我现在对于3个变量LNHP，LNLP和LNDL做了unit root test。他们的图形显示是有趋势上升，但当我选择ADFtest的trend+intercept的时候，得到两个变量level stationary，一个变量一阶平稳。如果是不加trend的话就3个变量都是I(1)。理论应该是3个变量应该同阶平稳才能做协整，那是否就是说Johansen co-integration 方程也只能用不加trend的方程来做？

这个是只有intercept的Johansen结论
Date: 03/21/11   Time: 21:58

Sample (adjusted): 2000Q1 2010Q3

Included observations: 43 after adjustments

Trend assumption: Linear deterministic trend

Series: LNHP LNLP LNDL

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 *
0.593747
42.07473
29.79707
0.0012
At most 1
0.074345
3.341269
15.49471
0.9493
At most 2
0.000450
0.019373
3.841466
0.8892


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 *
0.593747
38.73346
21.13162
0.0001
At most 1
0.074345
3.321896
14.26460
0.9230
At most 2
0.000450
0.019373
3.841466
0.8892


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):



LNHP
LNLP
LNDL

-27.16853
4.524538
6.748176

24.02210
-3.217646
-4.067153

-68.06757
64.78095
-4.132913





Unrestricted Adjustment Coefficients (alpha):



D(LNHP)
0.012561
-0.002259
0.000120

D(LNLP)
0.030357
0.001779
4.97E-05

D(LNDL)
0.015009
0.011993
0.002560





1 Cointegrating Equation(s):
Log likelihood
254.8786



Normalized cointegrating coefficients (standard error in parentheses)

LNHP
LNLP
LNDL

1.000000
-0.166536
-0.248382


(0.13776)
(0.04789)



Adjustment coefficients (standard error in parentheses)

D(LNHP)
-0.341270


(0.06939)

D(LNLP)
-0.824762


(0.12511)

D(LNDL)
-0.407768


(0.61947)





2 Cointegrating Equation(s):
Log likelihood
256.5396



Normalized cointegrating coefficients (standard error in parentheses)

LNHP
LNLP
LNDL

1.000000
0.000000
0.155676


(0.21844)

0.000000
1.000000
2.426248


(1.32134)



Adjustment coefficients (standard error in parentheses)

D(LNHP)
-0.395540
0.064103


(0.09149)
(0.01401)

D(LNLP)
-0.782037
0.131630


(0.16661)
(0.02551)

D(LNDL)
-0.119664
0.029318


(0.82331)
(0.12604)



（这里还想请问一下如果要写Johansen给出的方程，系数的t-value要在哪里看？）




谢谢！！！