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:
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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.
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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?
Best Answer
In the end, you are trying to compare two distributions. The answers to the following question will help you solve the problem quickly and in a theoretical manner: Test to measure statistical significance of z-scores?
Another option would be to perform a one-way ANOVA of all $n$ data sets, assuming equal variance. If the ANOVA identifies a significant difference in one or more groups, a Tukey multiple comparison procedure or pairwise t test can be conducted to identify the time series of interest.