Optimal sub-models selection algorithm for combination forecasting model

•Optimal sub-models are selected for combination forecasting model.•A selection criterion of Max-Linear-Relevance and Min-Linear-Redundancy is proposed.•Redundancy removing linear mutual information is measured to improve the accuracy.•Monthly time series is forecasted by a novel combination model.•The results confirm the applicability and superiority of the combination model.

It has been widely demonstrated in forecasting that combining forecasts can improve the forecast performance compared to individual forecasts. However, how to select the optimal sub-models from all the available models is a difficult problem in combination forecasting model. Consider that the redundancy information among the selected sub-models will reduce the performance of the combination forecasting model, it is advocated to select a sub-model only if it contributes to the redundancy removing mutual information between the outputs of the selected sub-models and the actual outputs. As linear combination method is promising and popular in the field of combination forecast, a novel Max-Linear-Relevance and Min-Linear-Redundancy based selection algorithm is proposed in this paper. The proposed selection algorithm provides a theoretical approach for the optimal sub-models selection, and tries to compute the redundancy removing linear mutual information between the outputs of the selected sub-models and the actual outputs. Three monthly time series from DataMarket are used as illustrative examples to evaluate the forecasting. As a result of the implementation, it is seen that the proposed combination forecasting model produces better forecasts than those produced by other models.