Stock Market Index Prediction Using CEEMDAN-LSTM-BPNN-Decomposition Ensemble Model

This study investigates the forecasting of the Deutscher Aktienindex (DAX) market index by addressing the nonlinear and nonstationary nature of financial time series data using the CEEMDAN decomposition method. The CEEMDAN technique is used to decompose the time series into intrinsic mode functions (IMFs) and residuals, which are classified into low-frequency (LF), medium-frequency (MF), and high-frequency (HF) components. Long short-term memory (LSTM) networks are applied to the MF and HF components, while the backpropagation neural network (BPNN) is utilized for the LF components, resulting in a robust hybrid model termed CEEMDAN-LSTM-BPNN. To evaluate the performance of the proposed model, we compare it against several benchmark models, including ARIMA, RNN, LSTM, GRU, BIGRU, BILSTM, BPNN, CEEMDAN-LSTM, CEEMDAN-GRU, CEEMDAN-BPNN, and CEEMDAN-GRU-BPNN, across different training–testing splits (70% training/30% testing, 80% training/20% testing, and 90% training/10% testing). The model’s predictive accuracy is measured using six metrics: root mean squared error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), symmetric mean absolute percentage error (SMAPE), root mean squared logarithmic error (RMSLE), and R-squared. To further assess model performance, we conduct the Diebold–Mariano (DM) test to compare forecast accuracy between the proposed and benchmark models and the model confidence set (MCS) test to evaluate the statistical significance of the improvement. The results demonstrate that the CEEMDAN-LSTM-BPNN model significantly outperforms other methods in terms of accuracy, with the DM and MCS tests confirming the superiority of the proposed model across multiple evaluation metrics. The findings highlight the importance of combining advanced decomposition methods and deep learning models for financial forecasting. This research contributes to the development of more accurate forecasting techniques, offering valuable implications for financial decision-making and risk management.