
论文都快写完了,突然发现好像对Johansen的协整结果理解错误,都快哭死了,大大们帮帮忙啊。
我的结果如下
Date: 08/18/09 Time: 19:02
Sample (adjusted): 1991 2007
Included observations: 17 after adjustments
Trend assumption: Linear deterministic trend
Series: LNGDPC LNFDIC
Lags interval (in first differences): 1 to 5
Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.919208 55.29719 15.49471 0.0000
At most 1 * 0.521403 12.52725 3.841466 0.0004
Trace test indicates 2 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 * 0.919208 42.76995 14.26460 0.0000
At most 1 * 0.521403 12.52725 3.841466 0.0004
Max-eigenvalue test indicates 2 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):
LNGDPC LNFDIC
-21.95875 4.531284
-12.84919 -6.198632
Unrestricted Adjustment Coefficients (alpha):
D(LNGDPC) -0.004567 0.001234
D(LNFDIC) -0.001078 0.027638
1 Cointegrating Equation(s): Log likelihood 119.6857
Normalized cointegrating coefficients (standard error in parentheses)
LNGDPC LNFDIC
1.000000 -0.206354
(0.04612)
Adjustment coefficients (standard error in parentheses)
D(LNGDPC) 0.100291
(0.02141)
D(LNFDIC) 0.023666
(0.37588)
我原来的理解是:虽然两个零假设都被拒绝了,但是这两个变量还是存在一个协整的。可是刚刚在一本书上看到说,Johansen协整检验如果所有的零假设都被拒绝了,含义是n个时间序列有n个平稳的线性关系,也就是说所有的时间序列都是平稳的,所以他们之间是不协整的。
那对于我这个两个时间序列的情况,现在有两个协整,岂不是就表示没有协整了吗,我还一直按照有协整来做的。不知道哪位好心的大大能帮忙解释一下?