Point Forecasts
A point forecast is one summary of a distribution. Reporting only the summary discards the part a decision usually needs.
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Forecast Error
Minimizing MAE produces forecasts of the median; minimizing RMSE produces forecasts of the mean. The metric is a modeling choice, not a scorecard.
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Mean Squared Error (MSE)
Square each error and average. Smooth to optimize and hard on big misses, but in squared units, so it is often reported as RMSE and minimized as MSE.
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MASE (Mean Absolute Scaled Error)
A forecast’s MAE divided by the training-set error of a naive forecast. Unit-free and comparable across series, and the denominator is easy to get wrong.
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Mean Absolute Error (MAE)
The average absolute gap between forecast and actual, in the target’s own units. Easy to read, linear in the error, and a forecast of the median when minimized.
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Mean Absolute Percentage Error (MAPE)
Error as a percentage of the actual, averaged. Comparable across series, but it breaks at zero, explodes near it, needs a real zero, and rewards low forecasts.
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Root Mean Squared Error (RMSE)
Square the errors, average, take the root: same units as the target, but large misses count more. Minimizing it forecasts the mean; it is never below MAE.