. F(1,22) 0.0003 Obs*R-squared 11.02827 Prob. Chi-Square(1) 0.0009
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 04/18/20 Time: 19:55
Sample (adjusted): 1992 2015
Included observations: 24 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 8.66E+08 6.92E+08 1.251684 0.2238
RESID^2(-1) 0.817146 0.188944 4.324802 0.0003
R-squared 0.459511 Mean dependent var 2.37E+09 Adjusted R-squared 0.434944 S.D. dependent var 3.90E+09 S.E. of regression 2.93E+09 Akaike info criterion 46.51293 Sum squared resid 1.89E+20 Schwarz criterion 46.61110 Log likelihood -556.1552 Hannan-Quinn criter. 46.53898 F-statistic 18.70391 Durbin-Watson stat 0.888067 Prob(F-statistic) 0.000273
（3）修正：加权最小二乘法修正
Dependent Variable: Y
Method: Least Squares
Date: 04/18/20 Time: 20:46
Sample: 1991 2015
Included observations: 25
Weighting series: W2
Weight type: Inverse variance (average scaling)
Variable Coefficient Std. Error t-Statistic Prob.
C 10781.17 2188.706 4.925821 0.0001
X 3.931606 0.192004 20.47667 0.0000
Weighted Statistics
R-squared 0.947998 Mean dependent var 51703.40 Adjusted R-squared 0.945737 S.D. dependent var 11816.72 S.E. of regression 8420.515 Akaike info criterion 20.99135 Sum squared resid 1.63E+09 Schwarz criterion 21.08886