I have a dataset with x number of time series functions (shared x values) which are highly correlated (Spearman, between 0.8 and 0.99) most of the time.

There are 3 hypothesis of mine which I am trying to either validate or reject, but I am not sure what approach would make the most sense.

Given the set of correlated functions, the hypotheses are:

1) One of the time series functions is leading, the other ones follow, but the following functions react with a higher swings (up and down) than the leading function.

2) There are times when the correlation of certain following functions breaks down. After a period they become again correlated to the leading function.

3) There is a time lag between the leading function and the reaction of the following functions.

Does anyone have an idea how to quantify / test those three hypotheses?

Best,

nocciolate