How to find lead-lag relation in two time series?

But we trade on prices, right? How do you trade on returns? 

My preliminary understanding is "whatever we trade on, we should find
correlation, etc. there...". 

If you find lead-lag relations on returns, how do you trade them?
  

You've already been given the answer. 

Correlations on prices produce spurious results. 

Go do some research.  The literature will agree with what you've been 
told here.

Returns may be turned back into prices (or more appropriately, a wealth 
index)

  - Brian

Brian G. Peterson
http://braverock.com/brian/
Ph: 773-459-4973
IM: bgpbraverock