表八：序列相关LM检验结果
Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared
Test Equation:
Dependent Variable: RESID Method: Least Squares Date: 06/18/09 Time: 00:51
Presample missing value lagged residuals set to zero.
Variable
C H R M RESID(-1) RESID(-2)
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient -0.000523 -0.001534 -0.001503 0.029622 0.351790 -0.164850
Std. Error 0.064946 0.106230 0.052800 0.102917 0.258828 0.289457
t-Statistic -0.008049 -0.014443 -0.028467 0.287822 1.359165 -0.569515
Prob. 0.9937 0.9886 0.9776 0.7770 0.1919 0.5765 2.17E-17 0.081636 -1.812466 -1.516250 0.420752 0.827853
1.051880 Probability 2.532825 Probability
0.370942 0.281841
0.110123 Mean dependent var -0.151606 S.D. dependent var 0.087606 Akaike info criterion 0.130473 Schwarz criterion 26.84335 F-statistic 1.734137 Prob(F-statistic)
在5%显著性下，没有通过检验，可以判断不存在自相关性（本例为2阶滞后）。
十六、单位根过程检验
以上的模型拟合性较好，但由于是时间序列，可能存在伪回归的问题。因此，需要进一步对各变量序列的平稳性进行判断。可以运用单位根过程检验，看各个变量序列是否存在单位根，如果存在，则序列为非平稳的。ADF检验结果如下：
1）y序列的检验
首先，对带有趋势项和截距项的模型
?yt????t??yt?1??1?yt?1??2?yt?2?ut进行估计，结果如下：
表九：带趋势项和截距项的y序列单位根检验
Null Hypothesis: Y has a unit root Exogenous: Constant, Linear Trend Lag Length: 2 (Fixed)
t-Statistic -1.356615 -4.498307 -3.658446 -3.268973
Std. Error 0.159922 0.251202 0.261794 0.467744 0.008373
t-Statistic -1.356615 0.699452 -0.049259 1.172718 -0.547435
Prob.* 0.8421
Prob. 0.1950 0.4950 0.9614 0.2592 0.5921 -0.034917 0.144451 -0.735410 -0.486477 0.617182 0.657015
Augmented Dickey-Fuller test statistic Test critical values:
1% level 5% level 10% level
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(Y) Method: Least Squares Date: 06/18/09 Time: 01:04 Sample (adjusted): 1988 2007
Augmented Dickey-Fuller Test Equation
Included observations: 20 after adjustments
Variable Y(-1) D(Y(-1)) D(Y(-2)) C
@TREND(1985) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient -0.216952 0.175704 -0.012896 0.548532 -0.004584
0.141323 Mean dependent var -0.087658 S.D. dependent var 0.150649 Akaike info criterion 0.340427 Schwarz criterion 12.35410 F-statistic 1.861231 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
?yt????yt?1??1?yt?1??2?yt?2?ut，检验结果如下：
表十：带截距项的y序列单位根检验
Null Hypothesis: Y has a unit root Exogenous: Constant Lag Length: 2 (Fixed)
t-Statistic -1.366217 -3.808546 -3.020686 -2.650413
Std. Error 0.115676 0.231291 0.233808 0.280772
t-Statistic -1.366217 0.559413 -0.304792 1.233718
Prob.* 0.5775
Prob. 0.1908 0.5836 0.7645 0.2351 -0.034917 0.144451 -0.815628 -0.616481 0.756109 0.534876
Augmented Dickey-Fuller test statistic Test critical values:
1% level 5% level 10% level
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(Y) Method: Least Squares Date: 06/18/09 Time: 01:07 Sample (adjusted): 1988 2007
Augmented Dickey-Fuller Test Equation
Included observations: 20 after adjustments
Variable Y(-1) D(Y(-1)) D(Y(-2)) C
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient -0.158039 0.129387 -0.071263 0.346393
0.124167 Mean dependent var -0.040051 S.D. dependent var 0.147315 Akaike info criterion 0.347228 Schwarz criterion 12.15628 F-statistic 1.809828 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
?yt??yt?1??1?yt?1??2?yt?2?ut，检验结果如下：
表十一：不带趋势项及截距项的y序列单位根检验
Null Hypothesis: Y has a unit root Exogenous: None Lag Length: 2 (Fixed)
t-Statistic -1.128877 -2.685718 -1.959071 -1.607456
Std. Error 0.014551 0.233762 0.235199
t-Statistic -1.128877 0.437966 -0.468537
Prob.* 0.2263
Prob. 0.2746 0.6669 0.6454 -0.034917 0.144451 -0.824756 -0.675396 1.829790
Augmented Dickey-Fuller test statistic Test critical values:
1% level 5% level 10% level
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(Y) Method: Least Squares Date: 06/18/09 Time: 01:08 Sample (adjusted): 1988 2007
Augmented Dickey-Fuller Test Equation
Included observations: 20 after adjustments
Variable Y(-1) D(Y(-1)) D(Y(-2))
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood
Coefficient -0.016427 0.102380 -0.110199
0.040850 Mean dependent var -0.071991 S.D. dependent var 0.149560 Akaike info criterion 0.380260 Schwarz criterion 11.24756 Durbin-Watson stat
同样，不能拒绝原假设。根据以上三个检验，y序列为非平稳序列。
2）h序列的检验
首先，对带有趋势项和截距项的模型进行估计，结果如下：
?ht????t??ht?1??1?ht?1??2?ht?2?ut表十二：带趋势项和截距项的h序列单位根检验
Null Hypothesis: H has a unit root Exogenous: Constant, Linear Trend Lag Length: 2 (Fixed)
t-Statistic -1.156581 -4.498307 -3.658446 -3.268973
Std. Error 0.192873 0.277233 0.256432 0.276017 0.012837
t-Statistic -1.156581 0.410758 0.256667 0.743720 -0.675128
Prob.* 0.8922
Prob. 0.2655 0.6871 0.8009 0.4685 0.5099 -0.039198 0.146345 -0.673677 -0.424744 0.464131 0.761082
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: 01:10 Sample (adjusted): 1988 2007
Augmented Dickey-Fuller Test Equation
Included observations: 20 after adjustments
Variable H(-1) D(H(-1)) D(H(-2))
C
@TREND(1985) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient -0.223073 0.113876 0.065818 0.205280 -0.008667
0.110137 Mean dependent var -0.127160 S.D. dependent var 0.155372 Akaike info criterion 0.362105 Schwarz criterion 11.73677 F-statistic 1.942982 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
?ht????ht?1??1?ht?1??2?ht?2?ut，检验结果如下：