表十八：y序列一阶差分单位根检验（带截距项）
Null Hypothesis: D(Y) has a unit root Exogenous: Constant Lag Length: 1 (Fixed)
t-Statistic -3.095556 -3.808546 -3.020686 -2.650413
Std. Error 0.322486 0.238201 0.035665
t-Statistic -3.095556 0.448598 -0.960215
Prob.* 0.0432
Prob. 0.0066 0.6594 0.3504 0.003371 0.195215 -0.805286 -0.655926 7.373074 0.004948
Augmented Dickey-Fuller test statistic Test critical values:
1% level 5% level 10% level
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(Y,2) Method: Least Squares Date: 06/18/09 Time: 02:00 Sample (adjusted): 1988 2007
Augmented Dickey-Fuller Test Equation
Included observations: 20 after adjustments
Variable D(Y(-1)) D(Y(-1),2)
C
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient -0.998273 0.106856 -0.034246
0.464502 Mean dependent var 0.401502 S.D. dependent var 0.151023 Akaike info criterion 0.387736 Schwarz criterion 11.05286 F-statistic 1.838472 Prob(F-statistic)
表十九：y序列一阶差分单位根检验（不带截距项）
Null Hypothesis: D(Y) has a unit root Exogenous: None Lag Length: 1 (Fixed)
t-Statistic -2.949451 -2.685718 -1.959071 -1.607456
Std. Error 0.304819 0.232965
t-Statistic -2.949451 0.264013
Prob.* 0.0054
Prob. 0.0086 0.7948 0.003371 0.195215 -0.852470 -0.752897 1.870272
Augmented Dickey-Fuller test statistic Test critical values:
1% level 5% level 10% level
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(Y,2) Method: Least Squares Date: 06/18/09 Time: 02:01 Sample (adjusted): 1988 2007
Augmented Dickey-Fuller Test Equation
Included observations: 20 after adjustments
Variable D(Y(-1)) D(Y(-1),2)
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood
Coefficient -0.899048 0.061506
0.435459 Mean dependent var 0.404095 S.D. dependent var 0.150696 Akaike info criterion 0.408765 Schwarz criterion 10.52470 Durbin-Watson stat
拒绝原假设，因此不存在单位根，序列平稳。可以认为y序列为1阶单整。 H序列一阶差分单位根检验如下：
表二十：h序列一阶差分单位根检验（带截距项）
Null Hypothesis: D(H) has a unit root Exogenous: Constant Lag Length: 1 (Fixed)
t-Statistic -3.060971 -3.808546 -3.020686 -2.650413
Std. Error 0.337756 0.230492 0.037218
t-Statistic -3.060971 0.186353 -1.085475
Prob.* 0.0462
Prob. 0.0071 0.8544 0.2929 0.004840 0.207280 -0.759146 -0.609786 8.588783 0.002643
Augmented Dickey-Fuller test statistic Test critical values:
1% level 5% level 10% level
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(H,2) Method: Least Squares Date: 06/18/09 Time: 02:03 Sample (adjusted): 1988 2007
Augmented Dickey-Fuller Test Equation
Included observations: 20 after adjustments
Variable D(H(-1)) D(H(-1),2)
C
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient -1.033861 0.042953 -0.040400
0.502598 Mean dependent var 0.444080 S.D. dependent var 0.154548 Akaike info criterion 0.406045 Schwarz criterion 10.59146 F-statistic 1.883574 Prob(F-statistic)
表二十一：h序列一阶差分单位根检验（不带截距项）
Null Hypothesis: D(H) has a unit root Exogenous: None Lag Length: 1 (Fixed)
t-Statistic -2.848428 -2.685718 -1.959071 -1.607456
Std. Error 0.315321 0.224824
t-Statistic -2.848428 -0.076753
Prob.* 0.0068
Prob. 0.0107 0.9397 0.004840 0.207280 -0.792133 -0.692560 1.933195
Augmented Dickey-Fuller test statistic Test critical values:
1% level 5% level 10% level
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(H,2) Method: Least Squares Date: 06/18/09 Time: 02:03 Sample (adjusted): 1988 2007
Augmented Dickey-Fuller Test Equation
Included observations: 20 after adjustments
Variable D(H(-1)) D(H(-1),2)
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood
Coefficient -0.898168 -0.017256
0.468123 Mean dependent var 0.438574 S.D. dependent var 0.155311 Akaike info criterion 0.434188 Schwarz criterion 9.921334 Durbin-Watson stat
拒绝原假设，因此不存在单位根，序列平稳。可以认为y序列为1阶单整。 r序列一阶差分单位根检验如下：
表二十二：h序列一阶差分单位根检验（不带截距项）
Null Hypothesis: D(R) has a unit root Exogenous: None Lag Length: 1 (Fixed)
t-Statistic -2.666224 -2.685718 -1.959071 -1.607456
Std. Error 0.287481 0.235661
t-Statistic -2.666224 0.189004
Prob.* 0.0105
Prob. 0.0157 0.8522 -0.005801 0.424663 0.819054 0.918628 2.001665
Augmented Dickey-Fuller test statistic Test critical values:
1% level 5% level 10% level
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(R,2) Method: Least Squares Date: 06/18/09 Time: 02:04 Sample (adjusted): 1988 2007
Augmented Dickey-Fuller Test Equation
Included observations: 20 after adjustments
Variable D(R(-1)) D(R(-1),2)
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood
Coefficient -0.766489 0.044541
0.365305 Mean dependent var 0.330044 S.D. dependent var 0.347590 Akaike info criterion 2.174741 Schwarz criterion -6.190545 Durbin-Watson stat
拒绝原假设，因此不存在单位根，序列平稳。可以认为y序列为1阶单整。 由于y,h,r均为1阶单整，可以进一步分析三个序列是否协整。 对模型
yt??ht??rt?ut进行拟合，结果如下：