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.

翻译：多步预测股票市场指数价格是金融领域的关键任务，在各类金融活动的决策中起着核心作用。然而，由于数据的随机性和波动性，预测结果往往不尽如人意。研究人员已做出多种尝试，这一探索过程仍在持续。受利用一维卷积神经网络进行特征提取以提升模型性能的卷积神经网络-长短期记忆（CNN-LSTM）网络启发，本研究探索使用胶囊网络（CapsNet）作为LSTM预测模型中的高级特征提取器，以增强多步预测效果。为此，引入了一种名为1D-CapsNet-LSTM的新型神经架构，该架构结合了一维CapsNet用于从一维时序数据中提取高级特征，以及LSTM层用于捕捉先前提取特征之间的时间依赖关系，并采用多输入多输出（MIMO）策略来维持不同时间步预测值之间的随机依赖性。基于多个真实股票市场指数（包括标准普尔500指数（S&P 500）、道琼斯工业平均指数（DJIA）、纳斯达克综合指数（IXIC）和纽约证券交易所指数（NYSE））对所提模型进行了评估，并与LSTM、循环神经网络（RNN）和CNN-LSTM等基线模型在多种评估指标上进行了比较。比较结果表明，1D-CapsNet-LSTM模型优于基线模型，在有效处理复杂预测任务方面具有巨大潜力。