# How to normalize two time series for comparison?

I have two time series a and b, which I want to compare. Due to their range difference I normalize them first.

a(i), b(i) are natural numbers for i=1,...,N

two different normalizations:

( mean and std_dev both refer to the whole time series )

1) a'(i) := a(i) / mean( a )

goal: mean( a' ) = 1

2) a'(i) := [ a(i) - mean( a ) ] / std_dev( a )

goal: usual normalization

what confuses me is how do the meanings after those transformations differ?

does the first transformation make any sense at all?

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are your series stationary --i.e. is mean(a) constant over time? –  user603 Jul 13 '12 at 9:52
no, the series' are highly volatile. there is nothing constant over time. –  Яaffael Jul 13 '12 at 9:56
I believe that your series can jump all over the place, but have a (near) constant mean. That's why people detrend or difference time series. –  Wayne Jul 13 '12 at 12:49

The first one will make two series indistinguishable, provided they are proportional to one another, i.e., $a_i = \lambda b_i$ for all $i$.
The second one will make two series indistinguishable, provided they are linear combinations of one another, i.e., $a_i = \lambda b_i + \mu$ for all $i$.