cointegration test_covariance stationary_unit root test

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。cointegration test

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。cointegration test

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):

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