Using the R-MAPE index as a resistant measure of forecast accuracy

Juan José Montaño Moreno · Alfonso Luis Palmer Pol · Albert Sesé · Berta Cajal Blasco

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Forecasting Techniques and Applications Time Series Analysis and Forecasting Statistical and numerical algorithms

Abstract

BACKGROUND: The mean absolute percentage error (MAPE) is probably the most widely used goodness-of-fit measure. However, it does not meet the validity criterion due to the fact that the distribution of the absolute percentage errors is usually skewed to the right, with the presence of outlier values. In these cases, MAPE overstates the corresponding population parameter. In this study, we propose an alternative index, called Resistant MAPE or R-MAPE based on the calculation of the Huber M-estimator, which allows overcoming the aforementioned limitation. METHOD: The results derived from the application of Artificial Neural Network (ANN) and Autoregressive Integrated Moving Average (ARIMA) models are used to forecast a time series. RESULTS: The arithmetic mean, MAPE, overstates the corresponding population parameter, unlike R-MAPE, on a set of error distributions with a statistically significant right skew, as well as outlier values. CONCLUSIONS: Our results suggest that R-MAPE represents a suitable alternative measure of forecast accuracy, due to the fact that it provides a valid assessment of forecast accuracy compared to MAPE.

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References

1977Time Series Analysis: Forecasting and Control 2011Reliability and Validity Assessment 1993Forecasting methods and applications 1992Error measures for generalizing about forecasting methods: Empirical comparisons 1996Designing a neural network for forecasting financial and economic time series 1982Industrial and business forecasting methods 1991Time series forecasting using neural networks vs. Box- Jenkins methodology

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