  Surveys show that the mean absolute percentage error (MAPE) is the most
widely used measure of forecast accuracy in businesses and organizations. It is
however, biased: When used to select among competing prediction methods it
systematically selects those whose predictions are too low. This is not widely
discussed and so is not generally known among practitioners. We explain why
this happens. We investigate an alternative relative accuracy measure which
avoids this bias: the log of the accuracy ratio: log (prediction / actual).
Relative accuracy is particularly relevant if the scatter in the data grows as
the value of the variable grows (heteroscedasticity). We demonstrate using
simulations that for heteroscedastic data (modelled by a multiplicative error
factor) the proposed metric is far superior to MAPE for model selection.
Another use for accuracy measures is in fitting parameters to prediction
models. Minimum MAPE models do not predict a simple statistic and so
theoretical analysis is limited. We prove that when the proposed metric is used
instead, the resulting least squares regression model predicts the geometric
mean. This important property allows its theoretical properties to be
understood.
