In the domain of financial markets, deep learning techniques have emerged as a significant tool for the development of investment strategies. The present study investigates the potential of time series forecasting (TSF) in financial application scenarios, aiming to predict future spreads and inform investment decisions more effectively. However, the inherent nonlinearity and high volatility of financial time series pose significant challenges for accurate forecasting. To address these issues, this paper proposes the IGWO-MALSTM model, a hybrid framework that integrates Improved Grey Wolf Optimization (IGWO) for hyperparameter tuning and a multi-head attention (MA) mechanism to enhance long-term sequence modeling within the long short-term memory (LSTM) architecture. The IGWO algorithm improves population diversity during initialization using the Mersenne Twister, thereby enhancing the convergence speed and search capability of the optimizer. Simultaneously, the MA mechanism mitigates gradient vanishing and explosion problems, enabling the model to better capture long-range dependencies in financial sequences. Experimental results on real futures market data demonstrate that the proposed model reduces Mean Square Error (MSE) by up to 61.45% and Mean Absolute Error (MAE) by 44.53%, and increases the R² score by 0.83% compared to existing benchmark models. These findings confirm that IGWO-MALSTM offers improved predictive accuracy and stability for financial time series forecasting tasks.

Deep learning models struggle to effectively capture data features and make accurate predictions because of the strong non-linear characteristics of arbitrage data. Therefore, to fully exploit the model performance, researchers have focused on network structure and hyperparameter selection using various swarm intelligence algorithms for optimization. Sparrow Search Algorithm (SSA), a classic heuristic method that simulates the sparrows’ foraging and anti-predatory behavior, has demonstrated excellent performance in various optimization problems. Hence, in this study, the Multi-Strategy Modified Sparrow Search Algorithm (MSMSSA) is applied to the Long Short-Term Memory (LSTM) network to construct an arbitrage spread prediction model (MSMSSA-LSTM). In the modified algorithm, the good point set theory, the proportion-adaptive strategy, and the improved location update method are introduced to further enhance the spatial exploration capability of the sparrow. The proposed model was evaluated using the real spread data of rebar and hot coil futures in the Chinese futures market. The obtained results showed that the mean absolute percentage error, root mean square error, and mean absolute error of the proposed model had decreased by a maximum of 58.5%, 65.2%, and 67.6% compared to several classical models. The model has high accuracy in predicting arbitrage spreads, which can provide some reference for investors.

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%.

The long short-term memory (LSTM) network is especially suitable for dealing with time series-related problems, which has led to a wide range of applications in analyzing stock market quotations and predicting future price trends. However, the selection of hyperparameters in LSTM networks was often based on subjective experience and existing research. The inability to determine the optimal values of the parameters results in a reduced generalization capability of the model. Therefore, we proposed a sparrow search algorithm-optimized LSTM (SSA-LSTM) model for stock trend prediction. The SSA was used to find the optimal hyperparameters of the LSTM model to adapt the features of the data to the structure of the model, so as to construct a highly accurate stock trend prediction model. With the Shanghai Composite Index stock data in the last decade, the mean absolute percentage error, root mean square error, mean absolute error, and coefficient of determination between stock prices predicted by the SSA-LSTM method and actual prices are 0.0093, 41.9505, 30.5300, and 0.9754. The result indicates that the proposed model possesses higher forecasting precision than other traditional stock forecasting methods and enhances the interpretability of the network model structure and parameters.

Arbitrage spread prediction can provide valuable insights into the identification of arbitrage signals and assessing associated risks in algorithmic trading. However, achieving precise forecasts by increasing model complexity remains a challenging task. Moreover, uncertainty in the development and maintenance of model often results in extremely unstable returns. To address these challenges, we propose a K-fold cross-search algorithm-optimized LSTM (KCS-LSTM) network for arbitrage spread prediction. The KCS heuristic algorithm incorporates an iterative updating mechanism of the search space with intervals as the basic unit into the traditional ant colony optimization. It optimized the hyperparameters of the LSTM model with a modified fitness function to automatically adapt to various data sets, thereby simplified and enhanced the efficiency of model development. The KCS-LSTM network was validated using real spread data of rebar and hot-rolled coil from the past three years. The results demonstrate that the proposed model outperforms several common models on sMAPE by improving up to 12.6% to 72.4%. The KCS-LSTM network is shown to be competitive in predicting arbitrage spreads compared to complex neural network models.

Federal learning and privacy protection are inseparable. The participants in federated learning need to be the targets of privacy protection. On the other hand, federated learning can also be used as a tool for privacy attacks. Group signature is regarded as an effective tool for preserving user privacy. Additionally, message recovery is a useful cryptographic primitive that ensures message recovery during the verification phase. In federated learning, message recovery can reduce the transmission of parameters and help protect parameter privacy. In this paper, we propose a lattice-based group signature with message recovery (GS-MR). We then prove that the GS-MR scheme has full anonymity and traceability under the random oracle model, and we reduce anonymity and traceability to the hardness assumptions of ring learning with errors (RLWE) and ring short integer solution (RSIS), respectively. Furthermore, we conduct some experiments to evaluate the sizes of key and signature, and make a performance comparison between three lattice-based group signature schemes and the GS-MR scheme. The results show that the message–signature size of GS-MR is reduced by an average of 39.17% for less than 2000 members.