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Trying to "understand" a time series' patterns it is intuitively tempting to use STL decomposition as the concept of distinguishing between trend, season and the rest makes sense.

But my experience tells me that no static algorithm will lead under all circumstances to useful results.

So my general question/s is/are when should you not apply STL decomposition and if you do, what observation in the STL result might in you experience indicate a faulty/useless decomposition?

Like you wouldn't blindly trust a correlation analysis of two variables without having a look at a scatter plot, b/c outliers might lead to a high correlation coefficient indicating a non-existant relation.

I'm a newbie in this area, so a more extensive answer would be great.

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I think with LOESS like any other smoother results will depend on the degree of smoothing. So I think that you can get very different decompositions depending on the amount of smoothing. How much waviness is do to periodicity and how much is just random noise? i think this could be difficult to say. Similar problem come up in kernel density estimation where a bump in a density may be real or may be an artifact of not enough smoothing.

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  • $\begingroup$ To be honest I am not really understanding your answer. Could you clarify it a bit more and how it relates to my specific question/s? $\endgroup$ – Raffael Jul 12 '12 at 21:00
  • $\begingroup$ You asked about the quality of the STL decomposition. Since STL involves LOESS which is a nonparametric smoothing algorithm that can be tuned based on the weight function for averaging neighboring points you control the amount of smoothing with LOESS. If it smooths too much some oscillations that could represent seasonal components could be lost. If it smoths too little there could be an too many bumps creating seasonal components that are not really in the series but are rether part of the random noise. So STL is not well defined and can create different decompostions based on smoothing. $\endgroup$ – Michael Chernick Jul 12 '12 at 21:08

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