Symmetric mean absolute percentage error

The symmetric mean absolute percentage error (SMAPE or sMAPE) is an accuracy measure based on percentage (or relative) errors. It is usually defined as follows:

${\text{SMAPE}}={\frac {2}{n}}\sum _{t=1}^{n}{\frac {\left|F_{t}-A_{t}\right|}{|A_{t}|+|F_{t}|}}$

where $A_{t}$ are the actual values and $F_{t}$ are the forecasted values. Note that if $A_{t}=F_{t}=0$, then term $t$ is undefined ($0/0$), and is usually ignored in the summation.

Explaining this equation in words, the absolute difference between A_t and F_t is divided by half the sum of absolute values of the actual value A_t and the forecast value F_t. The value of this calculation is summed for every fitted point t and divided again by the number of fitted points n.