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Say I want to forecast retail stock for 1 month, on daily basis. The error will be calculated using SMAPE, but I would weight the error using recency, i.e., the nearer the weight from now the higher weight. Is there a good weightage scheme I could I adopt?

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What is "good" will depend on what you want to do with your forecast. This has been called the "Cost of Forecast Error".

Another important aspect is whether it needs to be explainable to your (possibly non-technical) audience. (Or whether you want to impress them with your math-fu.)

Something like an exponentially decaying weighting scheme may make sense: weight next week's forecasts with $1$, the week's after with $0.9$, then $0.9^2=0.81$ and so forth.

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  • $\begingroup$ Thanks, I hope to have daily weight differences (rather than weekly), and exponentially decaying weighting cannot sum to 1 for all weight (and it can be decaying too fast if I used it for daily)..do you have some other suggestions? $\endgroup$ – william007 Sep 9 at 7:31
  • $\begingroup$ I am thinking of say 3 days horizon, day 1 with 3/(3+2+1),day 2 with 2/(3+2+1),day 13 with 1/(3+2+1)...how would you think of this? $\endgroup$ – william007 Sep 9 at 7:49
  • $\begingroup$ That is a possibility. I wouldn't say that weights need to sum to one. Especially if you use sMAPE, which is hard enough to interpret. (For instance, if your actual is zero, the sAPE contribution is 200%, regardless of the forecast.) $\endgroup$ – S. Kolassa - Reinstate Monica Sep 9 at 16:06

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