Mean Absolute Percentage Error (MAPE)
The MAPE is very similar to the MAE, however, it gives us a more clear indication of the significance of the size of the forecast error with respect to the actual value (i.e. is the error very large compared to the actual value?). We can assess this by taking the error as a percentage of the actual value, hence, the percentage error is defined as:
where e(t) is the error at time t and x(t) is the actual value at time t. Now that we can tally each PE across the horizon frame, we can now sum these percentages and spread them across the number of time points to calculate the MAPE:
so we are able to get an average percentage error for a model. The MAPE is the most widely used measure to assess the accuracy of a given model because of its innate ability to determine how serious the error is in relevance to the actual values. The lower the MAPE, the more accurate the model.