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Title: Distance measures implied by forecast evaluation criteria Authors:  Robert Kunst - Institute for Advanced Studies (Austria) [presenting]
Abstract: Traditional moment-based measures of predictive accuracy, such as the mean squared error (MSE) and the mean absolute error (MAE), assess the precision of forecasts in the framework of widely accepted metric spaces. Many researchers, however, pursue more complex targets, such as the mean absolute percentage error (MAPE), often motivated by an attempt to reduce the influence of scaling. We argue that most of these measures are characterized by asymmetry in the sense that moving the actual closer to the forecast has a quite different effect from moving the forecast, and also by non-convexity of the implied environments. For some of them, even paradox effects can be generated, such as a deterioration of accuracy as the actual approaches the forecast. We illustrate all effects using contour plots and other visualization tools. Our warning against the careless usage of relative asymmetric criteria adds to the recent argument that these criteria may be hampered by the non-existence of moments.