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A new accuracy measure based on bounded relative error for time series forecasting

Chen, Chao; Twycross, Jamie; Garibaldi, Jonathan M.



Zhong-Ke Gao


Many accuracy measures have been proposed in the past for time series forecasting comparisons. However, many of these measures suffer from one or more issues such as poor resistance to outliers and scale dependence. In this paper, while summarising commonly used accuracy measures, a special review is made on the symmetric mean absolute percentage error. Moreover, a new accuracy measure called the Unscaled Mean Bounded Relative Absolute Error (UMBRAE), which combines the best features of various alternative measures, is proposed to address the common issues of existing measures. A comparative evaluation on the proposed and related measures has been made with both synthetic and real-world data. The results indicate that the proposed measure, with user selectable benchmark, performs as well as or better than other measures on selected criteria. Though it has been commonly accepted that there is no single best accuracy measure, we suggest that UMBRAE could be a good choice to evaluate forecasting methods, especially for cases where measures based on geometric mean of relative errors, such as the geometric mean relative absolute error, are preferred.


Chen, C., Twycross, J., & Garibaldi, J. M. (2017). A new accuracy measure based on bounded relative error for time series forecasting. PLoS ONE, 12(3), Article e0174202.

Journal Article Type Article
Acceptance Date Mar 6, 2017
Online Publication Date Mar 24, 2017
Publication Date Mar 24, 2017
Deposit Date Mar 28, 2017
Publicly Available Date Mar 28, 2017
Journal PLoS ONE
Electronic ISSN 1932-6203
Publisher Public Library of Science
Peer Reviewed Peer Reviewed
Volume 12
Issue 3
Article Number e0174202
Keywords Forecasting performance; Accuracy measure; Relative measure; Bounded error; Unscaled mean bounded relative absolute error
Public URL
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