In search of the ideal measure of accuracy for subnational demographic forecasts

We examine nonlinear transformations of the forecast error distribution in hopes of finding a summary error measure that is not prone to an upward bia s and uses most of the information about that error. MAPE, the current stan dard for measuring error, often overstates the error represented by most of the values because the distribution underlying the MAPE is right skewed an d truncated at zero. Using a modification to the Box-Cox family of nonlinea r transformations, we transform these skewed forecast error distributions i nto symmetrical distributions for a wide range of size and growth rate cond itions. We verify this symmetry using graphical devices and statistical tes ts; examine the transformed errors to determine if reexpression to the scal e of the untransformed errors is necessary; and develop and implement a pro cedure for the re-expression. The MAPE-R developed by our process is lower than the MAPE based on the untransformed errors and is more consistent with a robust estimator of location.