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