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In this paper, we propose a novel hybrid model that extends prior work involving ensemble empirical mode decomposition (EEMD) by using fuzzy entropy and extreme learning machine (ELM) methods. We demonstrate this 3-stage model by applying it to forecast carbon futures prices which are characterized by chaos and complexity. First, we employ the EEMD method to decompose carbon futures prices into a couple of intrinsic mode functions (IMFs) and one residue. Second, the fuzzy entropy and K-means clustering methods are used to reconstruct the IMFs and the residue to obtain three reconstructed components, specifically a high frequency series, a low frequency series, and a trend series. Third, the ARMA model is implemented for the stationary high and low frequency series, while the extreme learning machine (ELM) model is utilized for the non-stationary trend series. Finally, all the component forecasts are aggregated to form final forecasts of the carbon price for each model. The empirical results show that the proposed reconstruction algorithm can bring more than 40% improvement in prediction accuracy compared to the traditional fine-to-coarse reconstruction algorithm under the same forecasting framework. The hybrid forecasting model proposed in this paper also well captures the direction of the price changes, with strong and robust forecasting ability, which is significantly better than the single forecasting models and the other hybrid forecasting models. [ABSTRACT FROM AUTHOR]

As stock data is characterized by highly noisy and non-stationary, stock price prediction is regarded as a knotty problem. In this paper, we propose new two-stage ensemble models by combining empirical mode decomposition (EMD) (or variational mode decomposition (VMD)), extreme learning machine (ELM) and improved harmony search (IHS) algorithm for stock price prediction, which are respectively named EMD–ELM–IHS and VMD–ELM–IHS. Furthermore, to demonstrate the efficiency and performance of the proposed models, the results were compared with those obtained by other methods, including EMD based ELM (EMD–ELM), VMD based ELM (VMD–ELM), autoregressive integrated moving average (ARIMA), ELM, multi-layer perception (MLP), support vector regression (SVR), and long short-term memory (LSTM) models. The results show that the proposed models have superior performance in terms of its accuracy and stability as compared to the other models. Also, we find that the sizes of sliding window and training set have a significant impact on the predictive performance. [ABSTRACT FROM AUTHOR]