1D-CapsNet-LSTM: A deep learning-based model for multi-step stock index forecasting

Multi -step stock index forecasting is vital in finance for informed decision -making. Current forecasting methods for this task frequently produce unsatisfactory results due to the inherent randomness and instability of the data, thereby underscoring the demand for advanced forecasting models. Given the superiority of the capsule network (CapsNet) over CNNs in various forecasting and classification tasks, this study investigates the potential of integrating a 1D CapsNet with an LSTM network for multi -step stock index forecasting. To this end, a hybrid 1DCapsNet-LSTM model is introduced, which utilizes a 1D CapsNet to generate high-level capsules from sequential data and an LSTM network to capture temporal dependencies. To maintain stochastic dependencies over different forecasting horizons, a multi -input multi -output (MIMO) strategy is employed. The model's performance is evaluated on real -world stock market indices, including S&P 500, DJIA, IXIC, and NYSE, and compared to baseline models, including LSTM, RNN, and CNN-LSTM, using metrics such as RMSE, MAE, MAPE, and TIC. The proposed 1D-CapsNet-LSTM model consistently outperforms the baseline models in two key aspects. It shows notable reductions in forecasting errors when compared to the baseline models. Additionally, it displays a slower rate of error escalation as forecast horizons lengthen, suggesting enhanced robustness for multi -step forecasting tasks.