The Mean Absolute Error (MAE) is a point forecast accuracy measure. In the forecasting literature, Mean Absolute Deviation (MAD) is used interchangeably.
For forecasts $\hat{y}_1, \dots, \hat{y}_n$ and corresponding actuals $y_1, \dots, y_n$, the MAE is defined as
$$\text{MAE}:=\frac{1}{n}\sum_{i=1}^n|\hat{y}_i-y_i|.$$
The MAE is not scale free, thus it is hard to compare across time series on different scales. The mase offers an alternative.
Note that the expected MAE is minimized by the median of the future distribution, not its mean. Therefore, optimizing forecasting methods to minimize the MAE may yield biased forecasts if the future distribution is asymmetric. This effect is most pronounced for count-data and intermittent-time-series.
Alternatives to the MAE as a point forecast accuracy measure include the mase, the mape and the mse.
