表18: 零阶滞后
ADF Test Statistic 0.020079 1% Critical Value* -4.9893
5% Critical Value -3.8730
10% Critical Value -3.3820
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(Y)
Method: Least Squares
Date: 06/14/05 Time: 20:13
Sample(adjusted): 1992 2003
Included observations: 12 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
Y(-1) 0.004567 0.227474 0.020079 0.9844
C 126.1659 82.79925 1.523757 0.1619
@TREND(1991) -23.29910 9.575827 -2.433117 0.0378
R-squared 0.400004 Mean dependent var -24.23375
Adjusted R-squared 0.266671 S.D. dependent var 132.6937
S.E. of regression 113.6317 Akaike info criterion 12.51612
Sum squared resid 116209.5 Schwarz criterion 12.63735
Log likelihood -72.09672 F-statistic 3.000046
Durbin-Watson stat 1.891016 Prob(F-statistic) 0.100385
表19: 一阶滞后
ADF Test Statistic -0.116574 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)
Method: Least Squares
Date: 06/14/05 Time: 20:14
Sample(adjusted): 1993 2003
Included observations: 11 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
Y(-1) -0.039919 0.342439 -0.116574 0.9105
D(Y(-1)) 0.089477 0.486319 0.183988 0.8592
C 128.1929 116.2949 1.102309 0.3068
@TREND(1991) -21.83870 15.89589 -1.373858 0.2119
R-squared 0.350436 Mean dependent var -35.16227
Adjusted R-squared 0.072052 S.D. dependent var 133.3861
S.E. of regression 128.4909 Akaike info criterion 12.82488
Sum squared resid 115569.4 Schwarz criterion 12.96957
Log likelihood -66.53685 F-statistic 1.258822
Durbin-Watson stat 1.961298 Prob(F-statistic) 0.359465
表20: 二阶滞后
ADF Test Statistic -0.466517 1% Critical Value* -5.2735
5% Critical Value -3.9948
10% Critical Value -3.4455
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(Y)
Method: Least Squares
Date: 06/14/05 Time: 20:15
Sample(adjusted): 1994 2003
Included observations: 10 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
Y(-1) -0.284948 0.610798 -0.466517 0.6605
D(Y(-1)) 0.293012 0.668398 0.438380 0.6794
D(Y(-2)) 0.264305 0.664511 0.397744 0.7072
C 178.5436 155.1397 1.150857 0.3018
@TREND(1991) -18.94503 26.78272 -0.707360 0.5109
R-squared 0.419693 Mean dependent var -39.15550
Adjusted R-squared -0.044552 S.D. dependent var 139.9065
S.E. of regression 142.9891 Akaike info criterion 13.07027
Sum squared resid 102229.4 Schwarz criterion 13.22156
Log likelihood -60.35133 F-statistic 0.904033
Durbin-Watson stat 2.177703 Prob(F-statistic) 0.525697
表21: 三阶滞后
ADF Test Statistic -0.667152 1% Critical Value* -5.4776
5% Critical Value -4.0815
10% Critical Value -3.4901
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(Y)
Method: Least Squares
Date: 06/14/05 Time: 20:16
Sample(adjusted): 1995 2003
Included observations: 9 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
Y(-1) -0.691240 1.036105 -0.667152 0.5524
D(Y(-1)) 0.499741 0.975543 0.512270 0.6438
D(Y(-2)) 0.610738 0.977396 0.624862 0.5764
D(Y(-3)) 0.301781 0.796486 0.378890 0.7300
C 294.4294 211.9747 1.388984 0.2590
@TREND(1991) -18.90662 41.97180 -0.450460 0.6829
R-squared 0.583390 Mean dependent var -40.48556
Adjusted R-squared -0.110960 S.D. dependent var 148.3262
S.E. of regression 156.3389 Akaike info criterion 13.17665
Sum squared resid 73325.54 Schwarz criterion 13.30813
Log likelihood -53.29493 F-statistic 0.840196
Durbin-Watson stat 2.199325 Prob(F-statistic) 0.597733
表22
ADF Test Statistic -4.367672 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(X3)
