I understand that Friedman and Kruskal Wallis are non-parametric tests to see if different groups come from same population.

I also gather from here that these tests are used to test for seasonality. Here it explains how Friedman test is used for seasonality.

Say we have a time series with quarterly frequency, for 10 years. So, for the purpose of Friedman test, we have four samples (forming different groups) of 10 observations each.

Small doubt: If the series has autocorrelation then observations in each row would not be independent. Would this affect the test? As in, is independence a requirement for the rank statistic to follow chi-squared?

Interestingly, I found a post by Hyndman on detecting seasonality which talks about log-likelihood test which seems more logical. Any mention of Friedman or Kruskal Wallis is conspicuously absent.

Note: I know a lot of people comment that formal tests for detecting seasonality are unimportant, especially for forecasting. I agree with that but my interest is purely theoretical.


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