Augmented Dickey-Fuller Test Equation
Dependent Variable: D(DLY)
Method: Least Squares
Date: 06/15/05 Time: 23:28
Sample(adjusted): 1987 2004
Included observations: 18 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
DLY(-1) -0.900357 0.224730 -4.006389 0.0011
C 0.389707 0.156538 2.489535 0.0250
@TREND(1985) -0.009683 0.012068 -0.802333 0.4349
R-squared 0.523494 Mean dependent var 0.036498
Adjusted R-squared 0.459960 S.D. dependent var 0.361229
S.E. of regression 0.265458 Akaike info criterion 0.336292
Sum squared resid 1.057020 Schwarz criterion 0.484688
Log likelihood -0.026631 F-statistic 8.239583
Durbin-Watson stat 1.913796 Prob(F-statistic) 0.003850
从检验的结果看其满足一阶单整
B.对LX1
ADF Test Statistic -3.735344 1% Critical Value* -4.5743
5% Critical Value -3.6920
10% Critical Value -3.2856
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(DLX1)
Method: Least Squares
Date: 06/15/05 Time: 23:20
Sample(adjusted): 1987 2004
Included observations: 18 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
DLX1(-1) -1.026168 0.274719 -3.735344 0.0020
C 0.144029 0.066727 2.158489 0.0475
@TREND(1985) 0.002295 0.004460 0.514691 0.6143
R-squared 0.485524 Mean dependent var 0.009985
Adjusted R-squared 0.416928 S.D. dependent var 0.128538
S.E. of regression 0.098151 Akaike info criterion -1.653614
Sum squared resid 0.144503 Schwarz criterion -1.505218
Log likelihood 17.88252 F-statistic 7.077948
Durbin-Watson stat 1.806585 Prob(F-statistic) 0.006843
从检验结果来看其也符合一阶单整
C.对LX2
ADF Test Statistic -3.442502 1% Critical Value* -4.6193
5% Critical Value -3.7119
10% Critical Value -3.2964
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(DLX2)
Method: Least Squares
Date: 06/15/05 Time: 23:21
Sample(adjusted): 1988 2004
Included observations: 17 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
DLX2(-1) -1.220053 0.354409 -3.442502 0.0044
D(DLX2(-1)) 0.411722 0.271383 1.517123 0.1532
C 0.074640 0.072799 1.025283 0.3239
@TREND(1985) 0.008886 0.006269 1.417496 0.1799
R-squared 0.505722 Mean dependent var 0.017653
Adjusted R-squared 0.391658 S.D. dependent var 0.151162
S.E. of regression 0.117901 Akaike info criterion -1.235626
Sum squared resid 0.180707 Schwarz criterion -1.039576
Log likelihood 14.50282 F-statistic 4.433665
Durbin-Watson stat 1.654742 Prob(F-statistic) 0.023529
从检验结果来看其符合一阶单整
D.LX3
ADF Test Statistic -2.881093 1% Critical Value* -3.8877
5% Critical Value -3.0521
10% Critical Value -2.6672
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(DLX3)
Method: Least Squares
Date: 06/15/05 Time: 23:23
Sample(adjusted): 1988 2004
Included observations: 17 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
DLX3(-1) -0.672828 0.233532 -2.881093 0.0121
D(DLX3(-1)) 0.423492 0.242983 1.742886 0.1033
C 0.135419 0.073052 1.853737 0.0850
R-squared 0.376190 Mean dependent var 0.006858
Adjusted R-squared 0.287074 S.D. dependent var 0.283078
S.E. of regression 0.239017 Akaike info criterion 0.134220
Sum squared resid 0.799807 Schwarz criterion 0.281258
Log likelihood 1.859130 F-statistic 4.221358
Durbin-Watson stat 1.706158 Prob(F-statistic) 0.036759
从检验结果来看其也符合一阶单整
(2)GRANGER因果关系检验
Pairwise Granger Causality Tests
Date: 06/15/05 Time: 23:24
Sample: 1985 2004
Lags: 2
Null Hypothesis: Obs F-Statistic Probability
X1 does not Granger Cause Y 18 1.40307 0.28071
Y does not Granger Cause X1 4.21887 0.03872
X2 does not Granger Cause Y 18 9.27388 0.00314
Y does not Granger Cause X2 2.18682 0.15182
X3 does not Granger Cause Y 18 5.83756 0.01552
Y does not Granger Cause X3 1.02952 0.38455
X2 does not Granger Cause X1 18 4.83349 0.02695
X1 does not Granger Cause X2 0.07556 0.92763
X3 does not Granger Cause X1 18 2.85820 0.09358
X1 does not Granger Cause X3 2.16285 0.15458
X3 does not Granger Cause X2 18 2.14288 0.15691
X2 does not Granger Cause X3 2.99361 0.08524
从检验的结果看其服从单项因果关系,为Y分别与X1、X2、X3有因果关系,且X1、X2、X3相互之间也存在因果关系。
(3)协整检验
A.
ADF Test Statistic -3.884608 1% Critical Value* -4.5743
5% Critical Value -3.6920
10% Critical Value -3.2856
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(EX)
Method: Least Squares
Date: 06/15/05 Time: 23:41
Sample(adjusted): 1987 2004
Included observations: 18 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
EX(-1) -1.109931 0.285725 -3.884608 0.0017
D(EX(-1)) 0.295013 0.190560 1.548136 0.1439
C -0.154837 0.109815 -1.409978 0.1804
@TREND(1985) 0.012394 0.009295 1.333515 0.2037
R-squared 0.522047 Mean dependent var -0.004161
Adjusted R-squared 0.419629 S.D. dependent var 0.247363
S.E. of regression 0.188446 Akaike info criterion -0.306877
Sum squared resid 0.497168 Schwarz criterion -0.109017
Log likelihood 6.761895 F-statistic 5.097198
Durbin-Watson stat 2.395081 Prob(F-statistic) 0.013642
LY = -5.918307075 + 2.536759476*LX1 - 1.086041786*LX2 + 0.3193576602*LX3
我们主要是从对数的回归结果中发现每个变量都服从一阶单整,且把其回归的参差项进行单位根检验发现其满足零阶单整,从而我们也就得到了上面的表达式。
B.
Date: 06/16/05 Time: 01:12
Sample: 1985 2004
Included observations: 19
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)
0.926068 99.74420 54.64 61.24 None **
0.764828 50.25664 34.55 40.49 At most 1 **
0.549935 22.75529 18.17 23.46 At most 2 *
0.329199 7.586373 3.74 6.40 At most 3 **
*(**) denotes rejection of the hypothesis at 5%(1%) significance level
L.R. test indicates 4 cointegrating equation(s) at 5% significance level