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The prediction research of the stock market prices is of great significance. Based on the secondary decomposition techniques of variational mode decomposition (VMD) and ensemble empirical mode decomposition (EEMD), this paper constructs a new hybrid prediction model by combining with extreme learning machine (ELM) optimized by the differential evolution (DE) algorithm. The hybrid model applies VMD technology to the original stock index price sequence to obtain different modal components and the residual item, then applies EEMD technology to the residual item, and then superimposes the prediction results of the DE-ELM model for each modal component and the residual item to obtain the final prediction results. In order to verify the validity of the model, this paper constructs a series of benchmark models and, respectively, tests the samples of the S&P 500 index and the HS300 index by one-step, three-step, and five-step forward forecasting. The empirical results show that the hybrid model proposed in this paper achieves the best prediction performance in all prediction scenarios, which indicates that the modeling idea focusing on the residual term effectively improves the prediction performance of the model. In addition, the prediction effect of the model combined with the decomposition technology is superior to the single DE-ELM model, where the secondary decomposition technique has a significant decomposition advantage compared to the single decomposition technique.

mathematical problems in engineering

Multistep-Ahead Stock Price Forecasting Based on Secondary Decomposition Technique and Extreme Learning Machine Optimized by the Differential Evolution Algorithm