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I have short daily time series (less than 4 years) representing sales and exhibiting two seasonalities (weekly and yearly) and I am seeking to identify outliers (not only data reporting errors but also particular events impacting the sales). Because of the presence of a trend and seasonalities, I think detrending and deseasonalising data beforehand is necessary; so I was thinking of using decomposition models based on moving averages to get the irregular component and then use statistical tests (Z score methods, use of interquartile range...) or distance/density based algorithms but the results will be closely related to the quality of the decomposition (that depends itself on the number of outliers) and I am not even sure it will work. Or I was thinking of using the method exposed by Tsay to detect the different types of outliers (additive, innovational, level shifts...) using regARIMA models with dummy variables for festivals, trends and seasonalities (I hope I will have enough data for that). I have only free software (R) at my disposal. Which would be the best approach to adopt ? I would be vey grateful for any help.

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You definitely want to select the latter "Or I was thinking of using the method exposed by Tsay to detect the different types of outliers (additive, innovational, level shifts...) using regARIMA models with dummy variables for festivals, trends and seasonalities (I hope I will have enough data for that)." . Care should be taken to

  1. distinguish between trends and level shifts
  2. distinguish between Pulse Outliers and pre,contemporary and post known events 3, distinguish between deterministic changes in variance versus Box-Cox types of transformations to normalize for heterogeneity.
  3. distinguish between parameter changes over time and othe Gaussian Violations
  4. distinguish between needed ARIMA structure and other effects.
  5. recognize that there may be weekly and/or monthly effects.
  6. recognize the simultaneous effect reflecting a known event and say a "weekend event"

Hope this helps.

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  • $\begingroup$ Thank you so much for your help. I am going to explore your leads $\endgroup$ – Jelly Sep 6 '11 at 19:48

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