表十三：带截距项的h序列单位根检验
Null Hypothesis: H has a unit root Exogenous: Constant Lag Length: 2 (Fixed)
t-Statistic -1.188467 -3.808546 -3.020686 -2.650413
Std. Error 0.091856 0.236458 0.229972 0.065839
t-Statistic -1.188467 0.088267 -0.021814 0.372178
Prob.* 0.6581
Prob. 0.2520 0.9308 0.9829 0.7146 -0.039198 0.146345 -0.743743 -0.544597 0.483349 0.698512
Augmented Dickey-Fuller test statistic Test critical values:
1% level 5% level 10% level
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(H) Method: Least Squares Date: 06/18/09 Time: 01:11 Sample (adjusted): 1988 2007
Augmented Dickey-Fuller Test Equation
Included observations: 20 after adjustments
Variable H(-1) D(H(-1)) D(H(-2))
C
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient -0.109167 0.020871 -0.005017 0.024504
0.083097 Mean dependent var -0.088822 S.D. dependent var 0.152706 Akaike info criterion 0.373108 Schwarz criterion 11.43743 F-statistic 1.883477 Prob(F-statistic)
不能拒绝原假设，存在单位根。进一步对不存在趋势项和截距项的模型进行估计，模型形式为:
?ht??ht?1??1?ht?1??2?ht?2?ut，检验结果如下：
表十四：不带趋势项及截距项的h序列单位根检验
Null Hypothesis: H has a unit root Exogenous: None Lag Length: 2 (Fixed)
t-Statistic -1.616541 -2.685718 -1.959071 -1.607456
Std. Error 0.049990 0.225870 0.217055
t-Statistic -1.616541 0.015618 -0.121001
Prob.* 0.0983
Prob. 0.1244 0.9877 0.9051 -0.039198 0.146345 -0.835123 -0.685763 1.874208
Augmented Dickey-Fuller test statistic Test critical values:
1% level 5% level 10% level
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(H) Method: Least Squares Date: 06/18/09 Time: 01:11 Sample (adjusted): 1988 2007
Augmented Dickey-Fuller Test Equation
Included observations: 20 after adjustments
Variable H(-1) D(H(-1)) D(H(-2))
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood
Coefficient -0.080811 0.003528 -0.026264
0.075159 Mean dependent var -0.033646 S.D. dependent var 0.148787 Akaike info criterion 0.376338 Schwarz criterion 11.35123 Durbin-Watson stat
同样，不能拒绝原假设。根据以上三个检验，h序列为非平稳序列。
3）r序列的检验
首先，对带有趋势项和截距项的模型行估计，结果如下：
?rt????t??rt?1??1?rt?1??2?rt?2?ut进
表十五：带趋势项和截距项的r序列单位根检验
Null Hypothesis: R has a unit root Exogenous: Constant, Linear Trend Lag Length: 2 (Fixed)
t-Statistic -2.476961 -4.498307 -3.658446 -3.268973
Std. Error 0.231897 0.237054 0.251269 0.406390 0.031236
t-Statistic -2.476961 1.997250 0.985774 -1.910842 2.073618
Prob.* 0.3342
Prob. 0.0256 0.0643 0.3399 0.0753 0.0557 0.073083 0.343134 0.733048 0.981981 1.924740 0.158530
Augmented Dickey-Fuller test statistic Test critical values:
1% level 5% level 10% level
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(R) Method: Least Squares Date: 06/18/09 Time: 01:12 Sample (adjusted): 1988 2007
Augmented Dickey-Fuller Test Equation
Included observations: 20 after adjustments
Variable R(-1) D(R(-1)) D(R(-2))
C
@TREND(1985) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient -0.574401 0.473456 0.247695 -0.776546 0.064772
0.339177 Mean dependent var 0.162957 S.D. dependent var 0.313934 Akaike info criterion 1.478315 Schwarz criterion -2.330475 F-statistic 1.989471 Prob(F-statistic)
不能拒绝原假设，该模型存在单位根。进一步需要对不存在趋势项的模型进行估计，模型形式为
?rt????rt?1??1?rt?1??2?rt?2?ut，检验结果如下：
表十六：带截距项的r序列单位根检验
Null Hypothesis: R has a unit root Exogenous: Constant Lag Length: 2 (Fixed)
t-Statistic -1.321375 -3.808546 -3.020686 -2.650413
Std. Error 0.100024 0.239995 0.250748 0.080736
t-Statistic -1.321375 1.178764 0.120015 0.647165
Prob.* 0.5986
Prob. 0.2050 0.2557 0.9060 0.5267 0.073083 0.343134 0.885097 1.084243 0.939298 0.444753
Augmented Dickey-Fuller test statistic Test critical values:
1% level 5% level 10% level
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(R) Method: Least Squares Date: 06/18/09 Time: 01:12 Sample (adjusted): 1988 2007
Augmented Dickey-Fuller Test Equation
Included observations: 20 after adjustments
Variable R(-1) D(R(-1)) D(R(-2))
C
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient -0.132170 0.282897 0.030094 0.052249
0.149746 Mean dependent var -0.009677 S.D. dependent var 0.344790 Akaike info criterion 1.902088 Schwarz criterion -4.850968 F-statistic 1.987707 Prob(F-statistic)
不能拒绝原假设，存在单位根。进一步对不存在趋势项和截距项的模型进行估计，模型形式为:
?ht??rt?1??1?rt?1??2?rt?2?ut，检验结果如下：
表十七：不带趋势项及截距项的h序列单位根检验
Null Hypothesis: R has a unit root Exogenous: None Lag Length: 2 (Fixed)
t-Statistic -1.393214 -2.685718 -1.959071 -1.607456
Std. Error 0.098066 0.231546 0.241906
t-Statistic -1.393214 1.349433 0.252279
Prob.* 0.1471
Prob. 0.1815 0.1949 0.8039 0.073083 0.343134 0.810937 0.960296 1.978344
Augmented Dickey-Fuller test statistic Test critical values:
1% level 5% level 10% level
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(R) Method: Least Squares Date: 06/18/09 Time: 01:12 Sample (adjusted): 1988 2007
Augmented Dickey-Fuller Test Equation
Included observations: 20 after adjustments
Variable R(-1) D(R(-1)) D(R(-2))
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood
Coefficient -0.136627 0.312456 0.061028
0.127489 Mean dependent var 0.024841 S.D. dependent var 0.338846 Akaike info criterion 1.951878 Schwarz criterion -5.109365 Durbin-Watson stat
同样，不能拒绝原假设。根据以上三个检验，r序列为非平稳序列。 由于变量序列均为非平稳，因此可能存在伪回归，需要进行协整检验。
十七、协整检验
首先，需对各变量序列的单整性进行判断。 Y序列一阶差分的单位根检验结果如下：