Table 2.

A comparison of scale-dependent error measures

Scale-dependent measures	Definition	Error spread	Error weights
Mean square error (MSE)	Mean(Ot–Ft)2	Yes	Yes
Root mean squared error (RMSE)	√MSE	Yes	Yes
Mean absolute error (MAE)	Mean|(Ot–Ft)|	Yes	No
Median absolute error (MdAE)	Median|(Ot–Ft)|	–	–
Mean absolute scaled error (MASE)	Mean|(Qt)|	Yes	Yes

Notes: Error spread refers to the ability of the measure to capture an error that is not localized and not widely distributed in the dataset. Error weights refers to the ability of the measure to differentiate the error at different points in history.

Abbreviations: t, at a time; O, observation; F, forecast; Q:A, scaled error independent of scale of data.⁵⁹