Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.972008 86.12572 47.85613 0.0000
At most 1 * 0.767661 36.06424 29.79707 0.0083
At most 2 * 0.663457 15.63045 15.49471 0.0477
At most 3 0.027059 0.384044 3.841466 0.5354
Trace test indicates 3 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 * 0.972008 50.06148 27.58434 0.0000
At most 1 0.767661 20.43379 21.13162 0.0624
At most 2 * 0.663457 15.24640 14.26460 0.0349
At most 3 0.027059 0.384044 3.841466 0.5354
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):
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.972008 86.12572 47.85613 0.0000
At most 1 * 0.767661 36.06424 29.79707 0.0083
At most 2 * 0.663457 15.63045 15.49471 0.0477
At most 3 0.027059 0.384044 3.841466 0.5354