首先我的model里面有3个变量,1个y,两个x。
三个变量都是time series的,而且都是non-stationary的。
但是他们的first difference都没有unit root。
我做了Johansen Cointegration test,
但是看不太懂,别人和我说如果Johansen Cointegration test通过了的话,
就能用普通的OLS做回归,这样也有意义。
求大神解释一下Johansen Cointegration test的结果。
帮我看看接下来该怎么做。
Date: 03/18/12 Time: 22:45
Sample (adjusted): 2008M01 2011M12
Included observations: 48 after adjustments
Trend assumption: No deterministic trend (restricted constant)
Series: UR GP FE
Lags interval (in first differences): 1 to 2
Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.420109 47.58235 35.19275 0.0015
At most 1 * 0.310540 21.42642 20.26184 0.0344
At most 2 0.071827 3.577794 9.164546 0.4786
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 * 0.420109 26.15593 22.29962 0.0138
At most 1 * 0.310540 17.84863 15.89210 0.0244
At most 2 0.071827 3.577794 9.164546 0.4786
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):
UR GP FE C
1.526343 3.989200 -2.591811 30.80669
-1.689682 -2.733144 4.963566 -85.82635
-0.497118 0.680323 0.078242 0.537296
Normalized cointegrating coefficients (standard error in parentheses)
UR GP FE C
1.000000 0.000000 -4.950574 100.5072
(0.76072) (16.6810)
0.000000 1.000000 1.244476 -30.73340
(0.33992) (7.45376)