Financial time series display inherent nonlinearity and high volatility, creating substantial challenges for accurate forecasting. Advancements in artificial intelligence have positioned deep learning as a critical tool for financial time series forecasting. However, conventional deep learning models often fail to accurately predict future trends in complex financial data due to inherent limitations. To address these challenges, this study introduces a WOA-BiLSTM-ARIMA hybrid forecasting model leveraging parameter optimization. Specifically, the whale optimization algorithm (WOA) optimizes hyperparameters for the Bidirectional Long Short-Term Memory (BiLSTM) network, overcoming parameter tuning challenges in conventional approaches. Due to its strong capacity for nonlinear feature extraction, BiLSTM excels at modeling nonlinear patterns in financial time series. To mitigate the shortcomings of BiLSTM in capturing linear patterns, the Autoregressive Integrated Moving Average (ARIMA) methodology is integrated. By exploiting ARIMA’s strengths in modeling linear features, the model refines BiLSTM’s prediction residuals, achieving more accurate and comprehensive financial time series forecasting. To validate the model’s effectiveness, this paper applies it to the prediction experiment of future spread data. Compared to classical models, WOA-BiLSTM-ARIMA achieves significant improvements across multiple evaluation metrics. The mean squared error (MSE) is reduced by an average of 30.5%, the mean absolute error (MAE) by 20.8%, and the mean absolute percentage error (MAPE) by 29.7%.

To address the challenges in forecasting crude oil and hot-rolled coil futures prices, the aim is to transcend the constraints of conventional approaches. This involves effectively predicting short-term price fluctuations, developing quantitative trading strategies, and modeling time series data. The goal is to enhance prediction accuracy and stability, thereby supporting decision-making and risk management in financial markets. A novel approach, the multi-dimensional fusion feature-enhanced (MDFFE) prediction method has been devised. Additionally, a data augmentation framework leveraging multi-dimensional feature engineering has been established. The technical indicators, volatility indicators, time features, and cross-variety linkage features are integrated to build a prediction system, and the lag feature design is used to prevent data leakage. In addition, a deep fusion model is constructed, which combines the temporal feature extraction ability of the convolution neural network with the nonlinear mapping advantage of an extreme gradient boosting tree. With the help of a three-layer convolution neural network structure and adaptive weight fusion strategy, an end-to-end prediction framework is constructed. Experimental results demonstrate that the MDFFE model excels in various metrics, including mean absolute error, root mean square error, mean absolute percentage error, coefficient of determination, and sum of squared errors. The mean absolute error reaches as low as 0.0068, while the coefficient of determination can be as high as 0.9970. In addition, the significance and stability of the model performance were verified by statistical methods such as a paired t-test and ANOVA analysis of variance. This MDFFE algorithm offers a robust and practical approach for predicting commodity futures prices. It holds significant theoretical and practical value in financial market forecasting, enhancing prediction accuracy and mitigating forecast volatility.

Financial Time Series Forecasting (TSF) remains a critical challenge in Artificial Intelligence (AI) due to the inherent complexity of financial data, characterized by strong non-linearity, dynamic non-stationarity, and multi-factor coupling. To address the performance limitations of Spiking Neural Networks (SNNs) caused by hyperparameter sensitivity, this study proposes an SNN model optimized by an Improved Cuckoo Search (ICS) algorithm (termed ICS-SNN). The ICS algorithm enhances global search capability through piecewise-mapping-based population initialization and introduces a dynamic discovery probability mechanism that adaptively increases with iteration rounds, thereby balancing exploration and exploitation. Applied to futures market price difference prediction, experimental results demonstrate that ICS-SNN achieves reductions of 13.82% in MAE, 21.27% in MSE, and 15.21% in MAPE, while improving the coefficient of determination (R²) from 0.9790 to 0.9822, compared to the baseline SNN. Furthermore, ICS-SNN significantly outperforms mainstream models such as Long Short-Term Memory (LSTM) and Backpropagation (BP) networks, reducing prediction errors by 10.8% (MAE) and 34.9% (MSE), respectively, without compromising computational efficiency. This work highlights that ICS-SNN provides a biologically plausible and computationally efficient framework for complex financial TSF, bridging the gap between neuromorphic principles and real-world financial analytics. The proposed method not only reduces manual intervention in hyperparameter tuning but also offers a scalable solution for high-frequency trading and multi-modal data fusion in future research.