what is the relationship between STL-decomposition and deterministic components of time series like trend or seasonality? I have a time series with deterministic trend and deterministic seasonality, so can I use the STL-decomposition? or what other options do I have to adjust my time series or to estimate the trend and seasonal component?

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    $\begingroup$ yes you could use STL decomposition. If the trend and seasonality are deterministic an alternative choice would be to do a multiple regression with seasonality coded as dummy variable and trend coded as linear or quadratic or any other trend. $\endgroup$ – forecaster Oct 16 '14 at 14:18
  • $\begingroup$ If you are using R, tslm function in forecast package automatically adjusts for trend(linear only) and seasonality. $\endgroup$ – forecaster Oct 16 '14 at 14:22
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    $\begingroup$ A little expansion on what @forecaster already noted. If you use seasonal dummies and a linear or quadratic trend, you will see quite clearly what their contribution is by looking at the estimated coefficients. Meanwhile, STL uses locally weighted regression to obtain the trend and the seasonal component. This is not as simple and "transparent" as the former. Of course, you can understand STL by reading the paper by Cleveland et al. (1990) where STL was introduced. Also, STL allows some nice flexibility through optional arguments. $\endgroup$ – Richard Hardy Oct 17 '14 at 14:57
  • $\begingroup$ very nice @RichardHardy. Here is the link to STL decomposition article by Cleveland et al also, there is an open source text book on forecasting and there is a chapter in the text book that shows how to use seasonal dummies and trend to formulate regression models for forecasting. $\endgroup$ – forecaster Oct 17 '14 at 15:07

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