This study proposes a novel distributionally robust portfolio optimization framework based on Wasserstein generative modeling, aiming to address the challenges of distributional uncertainty, tail risk, and structural drift in financial markets. The model integrates Wasserstein distance-based robust optimization with generative adversarial learning to jointly enhance risk control and return stability. Specifically, a Wasserstein generative adversarial network is employed to reconstruct the latent distribution of asset returns, enabling the capture of non-Gaussian features and tail dependencies in complex market environments. By constructing an uncertainty set under the Wasserstein metric, the optimization process achieves dynamic balance between empirical risk minimization and robustness to distributional perturbations. Furthermore, the framework incorporates a dual optimization mechanism that alternately updates generative and optimization parameters to adaptively align with changing market structures. Experimental evaluations on multi-asset datasets demonstrate that the proposed model achieves higher Sharpe ratios, lower maximum drawdowns, and improved robustness compared with conventional reinforcement learning-based and mean-variance methods. The results verify that integrating Wasserstein generative modeling into distributionally robust optimization provides an effective and interpretable pathway for achieving stable asset allocation and risk-aware decision-making under volatile financial conditions.

Time-series anomaly detection faces significant challenges when dealing with imbalanced data distributions, distribution shifts, and heterogeneous feature types. Traditional supervised methods struggle due to limited labeled anomaly samples, while unsupervised approaches often produce high false positive rates. We propose a novel self-supervised learning framework that integrates contrastive representation learning with adaptive distribution monitoring and explainable AI techniques. Our framework employs tailored augmentation strategies for time-series data, learns robust representations through contrastive objectives, and utilizes SHAP values to provide interpretable anomaly explanations across heterogeneous features. Experimental results on multiple benchmark datasets demonstrate that our approach achieves an F1-score of 0.823, outperforming state-of-the-art methods by 8.9% while maintaining interpretability and robustness to distribution shifts. The framework effectively handles imbalance ratios up to 1:100 and provides actionable insights for real-world deployment.

This study proposes a modeling method based on second-order differencing and residual regulation to address non-stationarity and noise in time series forecasting. Second-order differencing is first applied to weaken trend and seasonal components, making the data closer to a stationary state and providing stable inputs for subsequent modeling. On this basis, a residual regulation mechanism is introduced to dynamically incorporate prediction errors into model updates, reducing the negative impact of residual accumulation on stability. By combining linear regression with regularization, the method achieves parameter sparsity on differenced features, which enhances the characterization of key dynamic patterns while avoiding overfitting. Furthermore, a multi-step forecasting framework is constructed that considers both trends and fluctuations during recursive prediction, allowing the model to maintain high accuracy and robustness under complex conditions. Experiments conducted on the Kaggle retail transaction dataset include multidimensional comparative analysis, showing that the method outperforms baseline models in mean squared error, mean absolute error, mean absolute percentage error, and coefficient of determination. The results confirm its ability to capture both long-term trends and short-term fluctuations in retail transaction data. Graphical analysis further demonstrates that the proposed method fits well across different fluctuation ranges and remains consistent and reasonable even under abnormal volatility or extreme changes. In conclusion, the combination of second-order differencing and residual regulation provides a novel and effective solution for forecasting complex non-stationary time series and shows practical value in business data modeling tasks.

Non-stationary time-series data poses significant challenges for anomaly detection systems due to evolving patterns and distribution shifts that render traditional static models ineffective. This paper presents a novel continual learning framework that integrates dynamic distribution monitoring mechanisms to enable adaptive anomaly detection in non-stationary environments. The proposed framework employs a dual-module architecture consisting of a distribution drift detector and an adaptive learning component. The distribution drift detector utilizes statistical hypothesis testing to identify temporal shifts in data distributions, while the adaptive learning module employs rehearsal-based continual learning strategies with dynamic memory management to maintain model performance across evolving patterns. We introduce a hybrid loss function that balances stability and plasticity, preventing catastrophic forgetting while enabling rapid adaptation to new distributions. Experimental results demonstrate an average F1-score improvement of 11.3% over the best-performing baseline, highlighting the robustness and adaptability of the proposed framework under non-stationary conditions while maintaining computational efficiency suitable for real-time applications.