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Accurately measuring a population and its attributes at past, present, and future points in time has been of great interest to demographers. Within discussions of forecast accuracy, demographers have often been criticized for their inaccurate prognostications of the future. Discussions of methods and data are usually at the centre of these criticisms, along with suggestions for providing an idea of forecast uncertainty. The measures used to evaluate the accuracy of forecasts also have received attention and while accuracy is not the only criterion advocated for evaluating demographic forecasts, it is generally acknowledged to be the most important. In this paper, we continue the discussion of measures of forecast accuracy by concentrating on a rescaled version of a measure that is arguably the one used most often in evaluating cross-sectional, subnational forecasts, Mean Absolute Percent Error (MAPE). The rescaled version, MAPE-R, has not had the benefit of a major empirical test, which is the central focus of this paper. We do this by comparing 10-year population forecasts for U.S. counties to 2000 census counts. We find that the MAPE-R offers a significantly more meaningful representation of average error than MAPE in the presence of substantial outlying errors, and we provide guidelines for its implementation.

Mean absolute percentage error (MAPE), the measure most often used for evaluating subnational demographic estimates, is not always valid. We describe guidelines for determining when MAPE is valid. Applying them to case study data, we find that MAPE understates accuracy because it is unduly influenced by outliers. To overcome this problem, we calculate a transformed MAPE (MAPET) using a modified Box-Cox method. Because MAPE-T is not in the same scale as the untransformed absolute percentage errors, we provide a procedure for calculating MAPE-R, a measure in the same scale as the original observations. We argue that MAPE-R is a more appropriate summary measure of average absolute percentage error when the guidelines indicate that MAPE is not valid.

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