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I have predicted a time series with positive, zero and negative values. As error measurement I used the Mean Absolute Error (MAE).

In order to give the reader of my paper a better understanding whether the values of MAE are good or bad, I have considered presenting it as follows:

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Is it legitimate to present it this way? Or is it actually meaningless because of the negative values?

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Comparing error to predicted value is frequently done: the result is a relative error. Whether relative or absolute error is more important depends on your data/application/the task at hand.

However, relative errors are most useful if the denominator gives a good impression of what the encountered values are like. In some cases, the mean is suitable, sometimes the lower end of the absolute range is more suitable (you then get worst-case relative error). Sometimes also best case is used (maximum in denominator), particularly if values range from 0 to some maximum.

Ultimately, whether relative error is a good idea at all and which denominator to use should IMHO be decided in accordance with the application/task behind the data.

If your time series has positive and negative (and zero) values, then the mean is probably not a good summary of typically encountered values. max (abs (value)) may be an alternative if that makes sense for your data.

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It seems that you are relating the value of MAE to the value of mean of the time series? Thats not a good idea imho: if you shift the whole series by a constant, its mean would also shift by that constant, but the MEA / quality of your model should stay the same (if your model is e.g. some regression with intercept, the intercept would just shift by that constant.)
I would see a better approach to compare the MAE of the model with MAE of some simpler model, e.g. just predicting the average value of training samples all the time. (Doing that comparison for MSE is actually the R2 of your model.)

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