I think these situations arises if there is a problem in the model specification (including assumed direction of the relationship and the structural shifts). In a properly specified model, this problem shouldn't arise.

 Dear Mahdi,

Guess you can cover up this problem by changing your variable or check out integration through another tests.

Cheers

Sometimes checking the order of variable by just one test is not a gud idea as it might give different results.Its better to run multiple test like dicky fuller,Modified dicky fuller(dgls) and phillips pherron to be sure of the order of the variables and know whether co-integration exists between the variables or not.

I do not understand your question. It appears that you have done an ARDL cointegration test on a group of variables (Pesaran's bounds test) and that this test rejects cointegration.  With any statistical test there is always a probability of rejecting the true state (generally 5% or 1% - size of test). Do you have an economic or other theoretical reason for assuming that the variables are cointegrated? Did you have a reason for using the ARDL approach rather than say that of Johansen. 

First of all Thank you very much for all your replies.

Dear Dr. Frain,

Pesaran's bounds test does not reject cointegration. Calculated F is greater than I(1) bound in 1% significant level. Yes, I know about the cointegration test and long run relationships. I have 3 variables that are integrated in different order. So, I think it's reasonable to use ARDL approach. 

Best regards,

Mahdi Bastani

The insignificance of the long run coefficient in conjuction with the significance of the short run coefficient can be translated as this variable has weak causan effect.

When the long and the short run coefficients are both significance, this indicates a strong causal effect of the variable.

See an example in the link below:

https://nomanarshed.wordpress.com/2014/11/16/a-manual-for-ardl-approach-to-cointegration/