关键词: 经验模态分解, 模态混叠, 极限学习机, 粒子群优化, 股价预测

Abstract: With the rapid development of the social economy, the environmental economy is increasingly complex. Stocks, gold, and other financial product trading all have captured the attention of more and more investors. The market behaviors cover all information, and have a high degree of randomness and volatility, so investing stocks becomes a high risk, high return of economic behavior. As one of the main markets, China’s stock market plays a key role in the global financial market. The accurate prediction of the stock index not only attracts the attention of investors and many scholars but also has great significance to the government regulatory authorities.
At present, the study of the stock index price prediction method has achieved a lot of research results, mainly including the time series analysis method, machine learning, deep learning, and reinforcement learning algorithm. These methods have had a good effect on the stock index prediction. However, the stock market is a complex and nonlinear dynamic system, so the above single prediction model is powerless to explain the information contained in stock index data. Before predicting the stock price, it is necessary to stabilize it to ensure that the prediction model can obtain better prediction accuracy. Traditional stabilization algorithms, such as the differential method, cause the loss of information about the original data. In consideration of this problem, some scholars have used the multi-scale decomposition algorithm to stabilize the stock index price, and achieved good results.
To avoid error accumulation in the single model forecasting process, this paper adopts a hybrid model combining the improved empirical mode decomposition algorithm(HF-EMD) and the extreme learning machine(ELM) optimized by the particle swarm algorithm(PSO) for the short-term prediction of stock index price. Firstly, in terms of data preprocessing, this paper adds the high-frequency harmonic signal to improve EMD. Under the aid of high-frequency harmonic, the extracted signal component is more stable, effectively reducing the influence of noise signal in the stock index data. Therefore, the original stock index data is decomposed by the HF-EMD algorithm to obtain several stable mode components.
Then, considering the defects of the traditional neural network model, such as slow convergence speed, being easy to get into local optimum, and too many parameters, this paper uses the ELM model to predict the stock index data, since it has better calculation speed and prediction accuracy. In the process of using the ELM model to predict the stock index price, because the initialization weight and threshold are random, they usually only adjust the number of neurons in the hidden layer, which can shorten the parameter adjustment time and effectively meet the requirements of real-time prediction of the stock index price. However, since the initialization weights and thresholds of the ELM are random, the forecasting results are unstable. In this paper, the PSO algorithm is used to optimize the ELM model. It can reduce the deviation of the network model output and improve the stability and robustness of the model. Therefore, the PSO-ELM model is used to predict the decomposed components, and the predicted value of each component is added up to obtain the total predicted value of the stock index price.
Based on the four sets of the representative stock index data such as SSEC and Heng Sheng Index, we show that the hybrid model proposed in this paper can effectively grasp the variation law of stock index data and has a good prediction effect. This project has been supported by the National Natural Science Foundation of China under Grant 51877161.

Key words: EMD, mode mixing, ELM, PSO, stock price forecast