异方差、自相关检验

计量经济学作业

一、异方差

（1）

Dependent Variable: Y

Method: Least Squares

Date: 09/29/11 Time: 22:09

Sample: 1 29

Included observations: 29

Variable Coefficient Std. Error t-Statistic Prob.

C 58.31791 49.04935 1.188964 0.2448

X 0.795570 0.018373 43.30193 0.0000

R-squared 0.985805 Mean dependent var 2111.931 Adjusted R-squared 0.985279 S.D. dependent var 555.5470 S.E. of regression 67.40436 Akaike info criterion 11.32577 Sum squared resid 122670.4 Schwarz criterion 11.42006 Log likelihood -162.2236 F-statistic 1875.057 Durbin-Watson stat 1.893970 Prob(F-statistic) 0.000000

（1）戈徳菲尔德—匡特检验：简单步骤如下：

1、先排列

2、分成两组1-11，19-29，做回归检验，得残差平方和

3、得 F ，查表比较。

Dependent Variable: Y

Method: Least Squares

Date: 09/29/11 Time: 19:38

Sample: 1 11

Included observations: 11

Variable Coefficient Std. Error t-Statistic Prob.

C 55.84840 60.15527 0.928404 0.3774

X 0.802769 0.021586 37.18930 0.0000

R-squared 0.993535 Mean dependent var 2203.182 Adjusted R-squared 0.992816 S.D. dependent var 660.2351 S.E. of regression 55.95928 Akaike info criterion 11.05009 Sum squared resid 28182.97 Schwarz criterion 11.12244 Log likelihood -58.77550 F-statistic 1383.044

Durbin-Watson stat 1.657950 Prob(F-statistic) 0.000000

第一组：Sum squared resid（残差平方和）=28182.97

Dependent Variable: Y

Method: Least Squares

Date: 09/29/11 Time: 19:39

Sample: 19 29

Included observations: 11

Variable Coefficient Std. Error t-Statistic Prob.

C 92.44615 96.01293 0.962851 0.3608

X 0.782281 0.035369 22.11798 0.0000

R-squared 0.981935 Mean dependent var 2141.455

Adjusted R-squared 0.979928 S.D. dependent var 590.5276

S.E. of regression 83.66352 Akaike info criterion 11.85445

Sum squared resid 62996.26 Schwarz criterion 11.92679

Log likelihood -63.19947 F-statistic 489.2051

Durbin-Watson stat 1.770865 Prob(F-statistic) 0.000000

第二组：Sum squared resid（残差平方和）=62996.26

F=62996.26/28182.97=2.23526，给定显著性水平a=0.05

查F分布临界值表可得临界值F0.05（11,11）=2.85，

所以统计量F< F0.05（11,11）,支出模型不存在异方差。

（2）利用加权最小二乘法估计如下：

权重先用1/x，检验结果并不是很理想，因为R方较小，拟合比较差，所以陆续用了1/X^2，X^(-1/2)，效果还好。

Dependent Variable: Y

Method: Least Squares

Date: 09/29/11 Time: 19:47

Sample: 1 29

Included observations: 29

Weighting series: 1/X^2

Variable Coefficient Std. Error t-Statistic Prob.

C 103.7747 68.93265 1.505450 0.1438

X 0.776927 0.030854 25.18060 0.0000

Weighted Statistics

R-squared 0.978844 Mean dependent var 1922.584 Adjusted R-squared 0.978061 S.D. dependent var 431.8719 S.E. of regression 63.96817 Akaike info criterion 11.22112 Sum squared resid 110482.0 Schwarz criterion 11.31542 Log likelihood -160.7062 F-statistic 634.0624 Durbin-Watson stat 1.841591 Prob(F-statistic) 0.000000

Unweighted Statistics

R-squared 0.985240 Mean dependent var 2111.931 Adjusted R-squared 0.984693 S.D. dependent var 555.5470 S.E. of regression 68.73310 Sum squared resid 127554.5 Durbin-Watson stat 1.921310

利用加权最小二乘法估计模型如下：

Y=103.7747+0.776927X

Dependent Variable: Y

Method: Least Squares

Date: 09/29/11 Time: 22:29

Sample: 1 29

Included observations: 29

Weighting series: X^(-1/2)

Variable Coefficient Std. Error t-Statistic Prob.

C 73.82633 53.09180 1.390541 0.1757

X 0.789562 0.021139 37.35117 0.0000

Weighted Statistics

R-squared 0.932667 Mean dependent var 2053.653 Adjusted R-squared 0.930173 S.D. dependent var 251.3231 S.E. of regression 66.41175 Akaike info criterion 11.29610 Sum squared resid 119084.1 Schwarz criterion 11.39039 Log likelihood -161.7934 F-statistic 1395.110 Durbin-Watson stat 1.882707 Prob(F-statistic) 0.000000

Unweighted Statistics

R-squared 0.985749 Mean dependent var 2111.931 Adjusted R-squared 0.985221 S.D. dependent var 555.5470