Population forecast accuracy: does the choice of summary measure of error matter?

Abstract

Population projections are judged primarily by their accuracy. The most commonly used measure for the precision component of accuracy is the mean absolute percent error (MAPE). Recently, the MAPE has been criticized for overstating forecast error and other error measures have been proposed. This study compares the MAPE with two alternative measures of forecast error, the Median APE and an M-estimator. In addition, the paper also investigates forecast bias. The analysis extends previous studies of forecast error by examining a wide range of trend extrapolation techniques using a dataset that spans a century for a large sample of counties in the US. The main objective is to determine whether the choice of summary measure of error makes a difference from a practitioner’s standpoint. The paper finds that the MAPE indeed produces error values that exceed the robust measures. However, except for situations where extreme outliers rendered the MAPE meaningless, and which are rare in real world applications, there was not a single instance where using an alternative summary measure of error would have led to a fundamentally different evaluation of the projections. Moreover, where differences existed, it was not always clear that the values and patterns provided by the robust measures were necessarily more correct than those obtained with the MAPE. While research into refinements and alternatives to the MAPE and mean algebraic percent error are worthwhile, consideration of additional evaluation procedures that go beyond a single criterion might provide more benefits to producers and users of population forecasts. Copyright Springer Science+Business Media B.V. 2007Forecast accuracy, MAPE, Error measures, Population projections,

MAPE-R: a rescaled measure of accuracy for cross-sectional subnational population forecasts

“…For the MAPE, extreme values occur only at the high end because it is typically based on a rightskewed distribution of absolute percentage errors bounded on the left by zero and unbounded on the right. In a comprehensive analysis of county-level projections, the MAPE was on average higher by about 30-40% than robust measures of central tendency for most methods and projection horizons (Rayer 2007).…”

“…Of the preceding measures, MAPE is most commonly used to evaluate crosssectional, subnational forecasts (Ahlburg 1992(Ahlburg , 1995Campbell 2002;Hyndman and Koehler 2006;Isserman 1977;Miller 2001;Murdock et al 1984;Rayer 2007;Sink 1997;Smith 1987;Smith andSincich 1990, 1992;Smith et al 2001;Tayman et al 1998;Wilson 2007). It is a signal of MAPE's ubiquity that it is often found in software packages such as Autobox, ezForecaster, Nostradamus, SAS, and SmartForecast.…”

“…MAPE is a suitable measure in many instances (Campbell 2002;Rayer 2007). However, it is often based on a right skewed distribution of APEs, which pulls the average error upward and understates the forecast accuracy of the bulk of the observations.…”

Rainfall forecasting models using focused time-delay neural networks

“…The most common measure of accuracy is the Mean Absolute Percent Error (MAPE) [14]. Although several authors [14] have asserted that the Symmetrical Mean Absolute Percent Error (SMAPE) gives a better measurement of the accuracy, [15] has found out that if we consider positive and negative errors, SMAPE is far from symmetric, especially where these errors have large absolute values. Therefore, in this paper, MAPE has been adopted and it is given by: (2) A t = Observed value or true value or actual value.…”

Comprehensive Management and Modeling of Water Quantities: Utilizing an Existing Watershed Model for Comprehensive Water Management and Planning, and Optimal Design of Outlet Control Structures for Ecological Detention Ponds

“…Volumetric error for the entire simulation period (PVE) was used for volumetric accuracy over a long time scale. PVE, MAAVE, and MDARVE are calculated using variations on the equation for mean absolute percent error, a measure of accuracy frequently used to evaluate crosssectional forecasts (Ahlburg 1995;Hyndman and Koehler 2006;Rayer 2007 Table 3.1 show high accuracy at the entire period scale, acceptable accuracy at the annual scale (within the 15-20% acceptability ranges reported by Apse et al 2008), yet relatively low accuracy at the daily scale. Given the direct correlation between input and output of a modeled system, these results also suggest the possibility that the precipitation input to the hydrology model might be problematic with respect to both timing of precipitation events and precipitation depths.…”