Time series forecasting based on a novel ensemble-based network and variational mode decomposition

Statistical and computational intelligence methods contain weaknesses in handling nonlinearity, non-stationarity and noise. This research develops a novel decomposition ensemble-based network named VMD-DENetwork for time series forecasting over different horizons. A robust decomposition technique called variational mode decomposition (VMD) is applied to decompose the input sequence into several intrinsic modes in a non-recursive manner. The optimal number of intrinsic modes is selected based on a comprehensive analysis to ensure the stability of the framework. The proposed DENetwork is developed based on stacking architecture and constitutes heterogeneous learners to model the nonlinear and complex relationships. It combines a convolutional neural network, long short-term memory and an extreme learning machine. A firefly optimization algorithm is adopted for utilizing hyperparameters of the proposed model to enhance the efficiency of VMD-DENetwork. The forecasting performance is verified by using six real-world data sets from the New York Mercantile and International Petroleum Exchange. The final obtained results are compared with several peer-advanced algorithms using the root mean squared error (RMSE), mean absolute error (MAE), Theil inequality coefficient (TIC) and correlation coefficient (R) metrics. The experimental results confirm that the proposed model demonstrates outstanding prediction performance. The employed optimization algorithm is compared with three frequently used bio-inspired optimization algorithms, and their performance is tested using standard CEC benchmarks.