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Both Stable and Moving Seasonality are computed in Sliding span test (or D8 F-Stat test) and M7 statistics. But what is the purpose of finding out the presence of moving seasonality in seasonal adjustment test statistics? Does greater moving seasonality result in lower identifiable seasonality?

Intuitively, a greater moving seasonality also imply that the series is seasonal, so why should it lower identifiable seasonality?

Also what is the effect on the seasonally-adjusted series if it has a greater moving seasonality?

Thank you

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