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Knowing that the "Dickey-Fuller tests" tests if the times series is stationary or not by testing the existence of the unit root, after fitting the time series to AR(1) process. Does "Dickey-Fuller tests" gives a statistical significance while testing a seasonal time series, knowing that a seasonal time series is non-stationary and needs seasonal differencing? In another word, can I rely on "Dickey-Fuller tests" in judging that the series needs a seasonal differencing knowing that it has no trend (the reason of non-stationary is only due to seasonality)?

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