Multi-step forecasting of stock market index prices is a crucial task in the financial sector, playing a pivotal role in decision-making across various financial activities. However, forecasting results are often unsatisfactory owing to the stochastic and volatile nature of the data. Researchers have made various attempts, and this process is ongoing. Inspired by convolutional neural network long short-term memory (CNN-LSTM) networks that utilize a 1D CNN for feature extraction to boost model performance, this study explores the use of a capsule network (CapsNet) as an advanced feature extractor in an LSTM-based forecasting model to enhance multi-step predictions. To this end, a novel neural architecture called 1D-CapsNet-LSTM was introduced, which combines a 1D CapsNet to extract high-level features from 1D sequential data and an LSTM layer to capture the temporal dependencies between the previously extracted features and uses a multi-input multi-output (MIMO) strategy to maintain the stochastic dependencies between the predicted values at different time steps. The proposed model was evaluated based on several real-world stock market indices, including Standard & Poor's 500 (S&P 500), Dow Jones Industrial Average (DJIA), Nasdaq Composite Index (IXIC), and New York Stock Exchange (NYSE), and was compared with baseline models such as LSTM, recurrent neural network (RNN), and CNN-LSTM in terms of various evaluation metrics. The comparison results suggest that the 1D-CapsNet-LSTM model outperforms the baseline models and has immense potential for the effective handling of complex prediction tasks.

一项基于1D-CapsNet-LSTM模型的研究探索了如何提高多步预测，以应对金融部门中数据的随机和变动性所导致的不理想预测结果，并通过实际股票市场指数的比较评估表明，该模型优于基准模型，具有处理复杂预测任务的巨大潜力。

1D-CapsNet-LSTM：多步股票指数预测的深度学习模型