Methods for Determining Possible Causation Between Two Time Series
I find two possible solutions: Granger Causality and Convergent Cross Mapping (CCM). 

Granger Causality is based on the t-test of lagged value of first variable with the second variable. The limitation is that it could not eliminate the confounding effect.

The CCM first build the manifold for the first variable X. Then for each time point, weights of neighbors are estimated, and used to estimate Y. Then correlation between estimated Y and Y are tested.