# How to combine several time series into a useful average time series?

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 - to figure out if d is differing from the assumed trend and periodicity.

The problem is that a, b and c show 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?

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give an example –  user603 Jul 12 '12 at 16:10
I'm assuming that "trend" covers phase/delay differences. Your factors are essentially complicated ways of saying "normalize each series by its sum before comparing." For instance, let a'(i) = a(i)/sum(a), etc. You're essentially comparing the average of a', b', and c' to d. I'd compare it to d'. –  John Moeller Jul 12 '12 at 18:29
I edited the question. Basically I want to combine the information of a, b and c in a way that causes as little distortian to the original information as possible and then compare it. Basically I should normalize the mean of all series, I guess. What I have been wondering is if I would have to normalize the std dev as well ... I am pretty unsure. –  Яaffael Jul 12 '12 at 20:58