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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:

  1. 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.

  2. 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?

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  • $\begingroup$ Have you tried to check it yourself? $\endgroup$ – ttnphns Jul 13 '15 at 21:17
  • $\begingroup$ I am doing it empirically right now. Trying to do it theoretically seems a bit too complicated. $\endgroup$ – user133586 Jul 13 '15 at 21:53
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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.

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