Method: Least Squares
Date: 06/14/05 Time: 21:03
Sample(adjusted): 1993 2003
Included observations: 11 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
X3(-1) -0.753242 0.172458 -4.367672 0.0033
D(X3(-1)) 0.633474 0.179702 3.525143 0.0097
C -11.96263 3.614666 -3.309469 0.0130
@TREND(1991) 1.351285 0.427940 3.157650 0.0160
R-squared 0.794871 Mean dependent var 0.538182
Adjusted R-squared 0.706959 S.D. dependent var 5.768287
S.E. of regression 3.122562 Akaike info criterion 5.390472
Sum squared resid 68.25274 Schwarz criterion 5.535161
Log likelihood -25.64760 F-statistic 9.041642
Durbin-Watson stat 2.679921 Prob(F-statistic) 0.008342
由X3的趋势图也可以看出序列为平稳的。
2、对X1 X2 X3在没有滞后的情况下做协整
表23
Date: 06/14/05 Time: 20:35
Sample: 1991 2003
Included observations: 12
Test assumption: Quadratic deterministic trend in the data
Series: Y X1 X2 X3
Lags interval: No lags
Likelihood 5 Percent 1 Percent Hypothesized
Eigenvalue Ratio Critical Value Critical Value No. of CE(s)
0.964518 58.14258 54.64 61.24 None *
0.610537 18.07778 34.55 40.49 At most 1
0.429494 6.761949 18.17 23.46 At most 2
0.002262 0.027169 3.74 6.40 At most 3
*(**) denotes rejection of the hypothesis at 5%(1%) significance level
L.R. test indicates 1 cointegrating equation(s) at 5% significance level
表24
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 20:40
Sample: 1991 2003
Lags: 1
Null Hypothesis: Obs F-Statistic Probability
X1 does not Granger Cause Y 12 4.76033 0.05701
Y does not Granger Cause X1 0.65357 0.43969
表25
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 20:42
Sample: 1991 2003
Lags: 2
Null Hypothesis: Obs F-Statistic Probability
X1 does not Granger Cause Y 11 0.80069 0.49179
Y does not Granger Cause X1 8.04778 0.02002
表26
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 20:42
Sample: 1991 2003
Lags: 3
Null Hypothesis: Obs F-Statistic Probability
X1 does not Granger Cause Y 10 0.08139 0.96575
Y does not Granger Cause X1 11.8179 0.03612
Y和X2做因果分别滞后一阶,二阶,三阶,结果如下:
表27
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 20:42
Sample: 1991 2003
Lags: 1
Null Hypothesis: Obs F-Statistic Probability
X2 does not Granger Cause Y 12 1.85629 0.20617
Y does not Granger Cause X2 3.66478 0.08785
表28
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 20:42
Sample: 1991 2003
Lags: 2
Null Hypothesis: Obs F-Statistic Probability
X2 does not Granger Cause Y 11 1.40840 0.31515
Y does not Granger Cause X2 3.60525 0.09369
表29
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 20:43
Sample: 1991 2003
Lags: 3
Null Hypothesis: Obs F-Statistic Probability
X2 does not Granger Cause Y 10 2.64298 0.22294
Y does not Granger Cause X2 6.20495 0.08403
Y和X3做因果分别滞后一阶,二阶,三阶,结果如下:
表30
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 20:44
Sample: 1991 2003
Lags: 1
Null Hypothesis: Obs F-Statistic Probability
X3 does not Granger Cause Y 12 1.60216 0.23738
Y does not Granger Cause X3 0.45220 0.51818
表31
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 20:44
Sample: 1991 2003
Lags: 2
Null Hypothesis: Obs F-Statistic Probability
X3 does not Granger Cause Y 11 1.11025 0.38883
Y does not Granger Cause X3 0.68539 0.53940
表32
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 20:44
Sample: 1991 2003
Lags: 3
Null Hypothesis: Obs F-Statistic Probability
X3 does not Granger Cause Y 10 4.36351 0.12875
Y does not Granger Cause X3 0.43159 0.74596