Suppose you have n time series, and you want to study the difference between the value of any pair of these time series. There seems to be two ways to go about this:
One way is to simply calculate the difference between the value of each pair of the times series, and look at the z score of the that difference.
The other way is, for each time series, calculate the z score that compares its current value with its historical value. Then for each pair of the time series, calculate the difference between their z scores and look at the z score of that difference.
Will the two method produce significantly different results?