我用johansen协整检验 得到如下结果
Date: 07/09/10 Time: 16:11
Sample (adjusted): 1997Q1 2009Q2
Included observations: 50 after adjustments
Trend assumption: Linear deterministic trend
Series: LOGCPI LOGE LOGGDP_SA
Lags interval (in first differences): 1 to 3
Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.439023 39.74279 29.79707 0.0026
At most 1 0.194359 10.83904 15.49471 0.2216
At most 2 0.000663 0.033182 3.841466 0.8554
Trace test indicates 1 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized Max-Eigen 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.439023 28.90375 21.13162 0.0033
At most 1 0.194359 10.80586 14.26460 0.1642
At most 2 0.000663 0.033182 3.841466 0.8554
Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):
LOGCPI LOGE LOGGDP_SA
-42.30947 -21.53148 6.356762
58.59933 -18.75160 -5.731823
4.849178 11.41469 1.969624
Unrestricted Adjustment Coefficients (alpha):
D(LOGCPI) 0.001036 -0.000163 -4.94E-05
D(LOGE) -0.000218 0.003033 -2.62E-05
D(LOGGDP_SA) 0.007981 0.000957 0.000134
1 Cointegrating Equation(s): Log likelihood 567.2294
Normalized cointegrating coefficients (standard error in parentheses)
LOGCPI LOGE LOGGDP_SA
1.000000 0.508904 -0.150244
(0.13132) (0.01326)
Adjustment coefficients (standard error in parentheses)
D(LOGCPI) -0.043830
(0.01544)
D(LOGE) 0.009227
(0.04715)
D(LOGGDP_SA) -0.337672
(0.07210)
2 Cointegrating Equation(s): Log likelihood 572.6323
Normalized cointegrating coefficients (standard error in parentheses)
LOGCPI LOGE LOGGDP_SA
1.000000 0.000000 -0.118055
(0.01145)
0.000000 1.000000 -0.063253
(0.02554)
Adjustment coefficients (standard error in parentheses)
D(LOGCPI) -0.053357 -0.019257
(0.02630) (0.01039)
D(LOGE) 0.186966 -0.052180
(0.07249) (0.02864)
D(LOGGDP_SA) -0.281564 -0.189797
(0.12267) (0.04846)
我个人的理解是在5%的显著性水平下迹统计量和最大特征值都表示存在一个协整向量,可是下面却出现了两个协整方程,三个协整向量?不知道选择哪个?是不是看极大似然函数小的那个选择方程?协整向量如何判断呢?
问题2:协整向量个数和协整方程个数应该是相同的吗?
望高手指教