Help for Johansen cointegrating vectors test I used the Johansen cointegrating procedure to see how many cointegrating vectors are available in the long run and obtained ONE cointegrating vector from Maximum Eigenvalue statistic and FOUR cointegrating equations from the Trace Test statistic. Now, my question is which of the two statistics is good to make a decision and as to my problem which of the two you recommend to use based on the results I found?
 A: I realize that this answer comes rather late but better late than never. Although the trace/eigenvalue test is perhaps the most formal way there are several other things you could and should look at when setting the rank of the pi matrix. These are: 
1) The roots of the companion matrix. Ideally the largest root which is not 1 should not be close to 1. Note that it is not straightforward to calculate the significance of the roots so this should only be indicative.
2) The t-values on $\alpha$ of the $r+1$ cointegrating relations in the $\alpha$ matrix. the point with this is that if the t-values are small then we would not gain much from adding another cointegrating relationship. The problem with this approach is that we cannot be sure of the distribution of $\alpha$ so this should only be used as an informal testing approach.
3) You could look at the graphs of the cointegrating relations. These should look stationary (like I(0) series). If they do look non-stationary then you should probably lower the rank.
4) Look at the recursive trace test statistics. The cointegrating relations should ideally be trending since the eigenvalues should be non-zero.
5) A last approach to use although only indicative is to see how many equilibrium relations economic theory describes.
For further information see "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models" by Søren Johansen or the less technical and more applied book "The Cointegrated VAR Model: Methodology and Applications" by Katarina Juselius.
A: Maybe it is wise to look to economic theory, to which variables would be likely to have cointegrated relationships, and are the number of cointegrating vectors sensitive to lag length selection?
