Developing a deep learning framework with two-stage feature selection for multivariate financial time series forecasting

•Propose a novel feature selection method for dimensionality reduction.•Develop an improved multi-objective optimization algorithm.•Establish a forecasting framework based on feature selection and deep learning.•Experimental results demonstrate the effectiveness of the framework. Intelligent financial forecasting modeling plays an important role in facilitating investment-related decision-making activities in financial markets. However, accurate multivariate financial time series forecasting remains a challenge due to its complex nonlinear pattern. Aiming to fill the gap in the field, a novel forecasting framework, based on a two-stage feature selection model, deep learning model, and error correction model, is presented in this study, aiming at effectively capturing the nonlinearity inherent in multivariate financial time series. Concretely, the proposed two-stage feature selection model is utilized to determine the optimal feature set to further improve the generalization of the proposed deep learning model based on three deep learning units. Meanwhile, the error correction model is used to correct the forecasts and improve the accuracy further. To validate the performance of the forecasting framework, the case studies and the corresponding sensitivity analysis are carried out, consequently demonstrating its superiority, as compared to 16 benchmarks considered.