I have a large number (hundreds to thousands) of noisy time series that represent contemporaneous observations from different subjects.
I hypothesise that there exist lead-lag relationships between observations for different subjects (or groups of subjects.)
I would like to explore the potential use of such lead-lag relationships for the purposes of predicting the individual series.
What methods might I consider for this?
edit: To be clear, I am not looking at pairwise relationships. What I am looking for is a method that would look at the mountain of data at hand and attempt to discover (potentially non-linear) lead-lag relationships between arbitrary groups of series and the individual series to be predicted.