I want to know how I can test the causality among a series with 5 variables if Johansen test confirms they are not cointegrated and I want to study their long/short run relationship.
Yes, Christos Alexakis is right, you will perform Granger Causality test. Its available in E-Views.
Be sure to run the Johansen test with different specifications of the deterministic terms. If the series are really not cointegrated, there is no long run relationship. I assume that all series are integrated of order 1 (if they are stationary, you would have trivial cointegration vectors). Then, you should check pairwise causality by looking at the differenced series. This would give you the short run relationship. Granger causality tests are appropriate for this job. You should use the lag specification according to information criteria.
toda and yamamoto causality tests may be suitable for your data.
Though there are many tests, Granger Causality (pairwise) is the best.
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