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Feb 15, 2022 at 0:52 comment added Ben This is also a nice answer, notwithstanding the limitations. I suspect that this particular test might perfom badly on data that is far from a normal distribution, but helpful to look at it nonetheless.
Feb 14, 2022 at 21:42 comment added Gi_F. Hi thanks for the remarks and the nice answer below!..I will try the permutation test. I replied to the question some time ago while reading Fisher’s paper
Feb 14, 2022 at 20:34 comment added Ben A major limitation of this answer is that it assumes normally distributed data and it also assumes that the periodic component is a perfect sine wave. There are many periodic series that would not be identified as periodic under this restriction. (One slight additional complication --- if $\beta=0$ then the series $y_i^{(2)}$ is (trivially) periodic.)
Feb 14, 2022 at 19:39 history edited Gi_F. CC BY-SA 4.0
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Mar 12, 2021 at 17:30 history edited Alexis CC BY-SA 4.0
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Mar 12, 2021 at 17:13 history edited Alexis CC BY-SA 4.0
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Mar 12, 2021 at 17:08 history edited Alexis CC BY-SA 4.0
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Mar 12, 2021 at 15:06 history edited Gi_F. CC BY-SA 4.0
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Mar 12, 2021 at 14:54 history edited Gi_F. CC BY-SA 4.0
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Mar 12, 2021 at 14:46 history answered Gi_F. CC BY-SA 4.0