Forecast metrics turn a set of errors into a number that can be compared across methods.
The error for each period is the actual value minus the forecast.
No single metric suits every purpose, so the choice should follow the cost of being wrong.
MAE is the average size of the errors, in the units of the data, and is easy to explain.
RMSE squares errors before averaging, so one large miss weighs heavily, which suits cases where big misses are costly.
MAPE averages percentage errors, which makes it easy to compare series of different sizes.
MAPE cannot be calculated when an actual value is 0 and explodes when actual values are small.
It is also lopsided, since a forecast that runs low can miss by at most 100% while one that runs high has no limit.
MASE scales errors by those of a naive forecast, such as last period's value, which avoids dividing by small actuals.
A MASE below 1 means the method beats the naive forecast on average.
Bias, the average signed error, shows whether forecasts run consistently high or low.
A forecast with low error but a steady bias can still cause shortages or waste.
Prediction intervals need their own checks, such as whether 95% intervals contain about 95% of actual values.
In practice teams report a metric free of units, such as MASE, alongside a business measure such as units short.
The usual mistake is comparing methods on MAPE when many actual values are small, which rewards forecasts that run low.