I'm new to working with time-series so forgive my ignorance. I have - to start with - two time-series of which I calculated first differences to get rid of any underlying trends that are irrelevant for what I'm interested in. Now I want to know if when one goes up the other goes down and vice versa. Do I do this using cross-correlation?
I've done cross-correlation in R and get this plot, but I don't know how to interpret it. What am I looking at?
To make things more complicated, this is a fluid system with multiple time-series that may or may not be correlated. So, over the course of time, for example TS1 and TS2 may be correlated while later TS1 and TS3, then TS2 and 3, and back to TS1 and TS2. Does that make sense? How do I go about this?