Let's assume we have four time series a, b, c and d with 10 measurments.
a(1), ..., a(10) b(1), ..., b(10) c(1), ..., c(10) d(1), ..., d(10)
a, b and c are assumed to show the same trend and periodicity.
The question is how can I compare d to a combination of a, b and c in order to test whether d is differing from the assumed trend and periodicity.
The problem is that a, b and c have different ranges, so an average
X(i) := ( a(i) + b(i) + c(i) ) / 3
is not useful.
My question is what would be a good way to reach a meaningful combination?
Would it make sense to normalize the mean of all series a, b, c, d to 1 and then compare d to the average of a, b and c? Or would I also have to normalize the standard deviation of all four series to 1 first?