Trade-off between the global and extreme bias: An improved optimization approach in forecast combination

Forecast combination is an important branch of ensemble learning and it is also an effective tool to improve the forecasting accuracy. The global bias estimation method of the forecaster has a mature application in various aspects. For instance, ensemble model’s in-sample mean square error is a main objective of traditional weight optimization approaches in forecast combination. However, due to the risk of “overfitting”, the minimization of the training error does not necessarily imply a corresponding minimization of the generalization error. Therefore, to increase diversity of optimization objectives, reduce risk of weight overfitting, and control tail error of ensemble model, this paper defines a metric to capture extreme bias of combined forecaster. Furthermore, a novel objective function is proposed which can make a trade-off between the global and extreme bias to achieve optimal weights. Specifically, the particle swarm optimization method is introduced to achieve the optimal combination weights. The experimental results on gold price and oil price data demonstrate that the proposed forecast combination approach can efficiently reduce overfitting risk and improve the generalization ability, outperforming simple averaging, optimal weight method and other benchmark models. © 2023 Systems Engineering Society of China. All rights reserved.