对Y和U进行平稳性检验得:
首先,对Y进行平稳性检验
我们根据Akaike info criterion和Schwarz criterion可知Y的无约束方程为滞后0阶的方程。
ADF Test Statistic -2.041221 1% Critical Value* -4.6193
5% Critical Value -3.7119
10% Critical Value -3.2964
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(Y)
Method: Least Squares
Date: 12/27/04 Time: 11:02
Sample(adjusted): 1986 2002
Included observations: 17 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
Y(-1) -0.414769 0.203197 -2.041221 0.0605
C 0.063992 0.033407 1.915568 0.0761
@TREND(1985) -0.003052 0.001616 -1.888277 0.0799
R-squared 0.233250 Mean dependent var -0.004125
Adjusted R-squared 0.123714 S.D. dependent var 0.018618
S.E. of regression 0.017428 Akaike info criterion -5.102686
Sum squared resid 0.004252 Schwarz criterion -4.955648
Log likelihood 46.37283 F-statistic 2.129439
Durbin-Watson stat 1.911196 Prob(F-statistic) 0.155804
从ADF Test Statistic可知应接受,进入下一步,做F检验。有约束方程模型为D(Y)=C+,回归结果如下:
Dependent Variable: DY
Method: Least Squares
Date: 12/27/04 Time: 11:20
Sample(adjusted): 1986 2002
Included observations: 17 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C -0.004125 0.004515 -0.913594 0.3745
R-squared 0.000000 Mean dependent var -0.004125
Adjusted R-squared 0.000000 S.D. dependent var 0.018618
S.E. of regression 0.018618 Akaike info criterion -5.072386
Sum squared resid 0.005546 Schwarz criterion -5.023373
Log likelihood 44.11528 Durbin-Watson stat 2.189036
最后,用公式计算出标准的F值:
== 4.26058325494
因为F>F (1,14)=1.44,所以拒绝,意味着0, 含时间趋势。继续做t检验。
又因为=2.041221>=0.6912,所以拒绝,为退势平稳过程。
其次,对U进行平稳性检验
同理,根据Akaike info criterion和Schwarz criterion可知U的无约束方程为滞后0阶的方程。
ADF Test Statistic -1.963073 1% Critical Value* -4.6193
5% Critical Value -3.7119
10% Critical Value -3.2964
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(U)
Method: Least Squares
Date: 12/27/04 Time: 12:22
Sample(adjusted): 1986 2002
Included observations: 17 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
U(-1) -0.391698 0.199533 -1.963073 0.0698
C 0.104171 0.056124 1.856069 0.0846
@TREND(1985) -0.004325 0.002382 -1.816031 0.0908
R-squared 0.219257 Mean dependent var -0.006231
Adjusted R-squared 0.107722 S.D. dependent var 0.026813
S.E. of regression 0.025327 Akaike info criterion -4.355089
Sum squared resid 0.008981 Schwarz criterion -4.208052
Log likelihood 40.01826 F-statistic 1.965820
Durbin-Watson stat 1.812335 Prob(F-statistic) 0.176830
从ADF Test Statistic可知应接受,进入下一步,做F检验。有约束方程模型为D(Y)=C+,
回归结果如下:
Dependent Variable: DU
Method: Least Squares
Date: 12/27/04 Time: 12:24
Sample(adjusted): 1986 2002
Included observations: 17 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C -0.006231 0.006503 -0.958175 0.3522
R-squared 0.000000 Mean dependent var -0.006231
Adjusted R-squared 0.000000 S.D. dependent var 0.026813
S.E. of regression 0.026813 Akaike info criterion -4.342874
Sum squared resid 0.011503 Schwarz criterion -4.293861
Log likelihood 37.91443 Durbin-Watson stat 2.050608
最后,用公式计算出标准的F值:
==3.93141075604
因为F>F (1,14)=1.44,所以拒绝,意味着0, 含时间趋势。继续做t检验。
又因为=1.963073>=0.6912,所以拒绝,为退势平稳过程。
由此可得,Y和U均为退势平稳过程,下面对模型进行回归:
通过回归得:
Dependent Variable: Y
Method: Least Squares
Date: 12/05/04 Time: 11:13
Sample: 1985 2002
Included observations: 18
Variable Coefficient Std. Error t-Statistic Prob.
U 0.647892 0.039502 16.40134 0.0000
C -0.020314 0.007437 -2.731291 0.0148
R-squared 0.943860 Mean dependent var 0.095587
Adjusted R-squared 0.940352 S。D。 dependent var 0.040293
S。E。 of regression 0.009841 Akaike info criterion -6.300109
Sum squared resid 0.001549 Schwarz criterion -6.201179
Log likelihood 58.70098 F-statistic 269.0041
Durbin-Watson stat 2.189342 Prob(F-statistic) 0.000000
由Eviews回归得到如下回归模型:
Y=-0.020314+0.647892*U=0.647892(u-0.03135)
(0.039502)
T=-2.731291 16.40134
=0.94386 F=269.0041