Optimal Forecast Combination Based on Neural Networks for Time Series Forecasting

Research indicates that forecast combination is one of the most important and effective approaches for time series forecasting. The success of forecast combination depends on how well component models are selected and combination weights are determined. A forecast combination model resulting from a new neural networks-based linear ensemble framework (NNsLEF) is proposed in this study. The principle of the proposed framework adheres to three primary aspects. (a) Four kinds of neural network models, namely, back-propagation neural network, dynamic architecture for artificial neural network, Elman artificial neural network, and echo state network, are selected as component forecasting models. (b) An input-hidden selection heuristic (IHSH) is designed to determine the input-hidden neuron combination for each component neural network. (c) An in-sample training–validation pair-based neural network weighting (ITVPNNW) mechanism is studied to generate the associated combination weights. In particular, the four neural network models are applied to impart their superior performance to the combination approach while maintaining their diversity. Meanwhile, IHSH is investigated to improve the performance of each component neural network model by attempting to solve the familiar overfitting problem of networks. Lastly, the ITVPNNW mechanism is studied to search for a set of appropriate combination weights that will primarily affect the accuracy of the linear ensemble framework. Results: from experiments performed on eight time series data sets show that NNsLEF outperforms the four component neural network models and other well-recognized models.