BLS-QLSTM: a novel hybrid quantum neural network for stock index forecasting

With the rapid development of investment markets and the diversification of investment products, accurate prediction of stock price trends is particularly important for investors and researchers. The complexity of the stock market and the nonlinear characteristics of the data make it difficult for traditional prediction models to meet the demand for high-precision predictions. Although some existing machine learning methods and deep learning models perform well in certain cases, they still face limitations in handling high-dimensional data and time dependencies. To overcome these problems, we propose a novel hybrid quantum neural network model, BLS-QLSTM, which combines broad learning system (BLS) and quantum long short-term memory (QLSTM) network for chaotic time series prediction. Initially, the Cao method and mutual information approach are employed to determine the embedding dimensions and time delays, facilitating the reconstruction of the phase space of the original time series. Subsequently, BLS is introduced to enhance the feature representation of the data, while the gating structures within the long short-term memory (LSTM) network are replaced by variational quantum circuits (VQCs) to form QLSTM, thereby further improving prediction accuracy. BLS-QLSTM is a generalized prediction framework, which can be used to predict the price fluctuations of stocks based on historical data. Extensive experiments on three real stock indices—CSI 300, SSEC, and CSI 500—demonstrate that the BLS-QLSTM model outperforms traditional LSTM and QLSTM models in six performance evaluation metrics: the root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), coefficient of determination (R2), precision, and accuracy. The results validate the effectiveness and superiority of the BLS-QLSTM model in handling chaotic financial time series data and predicting stock index price trends.