Measures of Model Performance Based On the Log Accuracy Ratio

Abstract

Quantitative assessment of modeling and forecasting of continuous quantities uses a variety of approaches. We review existing literature describing metrics for forecast accuracy and bias, concentrating on those based on relative errors and percentage errors. Of these accuracy metrics, the mean absolute percentage error (MAPE) is one of the most common across many fields and has been widely applied in recent space science literature and we highlight the benefits and drawbacks of MAPE and proposed alternatives. We then introduce the log accuracy ratio and derive from it two metrics: the median symmetric accuracy and the symmetric signed percentage bias. Robust methods for estimating the spread of a multiplicative linear model using the log accuracy ratio are also presented. The developed metrics are shown to be easy to interpret, robust, and to mitigate the key drawbacks of their more widely used counterparts based on relative errors and percentage errors. Their use is illustrated with radiation belt electron flux modeling examples.Key PointsThe median symmetric accuracy and symmetric signed percentage bias are introduced to address some drawbacks of current metricsThe spread of a multiplicative linear model can be robustly estimated using the log accuracy ratioThe properties of the median symmetric accuracy and the symmetric signed percentage bias are demonstrated on radiation belt examples