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I actually read a lot about times eries and there I often read about "loess decomposition". But what is that exactly? It exists in package STL or packages about outlier-detection.

Can someone give me an easy example about the how loess decomposition works?

Example:

For example I got the timeseries with quadtr values:

2014: 4 5 3 9
2015: 5 4 4 8
2016: 4 5 3 8

I can see that the season is in the 4th quadtr, but how stl works in this example? –

Why duplicatet? I would like you understand STL with this small example. And in the other post you linked, there is no reproducable, simple example to understand the algorithm.

user43348044
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1 Answers1

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Loess is not a decomposition method, but rather a smoothing method. The STL algorithm uses the loess algorithm as a step in computing the season decomposition.

The basic idea of the loess smoother is pretty simple. If we have inputs $x$ and response $y$, to get an estimate at $x_o$, we first compute the weight distances of the points of $x$ from $x_o$ and then perform linear regression, where we downweight values of $x$ that are farther away from $x_o$. Our weighted regression model at $x_o$ then provides our loess estimate. You can also include polynomial expansions of $x$ as well.

Details on the standard methods for computing the weights can be found in the linked paper above.

Cliff AB
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    Thanks for your helpfull answer! Can you give me a simple example of smoother loess. What is exactly the weight distances? I edit my postbwith a small example – user43348044 Jul 29 '17 at 09:07