附录:
ADF Test Statistic -2.041785 1% Critical Value* -2.9677
5% Critical Value -1.9890
10% Critical Value -1.6382
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(X1,3)
Method: Least Squares
Date: 06/15/05 Time: 11:31
Sample(adjusted): 1996 2003
Included observations: 8 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(X1(-1),2) -3.952720 1.935913 -2.041785 0.1338
D(X1(-1),3) 2.332637 1.825397 1.277879 0.2912
D(X1(-2),3) 2.483238 1.524530 1.628855 0.2018
D(X1(-3),3) 2.716205 1.208655 2.247296 0.1102
D(X1(-4),3) 1.523530 0.688070 2.214208 0.1137
R-squared 0.904389 Mean dependent var -2.885000
Adjusted R-squared 0.776908 S.D. dependent var 160.1041
S.E. of regression 75.62137 Akaike info criterion 11.75853
Sum squared resid 17155.77 Schwarz criterion 11.80818
Log likelihood -42.03410 Durbin-Watson stat 1.549197
ADF Test Statistic -3.174707 1% Critical Value* -4.8870
5% Critical Value -3.8288
10% Critical Value -3.3588
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(X2)
Method: Least Squares
Date: 06/15/05 Time: 11:32
Sample(adjusted): 1991 2003
Included observations: 13 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
X2(-1) -0.583030 0.183648 -3.174707 0.0113
D(X2(-1)) 0.731305 0.214746 3.405444 0.0078
C 46.82761 14.98021 3.125965 0.0122
@TREND(1989) -0.637363 0.204613 -3.114968 0.0124
R-squared 0.632937 Mean dependent var -1.193846
Adjusted R-squared 0.510583 S.D. dependent var 0.814172
S.E. of regression 0.569581 Akaike info criterion 1.959830
Sum squared resid 2.919806 Schwarz criterion 2.133660
Log likelihood -8.738892 F-statistic 5.172982
Durbin-Watson stat 2.457944 Prob(F-statistic) 0.023781
ADF Test Statistic -3.100689 1% Critical Value* -4.1366
5% Critical Value -3.1483
10% Critical Value -2.7180
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(X5,2)
Method: Least Squares
Date: 06/15/05 Time: 11:33
Sample(adjusted): 1992 2003
Included observations: 12 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(X5(-1)) -1.753011 0.565362 -3.100689 0.0127
D(X5(-1),2) 0.189985 0.340173 0.558494 0.5901
C 61.22057 33.07359 1.851041 0.0972
R-squared 0.740570 Mean dependent var 7.898333
Adjusted R-squared 0.682919 S.D. dependent var 168.1411
S.E. of regression 94.68015 Akaike info criterion 12.15120
Sum squared resid 80678.97 Schwarz criterion 12.27243
Log likelihood -69.90722 F-statistic 12.84573
Durbin-Watson stat 1.956846 Prob(F-statistic) 0.002307
ADF Test Statistic -4.136135 1% Critical Value* -5.1152
5% Critical Value -3.9271
10% Critical Value -3.4104
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(Y,2)
Method: Least Squares
Date: 06/15/05 Time: 11:34
Sample(adjusted): 1993 2003
Included observations: 11 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(Y(-1)) -0.896985 0.216866 -4.136135 0.0061
D(Y(-1),2) 0.461673 0.204438 2.258252 0.0647
D(Y(-2),2) 0.581961 0.276255 2.106606 0.0797
C 244.9544 73.74035 3.321850 0.0160
@TREND(1989) -11.05070 5.551833 -1.990460 0.0937
R-squared 0.820398 Mean dependent var 6.601818
