When generating forecasts (e.g., product-customer time series data), should we choose an average-based forecast or median-based forecast? I recently read a very nice article by Nicholas Vandeput on LinkedIn wherein he linked the forecast type to use of different best fit selection criteria.
Optimization on RMSE yields an average-based number... whereas on MAE yields a median-based forecast
Advantages of using median forecast: robust to outliers
Disadvantages of using median forecast: bad for intermittent time series data, medians can be biased for non-normal data, median forecasts are not additive
Q: If that is the case, should we ever use median-based forecasts?
Q: Alternatively, can we correct the data for outliers through outlier correction or "de-promotionalization" and then generate an average-based forecast?