دانلود رایگان مقاله مقیاس درصد خطای مطلق برای پیش بینی تقاضای متناوب

abstract

The mean absolute percentage error (MAPE) is one of the most widely used measures of forecast accuracy, due to its advantages of scale-independency and interpretability. However, MAPE has the significant disadvantage that it produces infinite or undefined values for zero or close-to-zero actual values. In order to address this issue in MAPE, we propose a new measure of forecast accuracy called the mean arctangent absolute percentage error (MAAPE). MAAPE has been developed through looking at MAPE from a different angle. In essence, MAAPE is a slope as an angle, while MAPE is a slope as a ratio, considering a triangle with adjacent and opposite sides that are equal to an actual value and the difference between the actual and forecast values, respectively. MAAPE inherently preserves the philosophy of MAPE, overcoming the problem of division by zero by using bounded influences for outliers in a fundamental manner through considering the ratio as an angle instead of a slope. The theoretical properties of MAAPE are investigated, and the practical advantages are demonstrated using both simulated and real-life data. © 2016 The Authors. Published by Elsevier B.V. on behalf of International Institute of Forecasters. This is an open access article under the CC BY license.

6. Conclusion

We have developed a novel accuracy measure called the mean arctangent absolute percentage error (MAAPE) by modifying MAPE, which is the most popular accuracy measure. As the proposed measure is a MAPE that has been transformed using the arctangent (inverse tangent) function, it inherently preserves the advantages of MAPE; thus, MAAPE is scale-independent, can be interpreted intuitively as an absolute percentage error, and is simple to calculate. In addition, the bounded range of the arctangent function allows the MAAPE to overcome the MAPE’s limitation of going to infinity as the actual value goes to zero. We visualized MAAPE in order to demonstrate its advantages over MAPE, and proved that AAPE is a concave-down function for F > 2A > 0, which enables MAAPE to obtain a more balanced penalty between positive and negative errors than MAPE, although the penalty function of MAAPE remains asymmetric. MAAPE is also more robust than MAPE due to the bounded influences of outliers; thus, MAAPE can be particularly useful when extremely large errors are due to mistaken or incorrect observations. However, if extremely large errors are considered as having important business implications, rather than merely being due to mistaken observations, MAAPE is not recommended. Via a simulation, we have also compared APE and AAPE based on their optimal point predictions under three strategies, and have demonstrated that MAAPE is less biased than MAPE. Our applications to real and simulated data have also demonstrated the effectiveness of MAAPE in practice.