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I have a time series y that has both positive and negative that I want to predict. For the prediction I normalize the values to a range between 0 and 1. If I give the normalized actual and forecast data in WAPE / WMAPE, I get an error of ~5%.

However, if I denormalize the actual data and forecast data back to the original span with negative and positive values and then put them into WAPE \ WMAPE, I get an error of ~15%.

Which of the error measurements is correct?

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Both, or neither. The MAPE and the wMAPE are not invariant under affine transformations, i.e., scaling and shifting, which is what you do when you normalize. (They are invariant under scaling only, i.e., if you multiply each forecast and actual by the same number.)

I would be more concerned about what a percentage error of an underlying negative value is supposed to mean. I do not think the (w)MAPE tells you anything useful in such a situation (and, to be more precise, that the (w)MAPE is very helpful at all): What are the shortcomings of the Mean Absolute Percentage Error (MAPE)?

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  • $\begingroup$ Thank you very much for your informative answer. The time series I predict are day-ahead prices on the power exchange (which can also be negative). Almost all papers use adapted versions of the MAPE for their prediction - like the IEEE Transactions Paper: link. Do you have an explanation for this? $\endgroup$ – MerklT Oct 2 at 20:55
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    $\begingroup$ To be quite honest, it looks like an academic discipline perpetuating bad practice "because everybody is doing it that way, so (a) it can't be wrong, right? (b) even if it's wrong, we need to make our paper comparable to previous ones, so we need to use the same flawed approach". I see this kind of error in other subfields of forecasting, and also in statistical analyses of medical and psychological data. $\endgroup$ – S. Kolassa - Reinstate Monica Oct 3 at 8:47
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    $\begingroup$ Which does not change my opinion of the (w)MAPE for data that can take negative values. $\endgroup$ – S. Kolassa - Reinstate Monica Oct 3 at 8:48
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    $\begingroup$ Also, note that other power forecasting applications use much more reasonable error measures, e.g., GEFCOM2017 (though this is load forecasting, not price forecasting). $\endgroup$ – S. Kolassa - Reinstate Monica Oct 3 at 8:49

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