How to identify relationships between stationary series? 
*

*I have 20 predictor variables and 1 response variable.

*The predictor variables are non-stationary and hence I differenced them to get a stationary series for 20 predictors.

*When I check the correlations between 20 predictors and 1 response (all stationary) the correlations are less than 0.01.


Does that mean I cannot use these predictors? 
How else can I approach this problem? 
 A: As you found out, once properly detrended, your prospective independent variables do not explain at all the behavior of your independent variable.  That is a correct answer.  In other words, you have to research the topic and the data some more to uncover if your dependent variable can be explained or predicted by another set of independent variables that you have not uncovered now.  
I know one can propose a Cointegration model with a nonstationary Y and one or more nonstationary Xs variables.  And, if the residuals of such a model are stationary, you could be deemed to have a successful Cointegration model (based on the pioneering work of Clive Granger on how to overcome unit root issues with level variables).  However, I am not entirely sure such models truly overcome the concerns of "spurious regressions" when using level variables (Clive Granger also researched that issue).  
At this stage, I think you are much better off uncovering that your existing independent variables do not explain at all your dependent variable, when all variables are correctly detrended; Instead of attempting to torture the data and variables structures to come up with a model that generates what is apparently a good Goodness-of-fit.  Meanwhile, the specification of such a model could be truly questionable.  
The truth is better than chasing R Square.     
