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if data series are stationary, you may apply pairwise Granger causality test, however if your series are stationary after 1st difference, in that case you may apply VECM based Granger causality test 

Thanks Kazi,

The data series are non-stationary by the way.

Have you heard about convergent cross mapping(CCM)[1]? But , if your data are purely stochastic than it might not give you any result.. but , some data might appear as stochastic , but it might be the case that the data generteting process is deterministic dynamic … in that cause granger causality is not reliable [1] , and CCM is a really good solution.  CCM has its application in neuroscience [2][3].

1.       Sugihara, G., May, R., Ye, H., Hsieh, C. H., Deyle, E., Fogarty, M., & Munch, S. (2012). Detecting causality in complex ecosystems. science, 338(6106), 496-500.

2.       Anastas, J. (2013). Individual Differences on Multi-scale Measures of Executive Function.

3.       Kun, W., & Brenner, J. E. (2014). An informational ontology and epistemology of cognition. Foundations of Science, 1-31

Thanks Akanda

Are all the data in the time-series generated in-step? If so, You may get some use out of TimeSleuth (http://kamran-karimi.com/timesleuth.html). It is a temporal classifier. You select a number of condition attributes, and a single decision attribute.  It then uses C4.5 to create rules to predict the value of the decision attribute, using the current or previous values of the condition attributes. The best "explanation" for the decision attribute is the rule set that has the highest accuracy. Causality is based on whether using past observations improves the classification or not. The rules are  visualized so you can see which variables are affecting your decision attribute.