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I have a basic question in time series modeling. (using r but the question is not particularly about r)

For a time series with obvious seasonality, shall I use stl (Seasonal and Trend decomposition using Loess) to decompose it into trend, seasonal and remainder, and model the remainder part, or directly model it with a seasonal model such as seasonal arima? The end application would be either forecasting, or detecting outliers/anomalies.

One of the reason I'm asking this, aside from my confusion of which approach is theoretically/practically more sound/viable, is that building a seasonal arima model seems to be particularly slow using auto.arima for long time series, whereas if I remove seasonal effect first and use auto.arima to find a model for the remainder seems much faster.

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