实验报告：异方差的检验与修正——樊月 13241134
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实验报告一：异方差的检验与修正实验一：
Y=-1168.455+0.201557X(2001Q1-2007Q1) （-1.6147）（11.4080）
∑21=20333301 R2=0.849815 e
Y=4126.255+0.186574X(2009Q4-2015Q4) （0.8309）（5.2491）
∑22=521000000
R2=0.5450 e
求F 统计量 F=
e ∑2
2
/
e
∑2
1
=25.6229,查F 分布表，给定显著性水平α=0.05，得临界值
)25,25(05.0F =1.96，比较F=25.6229>)25,25(05.0F =1.96则拒绝σσ2
2210:
=H ，表明
随机误差项显著异方差。
异方差的修正 1.WLS 估计法
Dependent Variable: Y Method: Least Squares
Date: 03/28/16 Time: 22:20Sample: 2001Q1 2015Q4Included observations: 60Weighting series: X^(-0.5)
Weight type: Inverse standard deviation (EViews default scaling)
Variable
Coefficient Std. Error t-Statistic Prob. C -2141.584594.5232-3.6021870.0007X
0.228845
0.008247
27.74893
0.0000
Weighted Statistics
R-squared
0.929952 Mean dependent var 14420.76Adjusted R-squared 0.928744 S.D. dependent var 6208.501S.E. of regression 2666.201 Akaike info criterion 18.64746Sum squared resid 4.12E+08 Schwarz criterion 18.71727Log likelihood -557.4239 Hannan-Quinn criter.18.67477F-statistic
770.0030 Durbin-Watson stat 1.984442Prob(F-statistic)
0.000000 Weighted mean dep.11606.11
Unweighted Statistics
R-squared
0.911314 Mean dependent var 17655.45Adjusted R-squared 0.909785 S.D. dependent var 11690.49S.E. of regression 3511.338 Sum squared resid 7.15E+08Durbin-Watson stat
1.975033
2.对数变换法
Dependent Variable: LOG(Y)
Method: Least Squares
Date: 03/28/16 Time: 22:24
Sample: 2001Q1 2015Q4
Included observations: 60
Variable Coefficient Std. Error t-Statistic Prob.
C-3.6123320.423149-8.5367900.0000 LOG(X) 1.1740240.03775431.096990.0000 R-squared0.943416 Mean dependent var9.526445 Adjusted R-squared0.942440 S.D. dependent var0.750638 S.E. of regression0.180090 Akaike info criterion-0.557954 Sum squared resid 1.881081 Schwarz criterion-0.488143 Log likelihood18.73863 Hannan-Quinn criter.-0.530647 F-statistic967.0231 Durbin-Watson stat 2.078750 Prob(F-statistic)0.000000
实验二：
Y=-1168.455+0.201557X(2001Q1-2007Q1) （-1.6147）（11.4080）
21=20333301 R2=0.849815 e
Y=4126.255+0.186574X(2009Q4-2015Q4) （0.8309）（5.2491）
R
2
=0.5450
e
∑22
=521000000
求F 统计量
F=
e ∑2
2
/
e
∑2
1
=25.6229,查F 分布表，给定显著性水平α=0.05，得临界值
)25,25(05.0F =1.96，比较F=25.6229>)25,25(05.0F =1.96则拒绝σσ2
2210:
=H ，表明
随机误差项显著异方差。
异方差的修正 1.WLS 估计法
Method: Least Squares
Date: 03/28/16 Time: 22:45
Sample: 2001Q1 2015Q4
Included observations: 60
Weighting series: X^(-0.5)
Weight type: Inverse standard deviation (EViews default scaling)
Variable Coefficient Std. Error t-Statistic Prob.
C1369.5942784.4270.4918770.6247
X 2.1643060.03862456.034740.0000
Weighted Statistics
R-squared0.981863 Mean dependent var158114.8 Adjusted R-squared0.981550 S.D. dependent var47804.02 S.E. of regression12487.05 Akaike info criterion21.73554 Sum squared resid9.04E+09 Schwarz criterion21.80535 Log likelihood-650.0661 Hannan-Quinn criter.21.76284 F-statistic3139.893 Durbin-Watson stat 1.447536 Prob(F-statistic)0.000000 Weighted mean dep.131389.0
Unweighted Statistics
R-squared0.978336 Mean dependent var188600.8 Adjusted R-squared0.977962 S.D. dependent var105302.4 S.E. of regression15632.31 Sum squared resid 1.42E+10 Durbin-Watson stat 1.496518
2.对数变换法
Dependent Variable: LOG(Y)
Method: Least Squares
Date: 03/28/16 Time: 22:47
Sample: 2001Q1 2015Q4
Included observations: 60
Variable Coefficient Std. Error t-Statistic Prob.
C0.8347690.177092 4.7137650.0000 LOG(X)0.9950890.01580062.979370.0000 R-squared0.985588 Mean dependent var11.97105 Adjusted R-squared0.985339 S.D. dependent var0.622472 S.E. of regression0.075369 Akaike info criterion-2.300066 Sum squared resid0.329472 Schwarz criterion-2.230255 Log likelihood71.00198 Hannan-Quinn criter.-2.272759 F-statistic3966.400 Durbin-Watson stat 1.462479 Prob(F-statistic)0.000000
实验三：