Optimal selection of heterogeneous ensemble strategies of time series forecasting with multi-objective programming

The excellent generalization performance of time series ensemble forecasting depends on the accuracy and diversity of the individual models. In this paper, a heterogeneous ensemble forecasting model with multi-objective programming for nonlinear time series is proposed. Accordingly, an improved multi-objective particle swarm optimization (MOPSO) algorithm integrated with a dynamic heterogeneous mutation operator is designed. The nonlinear time series of the Baltic Dry Index (BDI) is selected as the forecasting object to train, validate and test the ensemble forecasting model established in this paper. To verify the superior forecasting performance of the proposed model, 20 forecasting models including statistical models, machine learning models, and optimization algorithm-based ensemble models are utilized and compared. The experimental results under different lead times revealed that: 1) the forecasting approach with multi-objective programming has excellent robustness and can effectively exert out-of-sample prediction under different lead times for nonlinear time series; 2) with the increase of lead time, the out-of-sample forecasting performance would gradually decrease for all models, and the precision of the ensemble forecasting model is better than that of the individual forecasting model; 3) the forecasting performance of the MOPSO with crowding distance (MOPSOCD)-based ensemble forecasting model is better than that of benchmark machine learning models and other optimal ensemble forecasting models in terms of the prediction accuracy and statistical test results.