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I'm trying to compare two time series and determine whether they have similar distribution, trends, seasonality etc. So far, I've seen that Dynamic Time Warping and auto-correlation plots can be used to this end.

However, in this paper, Generating energy data for machine learning, the author uses the Kruskal–Wallis and Mann–Whitney U test to compare the distributions of two time series, one real and one generated. I found this surprising since I thought those two tests required observations to be independent, which is not the case in time series data. Am I missing something here?

Is there a way to use the Kruskal–Wallis test for time series data? If not, is there any preprocessing that can be done to make time series data appropriate for the test? Finally, are there other statistical tests that are more appropriate for comparing time series?

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    $\begingroup$ I share your concern. Wilcoxon-Kruskal-Wallis tests need independence. $\endgroup$
    – Frank Harrell
    Jul 18, 2021 at 12:12
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    $\begingroup$ For what it is worth, that MDPI publisher does not have a great reputation. It even was on Beal’s list of predatory publishers (though he eventually removed it). // I have not done this with KW, but I have run simulations of t-tests when independence is violated, and both $\alpha$ and $\beta$ get wrecked (too powerful when the null is true, not powerful when the null is false). I share the same concerns as you and @FrankHarrell . $\endgroup$
    – Dave
    Jul 18, 2021 at 12:24
  • $\begingroup$ Thank you for clearing that up. I did think it was fishy. As a follow up though, what would be your advice on how to compare two time series? If you can point me to any relevant references that'd be great too. Thank you! $\endgroup$
    – Haris Naveed
    Jul 19, 2021 at 5:36

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