A high frequency stock price prediction model based on Hermite basis expansion and LSTM neural network

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Based on Hermite basis function expansion and ensemble learning, an improved LSTM neural network method is proposed in this paper. The proposed method can be used for high frequency stock price prediction. Considering the characteristics of high frequency time series data such as high dimensionality, large noise and instability, etc. In this paper, the function information extracted from the Hermite basis function expansion is used to predict the residual sequence predicted by the LSTM neural network. Since the components of the function feature vector are unknown to the underlying model structure of the response variable, the proposed method is processed by Bagging framework. It not only captures the structure of the latent model, but also balances the variance and bias of the model. In addition, the number of prediction periods of the LSTM neural network is a hyperparameter, and the model averaging method based on distance covariance weighting is considered in this paper for optimization. The results of actual data analysis show that the proposed method can effectively optimize the prediction accuracy of the LSTM neural network, and has certain robustness. Finally, on the one hand, this optimization framework can be used to improve other time series prediction models. On the other hand, the proposed method can play an important role in forecasting problems such as daily average temperature prediction and real-time monitoring of atmospheric environmental quality.