Despite being easy to calculate and understand, exponential smoothing is excessively affected by outliers and thus performs poorly when the data has a non-Gaussian probability distribution, such as a mixture or fat-tailed distribution. Is there a robust alternative or variation?

Regression also has the same problems with outliers so would not be an alternative, nor would forecasting methods that include regression such as ARIMA or GARCH.

I imagine that another option might be somehow pre-treating the data to make it more Gaussian. Supplementary question, would taking logs do this?

Trying to adapt the idea of, for example, the trimmed mean for exponentially weighted moving averages would be complicated and probably work poorly.

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    $\begingroup$ Two approaches - robust filtering and using a robust estimator of scale to identify and downweight outliers in a more traditional time-series approach - are described here: statistik.uni-dortmund.de/useR-2008/slides/… and here:rcrevits.files.wordpress.com/2016/09/…. Both have R packages available as well. $\endgroup$ – jbowman Aug 28 '18 at 20:08
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    $\begingroup$ Isn't "exponential soothing" something done with candles, aromatherapy, and compound interest? :-) $\endgroup$ – whuber Aug 28 '18 at 20:14
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    $\begingroup$ @whuber - I'd give that more than one upvote if I could! $\endgroup$ – jbowman Aug 28 '18 at 21:12
  • $\begingroup$ GARCH could make sense for data with ARCH patterns, non-Gaussian probability distribution and outliers. R packages fGarch and rugarch offer a relatively broad selection of distributions for standardized errors, including several heavy-tailed ones. However, if there is no autoregressive conditional heteroskedasticity in the data, GARCH need not make sense. $\endgroup$ – Richard Hardy Aug 29 '18 at 14:22

There is an R package (robets) for robust exponential smoothing based on this paper by Ruben Crevits and Christophe Croux.

Every aspect of the process is robustified including forecasting, initial values, smoothing parameter estimation and the information criterion.


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