A Combined Measure Based on Diversification and Accuracy Gains for Forecast Selection in Forecast Combination

Recent innovations in the field of forecast combination include integrated methods for forecast selection, weighting and regularization. The methods proposed in related articles first label whether or not forecasters should remain in the selection using information criteria from statistical learning theory. Depending on the selection status, the optimal weights of all forecasters in the sample are then used as baseline to shrink the weights either toward zero or the mean, with the degree of regularization determining the final selection of forecasters. In this paper, we propose a new information criterion reflecting the importance of diversification and accuracy gains in the selection of forecasters for integrated methods. In an iterative procedure motivated by forward feature selection, each forecaster is selected sequentially, while at each step the increase in accuracy and diversification due to the addition of a forecaster to the previous selection is measured. To quantify the increase in diversity, the multiple correlation coefficient is used, which captures the correlation between the previously selected forecasters and a candidate, where the lower the correlation between the candidate and the selection, the higher the gain in diversity for the combination. For the accuracy increase, the accuracy achieved by optimal weight combinations with the previously selected forecasters is compared with the accuracy after adding a candidate. A hyperparameter further enables the trade-off between accuracy and diversification gains in the criterion. Simulation-based studies show scenarios in which our presented information criterion achieves advantages in out-of-sample prediction accuracy over previous criteria for selection by accounting for accuracy and diversification gains.