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Is it true that regular differencing and seasonal differencing of a time-series to achieve stationarity, is the same thing as adjusting a time-series for trend and seasonality? If the above statement is true, does this mean that ARMA models are built on-trend and seasonally adjusted time-series? Does this also imply that I can decompose a time-series using a method like STL and then build an ARMA model on the irregular component?

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