Mean Absolute Error (MAE) / Mean Absolute Deviation (MAD)
The MAE is one of the widely used performance measures used in assessing the accuracy of a particular model. It is defined as the sum of all forecast errors for the horizon period spread across the number of forecasts. The forecast error for a given time t is defined as:
where x(t) is the actual value at time t and f(t) is the forecasted valued at time t. Hence, we can now derive the MAE as:
where the sum of the absolute values of all forecast errors for the horizon are spread across the forecast size.