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I have a time series of monthly data that is 40 observations ($3\frac{1}{3}$ seasonal cycles) long. HEGY test and CH test give contradicting results w.r.t. presence of a seasonal unit root. HEGY test gives that series have seasonal unit roots while CH test gives that all the series do not have seasonal unit roots.

  1. Since my sample size is small, which test has the highest power?
  2. Due to the relative short sample size, seasonal differencing would cause a significant fraction of observations to get removed. Can I go with CH test results?
Richard Hardy
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Geek_Tech
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    I have edited the post extensively. Feel free to revert back if you think I have misrepresented anything. – Richard Hardy Jan 22 '22 at 14:07
  • @RichardHardy Thank you so much! The question sounds much clear now. Exactly what I wanted to ask. – Geek_Tech Jan 22 '22 at 14:28
  • @RichardHardy [link](https://www.ssc.wisc.edu/~bhansen/papers/jbes_95.pdf) this paper mentions that HEGY has low power when it comes to small sample sizes. However I couldn't find evidence regarding the power of CH test when it comes to small samples. – Geek_Tech Jan 22 '22 at 14:40
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    I do not think there is a way around the small sample size. This is a very fundamental problem. All tests will have low power on such data. – Richard Hardy Jan 22 '22 at 14:44
  • @RichardHardy would a visual interpretation through an ACF plot be better? – Geek_Tech Jan 22 '22 at 14:54
  • When there is little data, there is little data. View it any way you like, you are not going to see much. Rather, consider investing your time in pondering what kind of situation is more plausible/likely (presence vs. absence of a unit root) and what kind of mistake is worse (assume integrated when it is not vs. assume stationary when it is not). For me seasonal integration does not seem plausible in most situations, as I am not expecting subsequent values (which belong to different seasons) to diverge from each other over time. – Richard Hardy Jan 22 '22 at 15:25
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    (I could perhaps clarify in this context my earlier request of visualizations. I thought your 40-long time series was quarterly. That is long enough for trying to visually assess presence of a seasonal unit root. Once I learned it was monthly, my view changed.) – Richard Hardy Jan 22 '22 at 21:58

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