in case of sales forecasting, errors are weighted by sales volume).. Effectively, this overcomes the 'infinite error' issue. Its formula is: Where is the weight, is a vector of the actual data and is the forecast or prediction. However, this effectively simplifies to a much simpler formula: Confusingly, sometimes when people refer to wMAPE they are talking about a different model in which the numerator and denominator of the wMAPE formula above are weighted again by another set of custom weights . Perhaps it would be more accurate to call this the double weighted MAPE (wwMAPE). Its formula is: Issues Although the concept of MAPE sounds very simple and convincing, it has major drawbacks in practical application, and there are many studies on shortcomings and misleading results from MAPE. It cannot be used if there are zero or close-to-zero values (which sometimes happens, for example in demand data) because there would be a division by zero or values of MAPE tending to infinity. For forecasts which are too low the percentage error cannot exceed 100%, but for forecasts which are too high there is no upper limit to the percentage error. MAPE puts a heavier penalty on negative errors, than on positive errors. As a consequence, when MAPE is used to compare the accuracy of prediction methods it is biased in that it will systematically select a method whose forecasts are too low. This little-known but serious issue can be overcome by using an accuracy measure based on the logarithm of the accuracy ratio (the ratio of the predicted to actual value), given by . This approach leads to superior statistical properties and also leads to predictions which can be interpreted in terms of the geometric mean. People often think the MAPE will be optimized at the median. But for example, a log normal has a median of where as it is MAPE optimized at . To overcome these issues with MAPE, there are some other measures proposed in literature: Mean Absolute Scaled Error (MASE) Symmetric Mean Absolute Percentage Error (sMAPE) Mean Directional Accuracy (MDA) Mean Arctangent Absolute Percentage Error (MAAPE): MAAPE can be considered a slope as an angle, while MAPE is a slope as a ratio. See also Least absolute deviations Mean absolute error Mean percentage error Symmetric mean absolute percentage error External links Mean Absolute Percentage Error for Regression Models Mean Absolute Percentage Error (MAPE) Errors on