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I have a daily data of sales. However, as seen on the graph, there is a clear shift in the mean values starting 2010. What could be the best prediction model to use in this case? I tried using several classical time series models like SARIMA and TBATS via Python but prediction performance is not satisfactory. Thank you.enter image description here

arvin62
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  • What time granularity are your data? One simple approach would be to just discard the data before the structural break - anything before that is over ten years old, anyway. Also, it's not only the shift in the mean that is striking, but also the vastly increased variance in your data. If "prediction performance is not satisfactory", that may simply be because your series is very hard to forecast. [How to know that your machine learning problem is hopeless?](https://stats.stackexchange.com/q/222179/1352) – Stephan Kolassa Oct 11 '21 at 15:43
  • It's not just the mean that is changing with time: variance is exploding after the mean jumps also. – Alexis Oct 11 '21 at 15:51
  • Also: Can you edit your question to clarify whether your aim is modeling/explanation, or solely prediction? – Alexis Oct 11 '21 at 15:52
  • Ah, apologies, I just saw that your data are daily. Then I would indeed simply start modeling after the shift in mean and variance, and look for drivers per the linked thread. – Stephan Kolassa Oct 11 '21 at 15:56
  • Hello. I have a daily data on hand but I set the frequency to 'B' = Business Days. I also set the period to m=7 because I noticed that that there is a pattern of increase and decrease every 7 business days. @StephanKolassa – arvin62 Oct 11 '21 at 16:01
  • That makes sense. You may also have year-over-year seasonality, where TBATS is appropriate. Or your sales may be driven by promotions or other external events, like Christmas. – Stephan Kolassa Oct 11 '21 at 16:10
  • @Alexis already edited. I mainly want to create predictions for future business days. Since Stephan already mentioned about external events, I may look into intervention analysis as well but my primary goal is to predict. – arvin62 Oct 11 '21 at 16:26

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