第五章：异方差性(作业)教学文案

第五章：异方差性(作

业)

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 =-

20.9463,25R 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