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The examples they give are periodic so removing the periodicity is the big win, not removing the noise.

How did ASAP perform better than ARIMA and other similar algos should be the main question, not how does ASAP compare to nothing.

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Isn't Arima used for forecasting? Pardon me I'm not very informed about it but how is Arima used for smoothing?

Various ARIMA methods are used to deseason data for forecasting, but yes a better more directly comparable example might have been methods like STAMP and STL.

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