Adjusted R-squared 0.700663 S.D. dependent var 90.78995
S.E. of regression 49.67271 Akaike info criterion 10.95174
Sum squared resid 14804.27 Schwarz criterion 11.13260
Log likelihood -55.23459 F-statistic 6.851797
Durbin-Watson stat 2.225803 Prob(F-statistic) 0.020052
Pairwise Granger Causality Tests
Date: 06/15/05 Time: 11:35
Sample: 1989 2003
Lags: 2
Null Hypothesis: Obs F-Statistic Probability
X1 does not Granger Cause Y 13 0.31809 0.73633
Y does not Granger Cause X1 3.20008 0.09526
Pairwise Granger Causality Tests
Date: 06/15/05 Time: 11:37
Sample: 1989 2003
Lags: 2
Null Hypothesis: Obs F-Statistic Probability
X2 does not Granger Cause Y 13 19.8361 0.00079
Y does not Granger Cause X2 1.40845 0.29919
Pairwise Granger Causality Tests
Date: 06/15/05 Time: 11:42
Sample: 1989 2003
Lags: 2
Null Hypothesis: Obs F-Statistic Probability
X1 does not Granger Cause Y 13 0.31809 0.02521
Y does not Granger Cause X1 3.20008 0.09526
Pairwise Granger Causality Tests
Date: 06/15/05 Time: 11:44
Sample: 1989 2003
Lags: 2
Null Hypothesis: Obs F-Statistic Probability
X5 does not Granger Cause Y 13 1.60492 0.00126
Y does not Granger Cause X5 15.5231 0.00176
ADF Test Statistic -4.136135 1% Critical Value* -5.1152
5% Critical Value -3.9271
10% Critical Value -3.4104
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(Y,2)
Method: Least Squares
Date: 06/15/05 Time: 11:46
Sample(adjusted): 1993 2003
Included observations: 11 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(Y(-1)) -0.896985 0.216866 -4.136135 0.0061
D(Y(-1),2) 0.461673 0.204438 2.258252 0.0647
D(Y(-2),2) 0.581961 0.276255 2.106606 0.0797
C 244.9544 73.74035 3.321850 0.0160
@TREND(1989) -11.05070 5.551833 -1.990460 0.0937
R-squared 0.820398 Mean dependent var 6.601818
Adjusted R-squared 0.700663 S.D. dependent var 90.78995
S.E. of regression 49.67271 Akaike info criterion 10.95174
Sum squared resid 14804.27 Schwarz criterion 11.13260
Log likelihood -55.23459 F-statistic 6.851797
Durbin-Watson stat 2.225803 Prob(F-statistic) 0.020052
滞后
Dependent Variable: Y
Method: Least Squares
Date: 06/15/05 Time: 11:28
Sample(adjusted): 1990 2003
Included observations: 14 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C 4586.606 1177.515 3.895158 0.0036
X1 -0.238249 0.250937 -0.949439 0.3672
X2 -55.29199 14.58694 -3.790513 0.0043
X5 -0.707172 0.249441 -2.835026 0.0196
Y(-1) 0.864233 0.091855 9.408643 0.0000
R-squared 0.994319 Mean dependent var 1714.775
Adjusted R-squared 0.991795 S.D. dependent var 711.1011
S.E. of regression 64.41353 Akaike info criterion 11.44098
Sum squared resid 37341.92 Schwarz criterion 11.66921
Log likelihood -75.08684 F-statistic 393.8381
Durbin-Watson stat 2.131358 Prob(F-statistic) 0.000000
对解释变量Y,X1 ,X3 ,X5和Y滞后一阶进行回归,其结果显示,T检验值、F检验值和R² 都显著,除了解释变量X1的T值较小。它的T值为-0.949439,绝对值都小于2,不显著。
H =(1-d/2)*√¯[n/1-n*Var(ß1*)]
=(1-2.131358/2) *√¯[14/(1-14*0.091855²)]
=-0.065679*√¯[14/(1-0.11812277435)]
=-0.065679*√¯[14/0.88187722565]
=-0.2617
在显著性水平为a=0.05上,查标准正态分布表地临界值h(a/2)=1.96,由于|h |=0.2617<h(a/2),所以接受原假设p=0,说明自回归模型不存在一阶自相关。