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. 2012 May 8;5:381–389. doi: 10.2147/IJGM.S31079

Table 1.

List of forecast accuracy measures

B. Scale-dependent measures

  1. Mean square error (MSE)

  2. Root mean squared error (RMSE)

  3. Mean absolute error (MAE)

  4. Median absolute error (MdAE)

C. Percentage error measures

  1. Mean absolute percentage error (MAPE)

  2. Median absolute percentage error (MdAPE)

  3. Root mean square percentage error (RMSPE)

  4. Root median square percentage error (RMdSPE)

D. Relative error measuresa

  1. Mean relative absolute error (MRAE)

  2. Median relative absolute error (MdRAE)

  3. Geometric mean relative absolute error (GMRAE)

Notes:

a

The relative error measures are obtained by dividing each forecast error by the error obtained using a benchmark procedure, such as the grand mean (ie, a reference or benchmark average, which could be determined by taking the average of all averages of several subsamples). The accuracy measures of GMRAE and MDRAE, for instance, were presented by Armstrong and Collopy (1992)61 and Fildes (1992).86 Even though both reports recommend the use of forecast accuracy measures based on relative errors, they express these measures in different and complicated forms. Hyndman and Koehler (2006)59 have however noted that these relative error methods could have some deficiencies that are associated with the difficulty of dealing with extremely small benchmark forecast error measures, resulting in the relative error measures having infinite variances.