| Citation: | ZHU S L，CHEN H Y，ZHANG Q，et al. Decomposition of logarithm mean square error of weighted geometric mean combined forecasting method[J]. Journal of Beijing University of Aeronautics and Astronautics，2025，51（10）：3535-3546 （in Chinese） doi: 10.13700/j.bh.1001-5965.2023.0553
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In addition to proposing the ideas of logarithm mean deviation, logarithm explanatory power coefficient, logarithm deviation error variance, and diversity measure of prediction methods, the nonlinear weighted geometric mean combination prediction model was introduced to the logarithm mean square error. On this basis, the logarithm mean square error of the combined prediction is decomposed into three components: the logarithm mean error, the logarithm variance due to the insufficient explanatory power of the model and the logarithm deviation variance based on the logarithm explanatory power coefficient. The source of the logarithm mean square error is discussed theoretically. Simultaneously, the logarithm mean square error of combination forecasting is broken down into the weighted average of the logarithm mean square error of single forecasting methods and the weighted average of diversity measure of forecasting methods. This yields the helpful conclusion that increasing the accuracy of single forecasting methods and the diversity measure level of forecasting methods helps to lower the logarithm mean square error of weighted geometric mean combined forecasting methods. A case study analyzed the influence of the diversity measure of each component and single forecasting method on the logarithm mean square error of combined forecasting.
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